%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU306+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:55 AM UTC 2026
% Result : Theorem 1.98s 2.25s
% Output : Proof 2.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(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_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_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_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_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_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ),
file('theBenchmark.p',cc4_membered) ).
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(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d12_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d12_funct_1) ).
fof(d12_relat_1,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('theBenchmark.p',d12_relat_1) ).
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_relat_2) ).
fof(d13_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d13_funct_1) ).
fof(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_relat_1) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d1_enumset1,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('theBenchmark.p',d1_enumset1) ).
fof(d1_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_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_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('theBenchmark.p',d1_relat_2) ).
fof(d1_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('theBenchmark.p',d1_relset_1) ).
fof(d1_setfam_1,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('theBenchmark.p',d1_setfam_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('theBenchmark.p',d1_wellord1) ).
fof(d1_wellord2,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('theBenchmark.p',d1_wellord2) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_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_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_relat_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('theBenchmark.p',d2_wellord1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_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_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_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_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('theBenchmark.p',d5_wellord1) ).
fof(d6_ordinal1,axiom,
! [A] :
( being_limit_ordinal(A)
<=> A = union(A) ),
file('theBenchmark.p',d6_ordinal1) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d6_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('theBenchmark.p',d6_relat_2) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
fof(d7_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('theBenchmark.p',d7_relat_1) ).
fof(d7_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
<=> ( ! [D,E] :
( in(ordered_pair(D,E),A)
<=> ( in(ordered_pair(apply(C,D),apply(C,E)),B)
& in(E,relation_field(A))
& in(D,relation_field(A)) ) )
& one_to_one(C)
& relation_rng(C) = relation_field(B)
& relation_dom(C) = relation_field(A) ) ) ) ) ),
file('theBenchmark.p',d7_wellord1) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(d8_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_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('theBenchmark.p',d8_relat_1) ).
fof(d8_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('theBenchmark.p',d8_relat_2) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_binop_1,axiom,
$true,
file('theBenchmark.p',dt_k1_binop_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_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_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_setfam_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_wellord1,axiom,
$true,
file('theBenchmark.p',dt_k1_wellord1) ).
fof(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)),
file('theBenchmark.p',dt_k1_wellord2) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_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_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_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_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_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_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_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_l1_lattices,axiom,
! [A] :
( meet_semilatt_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
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_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_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_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_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_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_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(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_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_funct_1,axiom,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
=> ( function(relation_inverse(A))
& relation(relation_inverse(A)) ) ),
file('theBenchmark.p',fc3_funct_1) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_difference(A,B)) ),
file('theBenchmark.p',fc3_relat_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(fc4_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) ) ),
file('theBenchmark.p',fc4_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',fc5_funct_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_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(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(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_wellord1,lemma,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('theBenchmark.p',l1_wellord1) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l25_zfmisc_1,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l29_wellord1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('theBenchmark.p',l29_wellord1) ).
fof(l2_wellord1,lemma,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('theBenchmark.p',l2_wellord1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l30_wellord2,lemma,
! [A,B] :
( relation(B)
=> ~ ( ! [C] :
( relation(C)
=> ~ well_orders(C,A) )
& equipotent(A,relation_field(B))
& well_ordering(B) ) ),
file('theBenchmark.p',l30_wellord2) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_wellord1,lemma,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('theBenchmark.p',l3_wellord1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_wellord1,lemma,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('theBenchmark.p',l4_wellord1) ).
fof(l4_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(l82_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(rc1_arytm_3,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_arytm_3) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( quasi_total(C,A,B)
& function(C)
& relation(C)
& relation_of2(C,A,B) ),
file('theBenchmark.p',rc1_funct_2) ).
fof(rc1_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_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_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_finset_1,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_finset_1) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_partfun1,axiom,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
file('theBenchmark.p',rc2_partfun1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
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(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_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_k5_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_rng_as_subset(A,B,C) = relation_rng(C) ),
file('theBenchmark.p',redefinition_k5_relset_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(redefinition_r2_wellord2,axiom,
! [A,B] :
( equipotent(A,B)
<=> are_equipotent(A,B) ),
file('theBenchmark.p',redefinition_r2_wellord2) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(reflexivity_r2_wellord2,axiom,
! [A,B] : equipotent(A,A),
file('theBenchmark.p',reflexivity_r2_wellord2) ).
fof(s1_funct_1__e10_24__wellord2__1,lemma,
! [A,B] :
( ( relation(B)
& ~ empty(A) )
=> ( ! [C,D,E] :
( ( ? [H] :
( ! [I] :
( in(I,H)
=> in(ordered_pair(E,I),B) )
& in(E,H)
& C = H )
& in(C,A)
& ? [F] :
( ! [G] :
( in(G,F)
=> in(ordered_pair(D,G),B) )
& in(D,F)
& C = F )
& in(C,A) )
=> D = E )
=> ? [C] :
( ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( ? [J] :
( ! [K] :
( in(K,J)
=> in(ordered_pair(E,K),B) )
& in(E,J)
& D = J )
& in(D,A)
& in(D,A) ) )
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
fof(s1_funct_1__e16_22__wellord2__1,lemma,
! [A] :
( ! [B,C,D] :
( ( D = singleton(B)
& in(B,A)
& C = singleton(B)
& in(B,A) )
=> C = D )
=> ? [B] :
( ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( D = singleton(C)
& in(C,A)
& in(C,A) ) )
& function(B)
& relation(B) ) ),
file('theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(s1_ordinal1__e8_6__wellord2,lemma,
! [A] :
( ? [B] :
( in(B,A)
& ordinal(B) )
=> ? [B] :
( ! [C] :
( ordinal(C)
=> ( in(C,A)
=> ordinal_subset(B,C) ) )
& in(B,A)
& ordinal(B) ) ),
file('theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(s1_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__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__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__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__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_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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(symmetry_r2_wellord2,axiom,
! [A,B] :
( equipotent(A,B)
=> equipotent(B,A) ),
file('theBenchmark.p',symmetry_r2_wellord2) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_ordinal1,lemma,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t115_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t117_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t118_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('theBenchmark.p',t118_relat_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('theBenchmark.p',t119_relat_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_pre_topc,conjecture,
! [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_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t13_finset_1,lemma,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t140_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('theBenchmark.p',t140_relat_1) ).
fof(t143_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('theBenchmark.p',t143_relat_1) ).
fof(t144_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t145_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('theBenchmark.p',t145_funct_1) ).
fof(t145_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)) ),
file('theBenchmark.p',t145_relat_1) ).
fof(t146_funct_1,lemma,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('theBenchmark.p',t146_funct_1) ).
fof(t146_relat_1,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_1) ).
fof(t147_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_1) ).
fof(t14_relset_1,lemma,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t14_relset_1) ).
fof(t15_finset_1,lemma,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',t15_finset_1) ).
fof(t160_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('theBenchmark.p',t160_relat_1) ).
fof(t166_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('theBenchmark.p',t166_relat_1) ).
fof(t167_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('theBenchmark.p',t167_relat_1) ).
fof(t16_relset_1,lemma,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t16_relset_1) ).
fof(t16_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t174_relat_1,lemma,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('theBenchmark.p',t174_relat_1) ).
fof(t178_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('theBenchmark.p',t178_relat_1) ).
fof(t17_finset_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('theBenchmark.p',t17_finset_1) ).
fof(t17_wellord1,lemma,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
file('theBenchmark.p',t17_wellord1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t18_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_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t20_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) ) ),
file('theBenchmark.p',t20_wellord1) ).
fof(t21_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t21_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
file('theBenchmark.p',t21_funct_2) ).
fof(t21_ordinal1,lemma,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t21_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t21_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('theBenchmark.p',t21_wellord1) ).
fof(t22_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t22_relset_1,lemma,
! [A,B,C] :
( relation_of2_as_subset(C,B,A)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(D,E),C)
& in(D,B) )
<=> relation_dom_as_subset(B,A,C) = B ) ),
file('theBenchmark.p',t22_relset_1) ).
fof(t22_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t22_wellord1) ).
fof(t23_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t23_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_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_wellord2,lemma,
! [A] :
? [B] :
( well_orders(B,A)
& relation(B) ),
file('theBenchmark.p',t26_wellord2) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_wellord2,lemma,
! [A] :
( ~ empty(A)
=> ~ ( ! [B] :
( ( function(B)
& relation(B) )
=> ~ ( ! [C] :
( in(C,A)
=> in(apply(B,C),C) )
& relation_dom(B) = A ) )
& ! [B] :
~ ( B = empty_set
& in(B,A) ) ) ),
file('theBenchmark.p',t28_wellord2) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_wellord2,lemma,
! [A] : reflexive(inclusion_relation(A)),
file('theBenchmark.p',t2_wellord2) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t31_ordinal1,lemma,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_ordinal1) ).
fof(t31_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t31_wellord1) ).
fof(t32_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('theBenchmark.p',t32_ordinal1) ).
fof(t32_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t32_wellord1) ).
fof(t33_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t34_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,lemma,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( ( subset(A,relation_field(B))
& well_ordering(B) )
=> relation_field(relation_restriction(B,A)) = A ) ),
file('theBenchmark.p',t39_wellord1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_ordinal1,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('theBenchmark.p',t3_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_wellord2,lemma,
! [A] : transitive(inclusion_relation(A)),
file('theBenchmark.p',t3_wellord2) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t41_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( B != empty_set
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(apply(D,E),C)
& in(E,A) ) ) ) ),
file('theBenchmark.p',t46_funct_2) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t49_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> relation_isomorphism(B,A,function_inverse(C)) ) ) ) ),
file('theBenchmark.p',t49_wellord1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_wellord2,lemma,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('theBenchmark.p',t4_wellord2) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t53_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('theBenchmark.p',t53_wellord1) ).
fof(t54_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t54_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('theBenchmark.p',t54_wellord1) ).
fof(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t5_wellord2,lemma,
! [A] : antisymmetric(inclusion_relation(A)),
file('theBenchmark.p',t5_wellord2) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
file('theBenchmark.p',t6_funct_2) ).
fof(t6_wellord2,lemma,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('theBenchmark.p',t6_wellord2) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_mcart_1,lemma,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('theBenchmark.p',t7_mcart_1) ).
fof(t7_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
fof(t7_wellord2,lemma,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('theBenchmark.p',t7_wellord2) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( subset(B,C)
=> ( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set ) ) ) ),
file('theBenchmark.p',t9_funct_2) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_3_2,plain,
! [U_5] :
( ! [U_4] :
( v1_xcmplx_0(U_4)
| ~ element(U_4,U_5) )
| ~ v1_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v1_xcmplx_0(U_4)
| ~ element(U_4,U_5)
| ~ v1_membered(U_5) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_7] :
( ! [U_6] :
( ( v1_xreal_0(U_6)
& v1_xcmplx_0(U_6) )
| ~ element(U_6,U_7) )
| ~ v2_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_xcmplx_0(U_6)
| ~ element(U_6,U_7)
| ~ v2_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( v1_xreal_0(U_6)
| ~ element(U_6,U_7)
| ~ v2_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_9] :
( ! [U_8] :
( ( v1_rat_1(U_8)
& v1_xreal_0(U_8)
& v1_xcmplx_0(U_8) )
| ~ element(U_8,U_9) )
| ~ v3_membered(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_xcmplx_0(U_8)
| ~ element(U_8,U_9)
| ~ v3_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( v1_xreal_0(U_8)
| ~ element(U_8,U_9)
| ~ v3_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( v1_rat_1(U_8)
| ~ element(U_8,U_9)
| ~ v3_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_11] :
( ! [U_10] :
( ( v1_rat_1(U_10)
& v1_int_1(U_10)
& v1_xreal_0(U_10)
& v1_xcmplx_0(U_10) )
| ~ element(U_10,U_11) )
| ~ v4_membered(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_xcmplx_0(U_10)
| ~ element(U_10,U_11)
| ~ v4_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_xreal_0(U_10)
| ~ element(U_10,U_11)
| ~ v4_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( v1_int_1(U_10)
| ~ element(U_10,U_11)
| ~ v4_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_6,plain,
( v1_rat_1(U_10)
| ~ element(U_10,U_11)
| ~ v4_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_13] :
( ! [U_12] :
( ( v1_rat_1(U_12)
& v1_int_1(U_12)
& v1_xreal_0(U_12)
& natural(U_12)
& v1_xcmplx_0(U_12) )
| ~ element(U_12,U_13) )
| ~ v5_membered(U_13) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_xcmplx_0(U_12)
| ~ element(U_12,U_13)
| ~ v5_membered(U_13) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( natural(U_12)
| ~ element(U_12,U_13)
| ~ v5_membered(U_13) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( v1_xreal_0(U_12)
| ~ element(U_12,U_13)
| ~ v5_membered(U_13) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_6,plain,
( v1_int_1(U_12)
| ~ element(U_12,U_13)
| ~ v5_membered(U_13) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_7,plain,
( v1_rat_1(U_12)
| ~ element(U_12,U_13)
| ~ v5_membered(U_13) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_14] :
( ( v5_membered(U_14)
& v4_membered(U_14)
& v3_membered(U_14)
& v2_membered(U_14)
& v1_membered(U_14) )
| ~ empty(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v1_membered(U_14)
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( v2_membered(U_14)
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( v3_membered(U_14)
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_6,plain,
( v4_membered(U_14)
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_7,plain,
( v5_membered(U_14)
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_9_2,plain,
! [U_16] :
( ! [U_15] :
( v1_membered(U_15)
| ~ element(U_15,powerset(U_16)) )
| ~ v1_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_membered(U_15)
| ~ element(U_15,powerset(U_16))
| ~ v1_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_18] :
( ! [U_17] :
( ( v2_membered(U_17)
& v1_membered(U_17) )
| ~ element(U_17,powerset(U_18)) )
| ~ v2_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v2_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v2_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v2_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_20] :
( ! [U_19] :
( ( v3_membered(U_19)
& v2_membered(U_19)
& v1_membered(U_19) )
| ~ element(U_19,powerset(U_20)) )
| ~ v3_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v3_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( v2_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v3_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v3_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v3_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_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_12_2,plain,
! [U_22] :
( ! [U_21] :
( ( v4_membered(U_21)
& v3_membered(U_21)
& v2_membered(U_21)
& v1_membered(U_21) )
| ~ element(U_21,powerset(U_22)) )
| ~ v4_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v4_membered(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( v2_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v4_membered(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( v3_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v4_membered(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_6,plain,
( v4_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v4_membered(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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_13_2,plain,
! [U_24] :
( ! [U_23] :
( ( ordinal(U_23)
& epsilon_connected(U_23)
& epsilon_transitive(U_23) )
| ~ element(U_23,U_24) )
| ~ ordinal(U_24) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( epsilon_transitive(U_23)
| ~ element(U_23,U_24)
| ~ ordinal(U_24) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( epsilon_connected(U_23)
| ~ element(U_23,U_24)
| ~ ordinal(U_24) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
( ordinal(U_23)
| ~ element(U_23,U_24)
| ~ ordinal(U_24) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_14_2,plain,
! [U_25] :
( finite(U_25)
| ~ empty(U_25) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( finite(U_25)
| ~ empty(U_25) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(fof_nnf,[status(thm)],[cc1_finsub_1]) ).
fof(f_15_2,plain,
! [U_26] :
( ( diff_closed(U_26)
& cup_closed(U_26) )
| ~ preboolean(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( cup_closed(U_26)
| ~ preboolean(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( diff_closed(U_26)
| ~ preboolean(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_16_2,plain,
! [U_27] :
( function(U_27)
| ~ empty(U_27) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( function(U_27)
| ~ empty(U_27) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_17_2,plain,
! [U_28] :
( v4_membered(U_28)
| ~ v5_membered(U_28) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( v4_membered(U_28)
| ~ v5_membered(U_28) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_18_2,plain,
! [U_29] :
( ( epsilon_connected(U_29)
& epsilon_transitive(U_29) )
| ~ ordinal(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( epsilon_transitive(U_29)
| ~ ordinal(U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( epsilon_connected(U_29)
| ~ ordinal(U_29) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_19_2,plain,
! [U_30] :
( relation(U_30)
| ~ empty(U_30) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( relation(U_30)
| ~ empty(U_30) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_20_2,plain,
! [U_33,U_32,U_31] :
( relation(U_31)
| ~ element(U_31,powerset(cartesian_product2(U_33,U_32))) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( relation(U_31)
| ~ element(U_31,powerset(cartesian_product2(U_33,U_32))) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_35] :
( ! [U_34] :
( ( v5_membered(U_34)
& v4_membered(U_34)
& v3_membered(U_34)
& v2_membered(U_34)
& v1_membered(U_34) )
| ~ element(U_34,powerset(U_35)) )
| ~ v5_membered(U_35) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( v1_membered(U_34)
| ~ element(U_34,powerset(U_35))
| ~ v5_membered(U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( v2_membered(U_34)
| ~ element(U_34,powerset(U_35))
| ~ v5_membered(U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_5,plain,
( v3_membered(U_34)
| ~ element(U_34,powerset(U_35))
| ~ v5_membered(U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_6,plain,
( v4_membered(U_34)
| ~ element(U_34,powerset(U_35))
| ~ v5_membered(U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_7,plain,
( v5_membered(U_34)
| ~ element(U_34,powerset(U_35))
| ~ v5_membered(U_35) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_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_22_2,plain,
! [U_36] :
( ( natural(U_36)
& ordinal(U_36)
& epsilon_connected(U_36)
& epsilon_transitive(U_36) )
| ~ ordinal(U_36)
| ~ empty(U_36) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( epsilon_transitive(U_36)
| ~ ordinal(U_36)
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( epsilon_connected(U_36)
| ~ ordinal(U_36)
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_5,plain,
( ordinal(U_36)
| ~ ordinal(U_36)
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_6,plain,
( natural(U_36)
| ~ ordinal(U_36)
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_23_2,plain,
! [U_38] :
( ! [U_37] :
( finite(U_37)
| ~ element(U_37,powerset(U_38)) )
| ~ finite(U_38) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( finite(U_37)
| ~ element(U_37,powerset(U_38))
| ~ finite(U_38) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(fof_nnf,[status(thm)],[cc2_finsub_1]) ).
fof(f_24_2,plain,
! [U_39] :
( preboolean(U_39)
| ~ diff_closed(U_39)
| ~ cup_closed(U_39) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( preboolean(U_39)
| ~ diff_closed(U_39)
| ~ cup_closed(U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_40] :
( ( one_to_one(U_40)
& function(U_40)
& relation(U_40) )
| ~ function(U_40)
| ~ empty(U_40)
| ~ relation(U_40) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( relation(U_40)
| ~ function(U_40)
| ~ empty(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( function(U_40)
| ~ function(U_40)
| ~ empty(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_5,plain,
( one_to_one(U_40)
| ~ function(U_40)
| ~ empty(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_26_2,plain,
! [U_41] :
( v3_membered(U_41)
| ~ v4_membered(U_41) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( v3_membered(U_41)
| ~ v4_membered(U_41) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_27_2,plain,
! [U_42] :
( ordinal(U_42)
| ~ epsilon_connected(U_42)
| ~ epsilon_transitive(U_42) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ordinal(U_42)
| ~ epsilon_connected(U_42)
| ~ epsilon_transitive(U_42) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_43] :
( ( natural(U_43)
& ordinal(U_43)
& epsilon_connected(U_43)
& epsilon_transitive(U_43) )
| ~ element(U_43,omega) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( epsilon_transitive(U_43)
| ~ element(U_43,omega) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( epsilon_connected(U_43)
| ~ element(U_43,omega) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_5,plain,
( ordinal(U_43)
| ~ element(U_43,omega) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_6,plain,
( natural(U_43)
| ~ element(U_43,omega) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_29_2,plain,
! [U_44] :
( v2_membered(U_44)
| ~ v3_membered(U_44) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( v2_membered(U_44)
| ~ v3_membered(U_44) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_30_2,plain,
! [U_45] :
( ( ordinal(U_45)
& epsilon_connected(U_45)
& epsilon_transitive(U_45) )
| ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( epsilon_transitive(U_45)
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
( epsilon_connected(U_45)
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_5,plain,
( ordinal(U_45)
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_31_2,plain,
! [U_46] :
( v1_membered(U_46)
| ~ v2_membered(U_46) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( v1_membered(U_46)
| ~ v2_membered(U_46) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_32_2,plain,
! [U_48,U_47] : unordered_pair(U_48,U_47) = unordered_pair(U_47,U_48),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
unordered_pair(U_48,U_47) = unordered_pair(U_47,U_48),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_33_2,plain,
! [U_50,U_49] : set_union2(U_50,U_49) = set_union2(U_49,U_50),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
set_union2(U_50,U_49) = set_union2(U_49,U_50),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_53,U_52,U_51] :
( join_commut(U_53,U_52,U_51) = join_commut(U_53,U_51,U_52)
| ~ element(U_51,the_carrier(U_53))
| ~ element(U_52,the_carrier(U_53))
| ~ join_semilatt_str(U_53)
| ~ join_commutative(U_53)
| empty_carrier(U_53) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( join_commut(U_53,U_52,U_51) = join_commut(U_53,U_51,U_52)
| ~ element(U_51,the_carrier(U_53))
| ~ element(U_52,the_carrier(U_53))
| ~ join_semilatt_str(U_53)
| ~ join_commutative(U_53)
| empty_carrier(U_53) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_35_2,plain,
! [U_55,U_54] : set_intersection2(U_55,U_54) = set_intersection2(U_54,U_55),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
set_intersection2(U_55,U_54) = set_intersection2(U_54,U_55),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_58,U_57,U_56] :
( meet_commut(U_58,U_57,U_56) = meet_commut(U_58,U_56,U_57)
| ~ element(U_56,the_carrier(U_58))
| ~ element(U_57,the_carrier(U_58))
| ~ meet_semilatt_str(U_58)
| ~ meet_commutative(U_58)
| empty_carrier(U_58) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( meet_commut(U_58,U_57,U_56) = meet_commut(U_58,U_56,U_57)
| ~ element(U_56,the_carrier(U_58))
| ~ element(U_57,the_carrier(U_58))
| ~ meet_semilatt_str(U_58)
| ~ meet_commutative(U_58)
| empty_carrier(U_58) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_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_37_2,plain,
! [U_60,U_59] :
( ordinal_subset(U_59,U_60)
| ordinal_subset(U_60,U_59)
| ~ ordinal(U_59)
| ~ ordinal(U_60) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( ordinal_subset(U_59,U_60)
| ordinal_subset(U_60,U_59)
| ~ ordinal(U_59)
| ~ ordinal(U_60) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_66,U_65] :
( ( ( U_65 = identity_relation(U_66)
| ? [U_64,U_63] :
( ( ~ in(ordered_pair(U_64,U_63),U_65)
& U_64 = U_63
& in(U_64,U_66) )
| ( ( U_64 != U_63
| ~ in(U_64,U_66) )
& in(ordered_pair(U_64,U_63),U_65) ) ) )
& ( ! [U_62,U_61] :
( ( in(ordered_pair(U_62,U_61),U_65)
| U_62 != U_61
| ~ in(U_62,U_66) )
& ( ( U_62 = U_61
& in(U_62,U_66) )
| ~ in(ordered_pair(U_62,U_61),U_65) ) )
| U_65 != identity_relation(U_66) ) )
| ~ relation(U_65) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_66,U_65] :
( ( ( U_65 = identity_relation(U_66)
| ? [U_74,U_72] :
( ~ in(ordered_pair(U_74,U_72),U_65)
& U_74 = U_72
& in(U_74,U_66) )
| ? [U_73,U_71] :
( ( U_73 != U_71
| ~ in(U_73,U_66) )
& in(ordered_pair(U_73,U_71),U_65) ) )
& ( ( ! [U_70,U_68] :
( in(ordered_pair(U_70,U_68),U_65)
| U_70 != U_68
| ~ in(U_70,U_66) )
& ! [U_69,U_67] :
( ( U_69 = U_67
& in(U_69,U_66) )
| ~ in(ordered_pair(U_69,U_67),U_65) ) )
| U_65 != identity_relation(U_66) ) )
| ~ relation(U_65) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
! [U_66,U_65] :
( ( ( U_65 = identity_relation(U_66)
| ? [U_74,U_72] :
( ~ in(ordered_pair(U_74,U_72),U_65)
& U_74 = U_72
& in(U_74,U_66) )
| ? [U_71] :
( ( sK1(U_66,U_65) != U_71
| ~ in(sK1(U_66,U_65),U_66) )
& in(ordered_pair(sK1(U_66,U_65),U_71),U_65) ) )
& ( ( ! [U_70,U_68] :
( in(ordered_pair(U_70,U_68),U_65)
| U_70 != U_68
| ~ in(U_70,U_66) )
& ! [U_69,U_67] :
( ( U_69 = U_67
& in(U_69,U_66) )
| ~ in(ordered_pair(U_69,U_67),U_65) ) )
| U_65 != identity_relation(U_66) ) )
| ~ relation(U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_73,sK1(U_66,U_65))],[f_38_3]) ).
fof(f_38_5,plain,
! [U_66,U_65] :
( ( ( U_65 = identity_relation(U_66)
| ? [U_74,U_72] :
( ~ in(ordered_pair(U_74,U_72),U_65)
& U_74 = U_72
& in(U_74,U_66) )
| ( ( sK1(U_66,U_65) != sK2(U_66,U_65)
| ~ in(sK1(U_66,U_65),U_66) )
& in(ordered_pair(sK1(U_66,U_65),sK2(U_66,U_65)),U_65) ) )
& ( ( ! [U_70,U_68] :
( in(ordered_pair(U_70,U_68),U_65)
| U_70 != U_68
| ~ in(U_70,U_66) )
& ! [U_69,U_67] :
( ( U_69 = U_67
& in(U_69,U_66) )
| ~ in(ordered_pair(U_69,U_67),U_65) ) )
| U_65 != identity_relation(U_66) ) )
| ~ relation(U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_71,sK2(U_66,U_65))],[f_38_4]) ).
fof(f_38_6,plain,
! [U_66,U_65] :
( ( ( U_65 = identity_relation(U_66)
| ? [U_72] :
( ~ in(ordered_pair(sK3(U_66,U_65),U_72),U_65)
& sK3(U_66,U_65) = U_72
& in(sK3(U_66,U_65),U_66) )
| ( ( sK1(U_66,U_65) != sK2(U_66,U_65)
| ~ in(sK1(U_66,U_65),U_66) )
& in(ordered_pair(sK1(U_66,U_65),sK2(U_66,U_65)),U_65) ) )
& ( ( ! [U_70,U_68] :
( in(ordered_pair(U_70,U_68),U_65)
| U_70 != U_68
| ~ in(U_70,U_66) )
& ! [U_69,U_67] :
( ( U_69 = U_67
& in(U_69,U_66) )
| ~ in(ordered_pair(U_69,U_67),U_65) ) )
| U_65 != identity_relation(U_66) ) )
| ~ relation(U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_74,sK3(U_66,U_65))],[f_38_5]) ).
fof(f_38_7,plain,
! [U_66,U_65] :
( ( ( U_65 = identity_relation(U_66)
| ( ~ in(ordered_pair(sK3(U_66,U_65),sK4(U_66,U_65)),U_65)
& sK3(U_66,U_65) = sK4(U_66,U_65)
& in(sK3(U_66,U_65),U_66) )
| ( ( sK1(U_66,U_65) != sK2(U_66,U_65)
| ~ in(sK1(U_66,U_65),U_66) )
& in(ordered_pair(sK1(U_66,U_65),sK2(U_66,U_65)),U_65) ) )
& ( ( ! [U_70,U_68] :
( in(ordered_pair(U_70,U_68),U_65)
| U_70 != U_68
| ~ in(U_70,U_66) )
& ! [U_69,U_67] :
( ( U_69 = U_67
& in(U_69,U_66) )
| ~ in(ordered_pair(U_69,U_67),U_65) ) )
| U_65 != identity_relation(U_66) ) )
| ~ relation(U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_72,sK4(U_66,U_65))],[f_38_6]) ).
cnf(f_38_8,plain,
( in(U_69,U_66)
| ~ in(ordered_pair(U_69,U_67),U_65)
| U_65 != identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_9,plain,
( U_69 = U_67
| ~ in(ordered_pair(U_69,U_67),U_65)
| U_65 != identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_10,plain,
( in(ordered_pair(U_70,U_68),U_65)
| U_70 != U_68
| ~ in(U_70,U_66)
| U_65 != identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_11,plain,
( in(sK3(U_66,U_65),U_66)
| in(ordered_pair(sK1(U_66,U_65),sK2(U_66,U_65)),U_65)
| U_65 = identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_12,plain,
( sK3(U_66,U_65) = sK4(U_66,U_65)
| in(ordered_pair(sK1(U_66,U_65),sK2(U_66,U_65)),U_65)
| U_65 = identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_13,plain,
( ~ in(ordered_pair(sK3(U_66,U_65),sK4(U_66,U_65)),U_65)
| in(ordered_pair(sK1(U_66,U_65),sK2(U_66,U_65)),U_65)
| U_65 = identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_14,plain,
( in(sK3(U_66,U_65),U_66)
| sK1(U_66,U_65) != sK2(U_66,U_65)
| ~ in(sK1(U_66,U_65),U_66)
| U_65 = identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_15,plain,
( sK3(U_66,U_65) = sK4(U_66,U_65)
| sK1(U_66,U_65) != sK2(U_66,U_65)
| ~ in(sK1(U_66,U_65),U_66)
| U_65 = identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_16,plain,
( ~ in(ordered_pair(sK3(U_66,U_65),sK4(U_66,U_65)),U_65)
| sK1(U_66,U_65) != sK2(U_66,U_65)
| ~ in(sK1(U_66,U_65),U_66)
| U_65 = identity_relation(U_66)
| ~ relation(U_65) ),
inference(clausify,[status(thm)],[f_38_7]) ).
fof(f_39_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_39_2,plain,
! [U_76,U_75] :
( ( U_76 = U_75
| ~ subset(U_75,U_76)
| ~ subset(U_76,U_75) )
& ( ( subset(U_75,U_76)
& subset(U_76,U_75) )
| U_76 != U_75 ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_80,U_78] :
( U_80 = U_78
| ~ subset(U_78,U_80)
| ~ subset(U_80,U_78) )
& ! [U_79,U_77] :
( ( subset(U_77,U_79)
& subset(U_79,U_77) )
| U_79 != U_77 ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( subset(U_79,U_77)
| U_79 != U_77 ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( subset(U_77,U_79)
| U_79 != U_77 ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
( U_80 = U_78
| ~ subset(U_78,U_80)
| ~ subset(U_80,U_78) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( ( U_85 = relation_dom_restriction(U_87,U_86)
| ? [U_84,U_83] :
( ( ~ in(ordered_pair(U_84,U_83),U_85)
& in(ordered_pair(U_84,U_83),U_87)
& in(U_84,U_86) )
| ( ( ~ in(ordered_pair(U_84,U_83),U_87)
| ~ in(U_84,U_86) )
& in(ordered_pair(U_84,U_83),U_85) ) ) )
& ( ! [U_82,U_81] :
( ( in(ordered_pair(U_82,U_81),U_85)
| ~ in(ordered_pair(U_82,U_81),U_87)
| ~ in(U_82,U_86) )
& ( ( in(ordered_pair(U_82,U_81),U_87)
& in(U_82,U_86) )
| ~ in(ordered_pair(U_82,U_81),U_85) ) )
| U_85 != relation_dom_restriction(U_87,U_86) ) )
| ~ relation(U_85) )
| ~ relation(U_87) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( ( U_85 = relation_dom_restriction(U_87,U_86)
| ? [U_95,U_93] :
( ~ in(ordered_pair(U_95,U_93),U_85)
& in(ordered_pair(U_95,U_93),U_87)
& in(U_95,U_86) )
| ? [U_94,U_92] :
( ( ~ in(ordered_pair(U_94,U_92),U_87)
| ~ in(U_94,U_86) )
& in(ordered_pair(U_94,U_92),U_85) ) )
& ( ( ! [U_91,U_89] :
( in(ordered_pair(U_91,U_89),U_85)
| ~ in(ordered_pair(U_91,U_89),U_87)
| ~ in(U_91,U_86) )
& ! [U_90,U_88] :
( ( in(ordered_pair(U_90,U_88),U_87)
& in(U_90,U_86) )
| ~ in(ordered_pair(U_90,U_88),U_85) ) )
| U_85 != relation_dom_restriction(U_87,U_86) ) )
| ~ relation(U_85) )
| ~ relation(U_87) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( ( U_85 = relation_dom_restriction(U_87,U_86)
| ? [U_95,U_93] :
( ~ in(ordered_pair(U_95,U_93),U_85)
& in(ordered_pair(U_95,U_93),U_87)
& in(U_95,U_86) )
| ? [U_92] :
( ( ~ in(ordered_pair(sK5(U_87,U_86,U_85),U_92),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86) )
& in(ordered_pair(sK5(U_87,U_86,U_85),U_92),U_85) ) )
& ( ( ! [U_91,U_89] :
( in(ordered_pair(U_91,U_89),U_85)
| ~ in(ordered_pair(U_91,U_89),U_87)
| ~ in(U_91,U_86) )
& ! [U_90,U_88] :
( ( in(ordered_pair(U_90,U_88),U_87)
& in(U_90,U_86) )
| ~ in(ordered_pair(U_90,U_88),U_85) ) )
| U_85 != relation_dom_restriction(U_87,U_86) ) )
| ~ relation(U_85) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_94,sK5(U_87,U_86,U_85))],[f_40_3]) ).
fof(f_40_5,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( ( U_85 = relation_dom_restriction(U_87,U_86)
| ? [U_95,U_93] :
( ~ in(ordered_pair(U_95,U_93),U_85)
& in(ordered_pair(U_95,U_93),U_87)
& in(U_95,U_86) )
| ( ( ~ in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86) )
& in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_85) ) )
& ( ( ! [U_91,U_89] :
( in(ordered_pair(U_91,U_89),U_85)
| ~ in(ordered_pair(U_91,U_89),U_87)
| ~ in(U_91,U_86) )
& ! [U_90,U_88] :
( ( in(ordered_pair(U_90,U_88),U_87)
& in(U_90,U_86) )
| ~ in(ordered_pair(U_90,U_88),U_85) ) )
| U_85 != relation_dom_restriction(U_87,U_86) ) )
| ~ relation(U_85) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_92,sK6(U_87,U_86,U_85))],[f_40_4]) ).
fof(f_40_6,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( ( U_85 = relation_dom_restriction(U_87,U_86)
| ? [U_93] :
( ~ in(ordered_pair(sK7(U_87,U_86,U_85),U_93),U_85)
& in(ordered_pair(sK7(U_87,U_86,U_85),U_93),U_87)
& in(sK7(U_87,U_86,U_85),U_86) )
| ( ( ~ in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86) )
& in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_85) ) )
& ( ( ! [U_91,U_89] :
( in(ordered_pair(U_91,U_89),U_85)
| ~ in(ordered_pair(U_91,U_89),U_87)
| ~ in(U_91,U_86) )
& ! [U_90,U_88] :
( ( in(ordered_pair(U_90,U_88),U_87)
& in(U_90,U_86) )
| ~ in(ordered_pair(U_90,U_88),U_85) ) )
| U_85 != relation_dom_restriction(U_87,U_86) ) )
| ~ relation(U_85) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_95,sK7(U_87,U_86,U_85))],[f_40_5]) ).
fof(f_40_7,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( ( U_85 = relation_dom_restriction(U_87,U_86)
| ( ~ in(ordered_pair(sK7(U_87,U_86,U_85),sK8(U_87,U_86,U_85)),U_85)
& in(ordered_pair(sK7(U_87,U_86,U_85),sK8(U_87,U_86,U_85)),U_87)
& in(sK7(U_87,U_86,U_85),U_86) )
| ( ( ~ in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86) )
& in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_85) ) )
& ( ( ! [U_91,U_89] :
( in(ordered_pair(U_91,U_89),U_85)
| ~ in(ordered_pair(U_91,U_89),U_87)
| ~ in(U_91,U_86) )
& ! [U_90,U_88] :
( ( in(ordered_pair(U_90,U_88),U_87)
& in(U_90,U_86) )
| ~ in(ordered_pair(U_90,U_88),U_85) ) )
| U_85 != relation_dom_restriction(U_87,U_86) ) )
| ~ relation(U_85) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_93,sK8(U_87,U_86,U_85))],[f_40_6]) ).
cnf(f_40_8,plain,
( in(U_90,U_86)
| ~ in(ordered_pair(U_90,U_88),U_85)
| U_85 != relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_9,plain,
( in(ordered_pair(U_90,U_88),U_87)
| ~ in(ordered_pair(U_90,U_88),U_85)
| U_85 != relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_10,plain,
( in(ordered_pair(U_91,U_89),U_85)
| ~ in(ordered_pair(U_91,U_89),U_87)
| ~ in(U_91,U_86)
| U_85 != relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_11,plain,
( in(sK7(U_87,U_86,U_85),U_86)
| in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_85)
| U_85 = relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_12,plain,
( in(ordered_pair(sK7(U_87,U_86,U_85),sK8(U_87,U_86,U_85)),U_87)
| in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_85)
| U_85 = relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_13,plain,
( ~ in(ordered_pair(sK7(U_87,U_86,U_85),sK8(U_87,U_86,U_85)),U_85)
| in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_85)
| U_85 = relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_14,plain,
( in(sK7(U_87,U_86,U_85),U_86)
| ~ in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86)
| U_85 = relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_15,plain,
( in(ordered_pair(sK7(U_87,U_86,U_85),sK8(U_87,U_86,U_85)),U_87)
| ~ in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86)
| U_85 = relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
cnf(f_40_16,plain,
( ~ in(ordered_pair(sK7(U_87,U_86,U_85),sK8(U_87,U_86,U_85)),U_85)
| ~ in(ordered_pair(sK5(U_87,U_86,U_85),sK6(U_87,U_86,U_85)),U_87)
| ~ in(sK5(U_87,U_86,U_85),U_86)
| U_85 = relation_dom_restriction(U_87,U_86)
| ~ relation(U_85)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_40_7]) ).
fof(f_41_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_41_2,plain,
! [U_104] :
( ! [U_103,U_102] :
( ( U_102 = relation_image(U_104,U_103)
| ? [U_101] :
( ( ~ in(U_101,U_102)
& ? [U_100] :
( U_101 = apply(U_104,U_100)
& in(U_100,U_103)
& in(U_100,relation_dom(U_104)) ) )
| ( ! [U_99] :
( U_101 != apply(U_104,U_99)
| ~ in(U_99,U_103)
| ~ in(U_99,relation_dom(U_104)) )
& in(U_101,U_102) ) ) )
& ( ! [U_98] :
( ( in(U_98,U_102)
| ! [U_97] :
( U_98 != apply(U_104,U_97)
| ~ in(U_97,U_103)
| ~ in(U_97,relation_dom(U_104)) ) )
& ( ? [U_96] :
( U_98 = apply(U_104,U_96)
& in(U_96,U_103)
& in(U_96,relation_dom(U_104)) )
| ~ in(U_98,U_102) ) )
| U_102 != relation_image(U_104,U_103) ) )
| ~ function(U_104)
| ~ relation(U_104) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ? [U_100] :
( U_108 = apply(U_104,U_100)
& in(U_100,U_112)
& in(U_100,relation_dom(U_104)) ) )
| ? [U_107] :
( ! [U_99] :
( U_107 != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104)) )
& in(U_107,U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( U_106 != apply(U_104,U_97)
| ~ in(U_97,U_111)
| ~ in(U_97,relation_dom(U_104)) ) )
& ! [U_105] :
( ? [U_96] :
( U_105 = apply(U_104,U_96)
& in(U_96,U_111)
& in(U_96,relation_dom(U_104)) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ function(U_104)
| ~ relation(U_104) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ? [U_100] :
( U_108 = apply(U_104,U_100)
& in(U_100,U_112)
& in(U_100,relation_dom(U_104)) ) )
| ? [U_107] :
( ! [U_99] :
( U_107 != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104)) )
& in(U_107,U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( U_106 != apply(U_104,U_97)
| ~ in(U_97,U_111)
| ~ in(U_97,relation_dom(U_104)) ) )
& ! [U_105] :
( ( U_105 = apply(U_104,sK9(U_104,U_111,U_109,U_105))
& in(sK9(U_104,U_111,U_109,U_105),U_111)
& in(sK9(U_104,U_111,U_109,U_105),relation_dom(U_104)) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ function(U_104)
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_96,sK9(U_104,U_111,U_109,U_105))],[f_41_3]) ).
fof(f_41_5,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ? [U_100] :
( U_108 = apply(U_104,U_100)
& in(U_100,U_112)
& in(U_100,relation_dom(U_104)) ) )
| ( ! [U_99] :
( sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104)) )
& in(sK10(U_104,U_112,U_110),U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( U_106 != apply(U_104,U_97)
| ~ in(U_97,U_111)
| ~ in(U_97,relation_dom(U_104)) ) )
& ! [U_105] :
( ( U_105 = apply(U_104,sK9(U_104,U_111,U_109,U_105))
& in(sK9(U_104,U_111,U_109,U_105),U_111)
& in(sK9(U_104,U_111,U_109,U_105),relation_dom(U_104)) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ function(U_104)
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_107,sK10(U_104,U_112,U_110))],[f_41_4]) ).
fof(f_41_6,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ( ~ in(sK11(U_104,U_112,U_110),U_110)
& ? [U_100] :
( sK11(U_104,U_112,U_110) = apply(U_104,U_100)
& in(U_100,U_112)
& in(U_100,relation_dom(U_104)) ) )
| ( ! [U_99] :
( sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104)) )
& in(sK10(U_104,U_112,U_110),U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( U_106 != apply(U_104,U_97)
| ~ in(U_97,U_111)
| ~ in(U_97,relation_dom(U_104)) ) )
& ! [U_105] :
( ( U_105 = apply(U_104,sK9(U_104,U_111,U_109,U_105))
& in(sK9(U_104,U_111,U_109,U_105),U_111)
& in(sK9(U_104,U_111,U_109,U_105),relation_dom(U_104)) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ function(U_104)
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_108,sK11(U_104,U_112,U_110))],[f_41_5]) ).
fof(f_41_7,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ( ~ in(sK11(U_104,U_112,U_110),U_110)
& sK11(U_104,U_112,U_110) = apply(U_104,sK12(U_104,U_112,U_110))
& in(sK12(U_104,U_112,U_110),U_112)
& in(sK12(U_104,U_112,U_110),relation_dom(U_104)) )
| ( ! [U_99] :
( sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104)) )
& in(sK10(U_104,U_112,U_110),U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( U_106 != apply(U_104,U_97)
| ~ in(U_97,U_111)
| ~ in(U_97,relation_dom(U_104)) ) )
& ! [U_105] :
( ( U_105 = apply(U_104,sK9(U_104,U_111,U_109,U_105))
& in(sK9(U_104,U_111,U_109,U_105),U_111)
& in(sK9(U_104,U_111,U_109,U_105),relation_dom(U_104)) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ function(U_104)
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_100,sK12(U_104,U_112,U_110))],[f_41_6]) ).
cnf(f_41_8,plain,
( in(sK9(U_104,U_111,U_109,U_105),relation_dom(U_104))
| ~ in(U_105,U_109)
| U_109 != relation_image(U_104,U_111)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_9,plain,
( in(sK9(U_104,U_111,U_109,U_105),U_111)
| ~ in(U_105,U_109)
| U_109 != relation_image(U_104,U_111)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_10,plain,
( U_105 = apply(U_104,sK9(U_104,U_111,U_109,U_105))
| ~ in(U_105,U_109)
| U_109 != relation_image(U_104,U_111)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_11,plain,
( in(U_106,U_109)
| U_106 != apply(U_104,U_97)
| ~ in(U_97,U_111)
| ~ in(U_97,relation_dom(U_104))
| U_109 != relation_image(U_104,U_111)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_12,plain,
( in(sK12(U_104,U_112,U_110),relation_dom(U_104))
| in(sK10(U_104,U_112,U_110),U_110)
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_13,plain,
( in(sK12(U_104,U_112,U_110),U_112)
| in(sK10(U_104,U_112,U_110),U_110)
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_14,plain,
( sK11(U_104,U_112,U_110) = apply(U_104,sK12(U_104,U_112,U_110))
| in(sK10(U_104,U_112,U_110),U_110)
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_15,plain,
( ~ in(sK11(U_104,U_112,U_110),U_110)
| in(sK10(U_104,U_112,U_110),U_110)
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_16,plain,
( in(sK12(U_104,U_112,U_110),relation_dom(U_104))
| sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104))
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_17,plain,
( in(sK12(U_104,U_112,U_110),U_112)
| sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104))
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_18,plain,
( sK11(U_104,U_112,U_110) = apply(U_104,sK12(U_104,U_112,U_110))
| sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104))
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
cnf(f_41_19,plain,
( ~ in(sK11(U_104,U_112,U_110),U_110)
| sK10(U_104,U_112,U_110) != apply(U_104,U_99)
| ~ in(U_99,U_112)
| ~ in(U_99,relation_dom(U_104))
| U_110 = relation_image(U_104,U_112)
| ~ function(U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_41_7]) ).
fof(f_42_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_42_2,plain,
! [U_119,U_118] :
( ! [U_117] :
( ( ( U_117 = relation_rng_restriction(U_119,U_118)
| ? [U_116,U_115] :
( ( ~ in(ordered_pair(U_116,U_115),U_117)
& in(ordered_pair(U_116,U_115),U_118)
& in(U_115,U_119) )
| ( ( ~ in(ordered_pair(U_116,U_115),U_118)
| ~ in(U_115,U_119) )
& in(ordered_pair(U_116,U_115),U_117) ) ) )
& ( ! [U_114,U_113] :
( ( in(ordered_pair(U_114,U_113),U_117)
| ~ in(ordered_pair(U_114,U_113),U_118)
| ~ in(U_113,U_119) )
& ( ( in(ordered_pair(U_114,U_113),U_118)
& in(U_113,U_119) )
| ~ in(ordered_pair(U_114,U_113),U_117) ) )
| U_117 != relation_rng_restriction(U_119,U_118) ) )
| ~ relation(U_117) )
| ~ relation(U_118) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_119,U_118] :
( ! [U_117] :
( ( ( U_117 = relation_rng_restriction(U_119,U_118)
| ? [U_127,U_125] :
( ~ in(ordered_pair(U_127,U_125),U_117)
& in(ordered_pair(U_127,U_125),U_118)
& in(U_125,U_119) )
| ? [U_126,U_124] :
( ( ~ in(ordered_pair(U_126,U_124),U_118)
| ~ in(U_124,U_119) )
& in(ordered_pair(U_126,U_124),U_117) ) )
& ( ( ! [U_123,U_121] :
( in(ordered_pair(U_123,U_121),U_117)
| ~ in(ordered_pair(U_123,U_121),U_118)
| ~ in(U_121,U_119) )
& ! [U_122,U_120] :
( ( in(ordered_pair(U_122,U_120),U_118)
& in(U_120,U_119) )
| ~ in(ordered_pair(U_122,U_120),U_117) ) )
| U_117 != relation_rng_restriction(U_119,U_118) ) )
| ~ relation(U_117) )
| ~ relation(U_118) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_119,U_118] :
( ! [U_117] :
( ( ( U_117 = relation_rng_restriction(U_119,U_118)
| ? [U_127,U_125] :
( ~ in(ordered_pair(U_127,U_125),U_117)
& in(ordered_pair(U_127,U_125),U_118)
& in(U_125,U_119) )
| ? [U_124] :
( ( ~ in(ordered_pair(sK13(U_119,U_118,U_117),U_124),U_118)
| ~ in(U_124,U_119) )
& in(ordered_pair(sK13(U_119,U_118,U_117),U_124),U_117) ) )
& ( ( ! [U_123,U_121] :
( in(ordered_pair(U_123,U_121),U_117)
| ~ in(ordered_pair(U_123,U_121),U_118)
| ~ in(U_121,U_119) )
& ! [U_122,U_120] :
( ( in(ordered_pair(U_122,U_120),U_118)
& in(U_120,U_119) )
| ~ in(ordered_pair(U_122,U_120),U_117) ) )
| U_117 != relation_rng_restriction(U_119,U_118) ) )
| ~ relation(U_117) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_126,sK13(U_119,U_118,U_117))],[f_42_3]) ).
fof(f_42_5,plain,
! [U_119,U_118] :
( ! [U_117] :
( ( ( U_117 = relation_rng_restriction(U_119,U_118)
| ? [U_127,U_125] :
( ~ in(ordered_pair(U_127,U_125),U_117)
& in(ordered_pair(U_127,U_125),U_118)
& in(U_125,U_119) )
| ( ( ~ in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_118)
| ~ in(sK14(U_119,U_118,U_117),U_119) )
& in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_117) ) )
& ( ( ! [U_123,U_121] :
( in(ordered_pair(U_123,U_121),U_117)
| ~ in(ordered_pair(U_123,U_121),U_118)
| ~ in(U_121,U_119) )
& ! [U_122,U_120] :
( ( in(ordered_pair(U_122,U_120),U_118)
& in(U_120,U_119) )
| ~ in(ordered_pair(U_122,U_120),U_117) ) )
| U_117 != relation_rng_restriction(U_119,U_118) ) )
| ~ relation(U_117) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_124,sK14(U_119,U_118,U_117))],[f_42_4]) ).
fof(f_42_6,plain,
! [U_119,U_118] :
( ! [U_117] :
( ( ( U_117 = relation_rng_restriction(U_119,U_118)
| ? [U_125] :
( ~ in(ordered_pair(sK15(U_119,U_118,U_117),U_125),U_117)
& in(ordered_pair(sK15(U_119,U_118,U_117),U_125),U_118)
& in(U_125,U_119) )
| ( ( ~ in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_118)
| ~ in(sK14(U_119,U_118,U_117),U_119) )
& in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_117) ) )
& ( ( ! [U_123,U_121] :
( in(ordered_pair(U_123,U_121),U_117)
| ~ in(ordered_pair(U_123,U_121),U_118)
| ~ in(U_121,U_119) )
& ! [U_122,U_120] :
( ( in(ordered_pair(U_122,U_120),U_118)
& in(U_120,U_119) )
| ~ in(ordered_pair(U_122,U_120),U_117) ) )
| U_117 != relation_rng_restriction(U_119,U_118) ) )
| ~ relation(U_117) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_127,sK15(U_119,U_118,U_117))],[f_42_5]) ).
fof(f_42_7,plain,
! [U_119,U_118] :
( ! [U_117] :
( ( ( U_117 = relation_rng_restriction(U_119,U_118)
| ( ~ in(ordered_pair(sK15(U_119,U_118,U_117),sK16(U_119,U_118,U_117)),U_117)
& in(ordered_pair(sK15(U_119,U_118,U_117),sK16(U_119,U_118,U_117)),U_118)
& in(sK16(U_119,U_118,U_117),U_119) )
| ( ( ~ in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_118)
| ~ in(sK14(U_119,U_118,U_117),U_119) )
& in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_117) ) )
& ( ( ! [U_123,U_121] :
( in(ordered_pair(U_123,U_121),U_117)
| ~ in(ordered_pair(U_123,U_121),U_118)
| ~ in(U_121,U_119) )
& ! [U_122,U_120] :
( ( in(ordered_pair(U_122,U_120),U_118)
& in(U_120,U_119) )
| ~ in(ordered_pair(U_122,U_120),U_117) ) )
| U_117 != relation_rng_restriction(U_119,U_118) ) )
| ~ relation(U_117) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_125,sK16(U_119,U_118,U_117))],[f_42_6]) ).
cnf(f_42_8,plain,
( in(U_120,U_119)
| ~ in(ordered_pair(U_122,U_120),U_117)
| U_117 != relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_9,plain,
( in(ordered_pair(U_122,U_120),U_118)
| ~ in(ordered_pair(U_122,U_120),U_117)
| U_117 != relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_10,plain,
( in(ordered_pair(U_123,U_121),U_117)
| ~ in(ordered_pair(U_123,U_121),U_118)
| ~ in(U_121,U_119)
| U_117 != relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_11,plain,
( in(sK16(U_119,U_118,U_117),U_119)
| in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_117)
| U_117 = relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_12,plain,
( in(ordered_pair(sK15(U_119,U_118,U_117),sK16(U_119,U_118,U_117)),U_118)
| in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_117)
| U_117 = relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_13,plain,
( ~ in(ordered_pair(sK15(U_119,U_118,U_117),sK16(U_119,U_118,U_117)),U_117)
| in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_117)
| U_117 = relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_14,plain,
( in(sK16(U_119,U_118,U_117),U_119)
| ~ in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_118)
| ~ in(sK14(U_119,U_118,U_117),U_119)
| U_117 = relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_15,plain,
( in(ordered_pair(sK15(U_119,U_118,U_117),sK16(U_119,U_118,U_117)),U_118)
| ~ in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_118)
| ~ in(sK14(U_119,U_118,U_117),U_119)
| U_117 = relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_16,plain,
( ~ in(ordered_pair(sK15(U_119,U_118,U_117),sK16(U_119,U_118,U_117)),U_117)
| ~ in(ordered_pair(sK13(U_119,U_118,U_117),sK14(U_119,U_118,U_117)),U_118)
| ~ in(sK14(U_119,U_118,U_117),U_119)
| U_117 = relation_rng_restriction(U_119,U_118)
| ~ relation(U_117)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_42_7]) ).
fof(f_43_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_43_2,plain,
! [U_128] :
( ( ( antisymmetric(U_128)
| ~ is_antisymmetric_in(U_128,relation_field(U_128)) )
& ( is_antisymmetric_in(U_128,relation_field(U_128))
| ~ antisymmetric(U_128) ) )
| ~ relation(U_128) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( is_antisymmetric_in(U_128,relation_field(U_128))
| ~ antisymmetric(U_128)
| ~ relation(U_128) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( antisymmetric(U_128)
| ~ is_antisymmetric_in(U_128,relation_field(U_128))
| ~ relation(U_128) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_133] :
( ! [U_132,U_131] :
( ( U_131 = relation_inverse_image(U_133,U_132)
| ? [U_130] :
( ( ~ in(U_130,U_131)
& in(apply(U_133,U_130),U_132)
& in(U_130,relation_dom(U_133)) )
| ( ( ~ in(apply(U_133,U_130),U_132)
| ~ in(U_130,relation_dom(U_133)) )
& in(U_130,U_131) ) ) )
& ( ! [U_129] :
( ( in(U_129,U_131)
| ~ in(apply(U_133,U_129),U_132)
| ~ in(U_129,relation_dom(U_133)) )
& ( ( in(apply(U_133,U_129),U_132)
& in(U_129,relation_dom(U_133)) )
| ~ in(U_129,U_131) ) )
| U_131 != relation_inverse_image(U_133,U_132) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& in(apply(U_133,U_137),U_141)
& in(U_137,relation_dom(U_133)) )
| ? [U_136] :
( ( ~ in(apply(U_133,U_136),U_141)
| ~ in(U_136,relation_dom(U_133)) )
& in(U_136,U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ~ in(apply(U_133,U_135),U_140)
| ~ in(U_135,relation_dom(U_133)) )
& ! [U_134] :
( ( in(apply(U_133,U_134),U_140)
& in(U_134,relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& in(apply(U_133,U_137),U_141)
& in(U_137,relation_dom(U_133)) )
| ( ( ~ in(apply(U_133,sK17(U_133,U_141,U_139)),U_141)
| ~ in(sK17(U_133,U_141,U_139),relation_dom(U_133)) )
& in(sK17(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ~ in(apply(U_133,U_135),U_140)
| ~ in(U_135,relation_dom(U_133)) )
& ! [U_134] :
( ( in(apply(U_133,U_134),U_140)
& in(U_134,relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_136,sK17(U_133,U_141,U_139))],[f_44_3]) ).
fof(f_44_5,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ( ~ in(sK18(U_133,U_141,U_139),U_139)
& in(apply(U_133,sK18(U_133,U_141,U_139)),U_141)
& in(sK18(U_133,U_141,U_139),relation_dom(U_133)) )
| ( ( ~ in(apply(U_133,sK17(U_133,U_141,U_139)),U_141)
| ~ in(sK17(U_133,U_141,U_139),relation_dom(U_133)) )
& in(sK17(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ~ in(apply(U_133,U_135),U_140)
| ~ in(U_135,relation_dom(U_133)) )
& ! [U_134] :
( ( in(apply(U_133,U_134),U_140)
& in(U_134,relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_137,sK18(U_133,U_141,U_139))],[f_44_4]) ).
cnf(f_44_6,plain,
( in(U_134,relation_dom(U_133))
| ~ in(U_134,U_138)
| U_138 != relation_inverse_image(U_133,U_140)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_7,plain,
( in(apply(U_133,U_134),U_140)
| ~ in(U_134,U_138)
| U_138 != relation_inverse_image(U_133,U_140)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_8,plain,
( in(U_135,U_138)
| ~ in(apply(U_133,U_135),U_140)
| ~ in(U_135,relation_dom(U_133))
| U_138 != relation_inverse_image(U_133,U_140)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_9,plain,
( in(sK18(U_133,U_141,U_139),relation_dom(U_133))
| in(sK17(U_133,U_141,U_139),U_139)
| U_139 = relation_inverse_image(U_133,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_10,plain,
( in(apply(U_133,sK18(U_133,U_141,U_139)),U_141)
| in(sK17(U_133,U_141,U_139),U_139)
| U_139 = relation_inverse_image(U_133,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_11,plain,
( ~ in(sK18(U_133,U_141,U_139),U_139)
| in(sK17(U_133,U_141,U_139),U_139)
| U_139 = relation_inverse_image(U_133,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_12,plain,
( in(sK18(U_133,U_141,U_139),relation_dom(U_133))
| ~ in(apply(U_133,sK17(U_133,U_141,U_139)),U_141)
| ~ in(sK17(U_133,U_141,U_139),relation_dom(U_133))
| U_139 = relation_inverse_image(U_133,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_13,plain,
( in(apply(U_133,sK18(U_133,U_141,U_139)),U_141)
| ~ in(apply(U_133,sK17(U_133,U_141,U_139)),U_141)
| ~ in(sK17(U_133,U_141,U_139),relation_dom(U_133))
| U_139 = relation_inverse_image(U_133,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_14,plain,
( ~ in(sK18(U_133,U_141,U_139),U_139)
| ~ in(apply(U_133,sK17(U_133,U_141,U_139)),U_141)
| ~ in(sK17(U_133,U_141,U_139),relation_dom(U_133))
| U_139 = relation_inverse_image(U_133,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_44_5]) ).
fof(f_45_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_45_2,plain,
! [U_150] :
( ! [U_149,U_148] :
( ( U_148 = relation_image(U_150,U_149)
| ? [U_147] :
( ( ~ in(U_147,U_148)
& ? [U_146] :
( in(U_146,U_149)
& in(ordered_pair(U_146,U_147),U_150) ) )
| ( ! [U_145] :
( ~ in(U_145,U_149)
| ~ in(ordered_pair(U_145,U_147),U_150) )
& in(U_147,U_148) ) ) )
& ( ! [U_144] :
( ( in(U_144,U_148)
| ! [U_143] :
( ~ in(U_143,U_149)
| ~ in(ordered_pair(U_143,U_144),U_150) ) )
& ( ? [U_142] :
( in(U_142,U_149)
& in(ordered_pair(U_142,U_144),U_150) )
| ~ in(U_144,U_148) ) )
| U_148 != relation_image(U_150,U_149) ) )
| ~ relation(U_150) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_150] :
( ( ! [U_158,U_156] :
( U_156 = relation_image(U_150,U_158)
| ? [U_154] :
( ~ in(U_154,U_156)
& ? [U_146] :
( in(U_146,U_158)
& in(ordered_pair(U_146,U_154),U_150) ) )
| ? [U_153] :
( ! [U_145] :
( ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,U_153),U_150) )
& in(U_153,U_156) ) )
& ! [U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ! [U_143] :
( ~ in(U_143,U_157)
| ~ in(ordered_pair(U_143,U_152),U_150) ) )
& ! [U_151] :
( ? [U_142] :
( in(U_142,U_157)
& in(ordered_pair(U_142,U_151),U_150) )
| ~ in(U_151,U_155) ) )
| U_155 != relation_image(U_150,U_157) ) )
| ~ relation(U_150) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_150] :
( ( ! [U_158,U_156] :
( U_156 = relation_image(U_150,U_158)
| ? [U_154] :
( ~ in(U_154,U_156)
& ? [U_146] :
( in(U_146,U_158)
& in(ordered_pair(U_146,U_154),U_150) ) )
| ? [U_153] :
( ! [U_145] :
( ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,U_153),U_150) )
& in(U_153,U_156) ) )
& ! [U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ! [U_143] :
( ~ in(U_143,U_157)
| ~ in(ordered_pair(U_143,U_152),U_150) ) )
& ! [U_151] :
( ( in(sK19(U_150,U_157,U_155,U_151),U_157)
& in(ordered_pair(sK19(U_150,U_157,U_155,U_151),U_151),U_150) )
| ~ in(U_151,U_155) ) )
| U_155 != relation_image(U_150,U_157) ) )
| ~ relation(U_150) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_142,sK19(U_150,U_157,U_155,U_151))],[f_45_3]) ).
fof(f_45_5,plain,
! [U_150] :
( ( ! [U_158,U_156] :
( U_156 = relation_image(U_150,U_158)
| ? [U_154] :
( ~ in(U_154,U_156)
& ? [U_146] :
( in(U_146,U_158)
& in(ordered_pair(U_146,U_154),U_150) ) )
| ( ! [U_145] :
( ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,sK20(U_150,U_158,U_156)),U_150) )
& in(sK20(U_150,U_158,U_156),U_156) ) )
& ! [U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ! [U_143] :
( ~ in(U_143,U_157)
| ~ in(ordered_pair(U_143,U_152),U_150) ) )
& ! [U_151] :
( ( in(sK19(U_150,U_157,U_155,U_151),U_157)
& in(ordered_pair(sK19(U_150,U_157,U_155,U_151),U_151),U_150) )
| ~ in(U_151,U_155) ) )
| U_155 != relation_image(U_150,U_157) ) )
| ~ relation(U_150) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_153,sK20(U_150,U_158,U_156))],[f_45_4]) ).
fof(f_45_6,plain,
! [U_150] :
( ( ! [U_158,U_156] :
( U_156 = relation_image(U_150,U_158)
| ( ~ in(sK21(U_150,U_158,U_156),U_156)
& ? [U_146] :
( in(U_146,U_158)
& in(ordered_pair(U_146,sK21(U_150,U_158,U_156)),U_150) ) )
| ( ! [U_145] :
( ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,sK20(U_150,U_158,U_156)),U_150) )
& in(sK20(U_150,U_158,U_156),U_156) ) )
& ! [U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ! [U_143] :
( ~ in(U_143,U_157)
| ~ in(ordered_pair(U_143,U_152),U_150) ) )
& ! [U_151] :
( ( in(sK19(U_150,U_157,U_155,U_151),U_157)
& in(ordered_pair(sK19(U_150,U_157,U_155,U_151),U_151),U_150) )
| ~ in(U_151,U_155) ) )
| U_155 != relation_image(U_150,U_157) ) )
| ~ relation(U_150) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_154,sK21(U_150,U_158,U_156))],[f_45_5]) ).
fof(f_45_7,plain,
! [U_150] :
( ( ! [U_158,U_156] :
( U_156 = relation_image(U_150,U_158)
| ( ~ in(sK21(U_150,U_158,U_156),U_156)
& in(sK22(U_150,U_158,U_156),U_158)
& in(ordered_pair(sK22(U_150,U_158,U_156),sK21(U_150,U_158,U_156)),U_150) )
| ( ! [U_145] :
( ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,sK20(U_150,U_158,U_156)),U_150) )
& in(sK20(U_150,U_158,U_156),U_156) ) )
& ! [U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ! [U_143] :
( ~ in(U_143,U_157)
| ~ in(ordered_pair(U_143,U_152),U_150) ) )
& ! [U_151] :
( ( in(sK19(U_150,U_157,U_155,U_151),U_157)
& in(ordered_pair(sK19(U_150,U_157,U_155,U_151),U_151),U_150) )
| ~ in(U_151,U_155) ) )
| U_155 != relation_image(U_150,U_157) ) )
| ~ relation(U_150) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_146,sK22(U_150,U_158,U_156))],[f_45_6]) ).
cnf(f_45_8,plain,
( in(ordered_pair(sK19(U_150,U_157,U_155,U_151),U_151),U_150)
| ~ in(U_151,U_155)
| U_155 != relation_image(U_150,U_157)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_9,plain,
( in(sK19(U_150,U_157,U_155,U_151),U_157)
| ~ in(U_151,U_155)
| U_155 != relation_image(U_150,U_157)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_10,plain,
( in(U_152,U_155)
| ~ in(U_143,U_157)
| ~ in(ordered_pair(U_143,U_152),U_150)
| U_155 != relation_image(U_150,U_157)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_11,plain,
( in(ordered_pair(sK22(U_150,U_158,U_156),sK21(U_150,U_158,U_156)),U_150)
| in(sK20(U_150,U_158,U_156),U_156)
| U_156 = relation_image(U_150,U_158)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_12,plain,
( in(sK22(U_150,U_158,U_156),U_158)
| in(sK20(U_150,U_158,U_156),U_156)
| U_156 = relation_image(U_150,U_158)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_13,plain,
( ~ in(sK21(U_150,U_158,U_156),U_156)
| in(sK20(U_150,U_158,U_156),U_156)
| U_156 = relation_image(U_150,U_158)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_14,plain,
( in(ordered_pair(sK22(U_150,U_158,U_156),sK21(U_150,U_158,U_156)),U_150)
| ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,sK20(U_150,U_158,U_156)),U_150)
| U_156 = relation_image(U_150,U_158)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_15,plain,
( in(sK22(U_150,U_158,U_156),U_158)
| ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,sK20(U_150,U_158,U_156)),U_150)
| U_156 = relation_image(U_150,U_158)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_16,plain,
( ~ in(sK21(U_150,U_158,U_156),U_156)
| ~ in(U_145,U_158)
| ~ in(ordered_pair(U_145,sK20(U_150,U_158,U_156)),U_150)
| U_156 = relation_image(U_150,U_158)
| ~ relation(U_150) ),
inference(clausify,[status(thm)],[f_45_7]) ).
fof(f_46_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_46_2,plain,
! [U_167] :
( ! [U_166,U_165] :
( ( U_165 = relation_inverse_image(U_167,U_166)
| ? [U_164] :
( ( ~ in(U_164,U_165)
& ? [U_163] :
( in(U_163,U_166)
& in(ordered_pair(U_164,U_163),U_167) ) )
| ( ! [U_162] :
( ~ in(U_162,U_166)
| ~ in(ordered_pair(U_164,U_162),U_167) )
& in(U_164,U_165) ) ) )
& ( ! [U_161] :
( ( in(U_161,U_165)
| ! [U_160] :
( ~ in(U_160,U_166)
| ~ in(ordered_pair(U_161,U_160),U_167) ) )
& ( ? [U_159] :
( in(U_159,U_166)
& in(ordered_pair(U_161,U_159),U_167) )
| ~ in(U_161,U_165) ) )
| U_165 != relation_inverse_image(U_167,U_166) ) )
| ~ relation(U_167) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_167] :
( ( ! [U_175,U_173] :
( U_173 = relation_inverse_image(U_167,U_175)
| ? [U_171] :
( ~ in(U_171,U_173)
& ? [U_163] :
( in(U_163,U_175)
& in(ordered_pair(U_171,U_163),U_167) ) )
| ? [U_170] :
( ! [U_162] :
( ~ in(U_162,U_175)
| ~ in(ordered_pair(U_170,U_162),U_167) )
& in(U_170,U_173) ) )
& ! [U_174,U_172] :
( ( ! [U_169] :
( in(U_169,U_172)
| ! [U_160] :
( ~ in(U_160,U_174)
| ~ in(ordered_pair(U_169,U_160),U_167) ) )
& ! [U_168] :
( ? [U_159] :
( in(U_159,U_174)
& in(ordered_pair(U_168,U_159),U_167) )
| ~ in(U_168,U_172) ) )
| U_172 != relation_inverse_image(U_167,U_174) ) )
| ~ relation(U_167) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
! [U_167] :
( ( ! [U_175,U_173] :
( U_173 = relation_inverse_image(U_167,U_175)
| ? [U_171] :
( ~ in(U_171,U_173)
& ? [U_163] :
( in(U_163,U_175)
& in(ordered_pair(U_171,U_163),U_167) ) )
| ? [U_170] :
( ! [U_162] :
( ~ in(U_162,U_175)
| ~ in(ordered_pair(U_170,U_162),U_167) )
& in(U_170,U_173) ) )
& ! [U_174,U_172] :
( ( ! [U_169] :
( in(U_169,U_172)
| ! [U_160] :
( ~ in(U_160,U_174)
| ~ in(ordered_pair(U_169,U_160),U_167) ) )
& ! [U_168] :
( ( in(sK23(U_167,U_174,U_172,U_168),U_174)
& in(ordered_pair(U_168,sK23(U_167,U_174,U_172,U_168)),U_167) )
| ~ in(U_168,U_172) ) )
| U_172 != relation_inverse_image(U_167,U_174) ) )
| ~ relation(U_167) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_159,sK23(U_167,U_174,U_172,U_168))],[f_46_3]) ).
fof(f_46_5,plain,
! [U_167] :
( ( ! [U_175,U_173] :
( U_173 = relation_inverse_image(U_167,U_175)
| ? [U_171] :
( ~ in(U_171,U_173)
& ? [U_163] :
( in(U_163,U_175)
& in(ordered_pair(U_171,U_163),U_167) ) )
| ( ! [U_162] :
( ~ in(U_162,U_175)
| ~ in(ordered_pair(sK24(U_167,U_175,U_173),U_162),U_167) )
& in(sK24(U_167,U_175,U_173),U_173) ) )
& ! [U_174,U_172] :
( ( ! [U_169] :
( in(U_169,U_172)
| ! [U_160] :
( ~ in(U_160,U_174)
| ~ in(ordered_pair(U_169,U_160),U_167) ) )
& ! [U_168] :
( ( in(sK23(U_167,U_174,U_172,U_168),U_174)
& in(ordered_pair(U_168,sK23(U_167,U_174,U_172,U_168)),U_167) )
| ~ in(U_168,U_172) ) )
| U_172 != relation_inverse_image(U_167,U_174) ) )
| ~ relation(U_167) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_170,sK24(U_167,U_175,U_173))],[f_46_4]) ).
fof(f_46_6,plain,
! [U_167] :
( ( ! [U_175,U_173] :
( U_173 = relation_inverse_image(U_167,U_175)
| ( ~ in(sK25(U_167,U_175,U_173),U_173)
& ? [U_163] :
( in(U_163,U_175)
& in(ordered_pair(sK25(U_167,U_175,U_173),U_163),U_167) ) )
| ( ! [U_162] :
( ~ in(U_162,U_175)
| ~ in(ordered_pair(sK24(U_167,U_175,U_173),U_162),U_167) )
& in(sK24(U_167,U_175,U_173),U_173) ) )
& ! [U_174,U_172] :
( ( ! [U_169] :
( in(U_169,U_172)
| ! [U_160] :
( ~ in(U_160,U_174)
| ~ in(ordered_pair(U_169,U_160),U_167) ) )
& ! [U_168] :
( ( in(sK23(U_167,U_174,U_172,U_168),U_174)
& in(ordered_pair(U_168,sK23(U_167,U_174,U_172,U_168)),U_167) )
| ~ in(U_168,U_172) ) )
| U_172 != relation_inverse_image(U_167,U_174) ) )
| ~ relation(U_167) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_171,sK25(U_167,U_175,U_173))],[f_46_5]) ).
fof(f_46_7,plain,
! [U_167] :
( ( ! [U_175,U_173] :
( U_173 = relation_inverse_image(U_167,U_175)
| ( ~ in(sK25(U_167,U_175,U_173),U_173)
& in(sK26(U_167,U_175,U_173),U_175)
& in(ordered_pair(sK25(U_167,U_175,U_173),sK26(U_167,U_175,U_173)),U_167) )
| ( ! [U_162] :
( ~ in(U_162,U_175)
| ~ in(ordered_pair(sK24(U_167,U_175,U_173),U_162),U_167) )
& in(sK24(U_167,U_175,U_173),U_173) ) )
& ! [U_174,U_172] :
( ( ! [U_169] :
( in(U_169,U_172)
| ! [U_160] :
( ~ in(U_160,U_174)
| ~ in(ordered_pair(U_169,U_160),U_167) ) )
& ! [U_168] :
( ( in(sK23(U_167,U_174,U_172,U_168),U_174)
& in(ordered_pair(U_168,sK23(U_167,U_174,U_172,U_168)),U_167) )
| ~ in(U_168,U_172) ) )
| U_172 != relation_inverse_image(U_167,U_174) ) )
| ~ relation(U_167) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_163,sK26(U_167,U_175,U_173))],[f_46_6]) ).
cnf(f_46_8,plain,
( in(ordered_pair(U_168,sK23(U_167,U_174,U_172,U_168)),U_167)
| ~ in(U_168,U_172)
| U_172 != relation_inverse_image(U_167,U_174)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_9,plain,
( in(sK23(U_167,U_174,U_172,U_168),U_174)
| ~ in(U_168,U_172)
| U_172 != relation_inverse_image(U_167,U_174)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_10,plain,
( in(U_169,U_172)
| ~ in(U_160,U_174)
| ~ in(ordered_pair(U_169,U_160),U_167)
| U_172 != relation_inverse_image(U_167,U_174)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_11,plain,
( in(ordered_pair(sK25(U_167,U_175,U_173),sK26(U_167,U_175,U_173)),U_167)
| in(sK24(U_167,U_175,U_173),U_173)
| U_173 = relation_inverse_image(U_167,U_175)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_12,plain,
( in(sK26(U_167,U_175,U_173),U_175)
| in(sK24(U_167,U_175,U_173),U_173)
| U_173 = relation_inverse_image(U_167,U_175)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_13,plain,
( ~ in(sK25(U_167,U_175,U_173),U_173)
| in(sK24(U_167,U_175,U_173),U_173)
| U_173 = relation_inverse_image(U_167,U_175)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_14,plain,
( in(ordered_pair(sK25(U_167,U_175,U_173),sK26(U_167,U_175,U_173)),U_167)
| ~ in(U_162,U_175)
| ~ in(ordered_pair(sK24(U_167,U_175,U_173),U_162),U_167)
| U_173 = relation_inverse_image(U_167,U_175)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_15,plain,
( in(sK26(U_167,U_175,U_173),U_175)
| ~ in(U_162,U_175)
| ~ in(ordered_pair(sK24(U_167,U_175,U_173),U_162),U_167)
| U_173 = relation_inverse_image(U_167,U_175)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_16,plain,
( ~ in(sK25(U_167,U_175,U_173),U_173)
| ~ in(U_162,U_175)
| ~ in(ordered_pair(sK24(U_167,U_175,U_173),U_162),U_167)
| U_173 = relation_inverse_image(U_167,U_175)
| ~ relation(U_167) ),
inference(clausify,[status(thm)],[f_46_7]) ).
fof(f_47_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_47_2,plain,
! [U_176] :
( ( ( connected(U_176)
| ~ is_connected_in(U_176,relation_field(U_176)) )
& ( is_connected_in(U_176,relation_field(U_176))
| ~ connected(U_176) ) )
| ~ relation(U_176) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( is_connected_in(U_176,relation_field(U_176))
| ~ connected(U_176)
| ~ relation(U_176) ),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( connected(U_176)
| ~ is_connected_in(U_176,relation_field(U_176))
| ~ relation(U_176) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_177] :
( ( ( transitive(U_177)
| ~ is_transitive_in(U_177,relation_field(U_177)) )
& ( is_transitive_in(U_177,relation_field(U_177))
| ~ transitive(U_177) ) )
| ~ relation(U_177) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( is_transitive_in(U_177,relation_field(U_177))
| ~ transitive(U_177)
| ~ relation(U_177) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( transitive(U_177)
| ~ is_transitive_in(U_177,relation_field(U_177))
| ~ relation(U_177) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_183,U_182,U_181,U_180] :
( ( U_180 = unordered_triple(U_183,U_182,U_181)
| ? [U_179] :
( ( ~ in(U_179,U_180)
& ( U_179 = U_181
| U_179 = U_182
| U_179 = U_183 ) )
| ( U_179 != U_181
& U_179 != U_182
& U_179 != U_183
& in(U_179,U_180) ) ) )
& ( ! [U_178] :
( ( in(U_178,U_180)
| ( U_178 != U_181
& U_178 != U_182
& U_178 != U_183 ) )
& ( U_178 = U_181
| U_178 = U_182
| U_178 = U_183
| ~ in(U_178,U_180) ) )
| U_180 != unordered_triple(U_183,U_182,U_181) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_195,U_193,U_191,U_189] :
( U_189 = unordered_triple(U_195,U_193,U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ( U_187 = U_191
| U_187 = U_193
| U_187 = U_195 ) )
| ? [U_186] :
( U_186 != U_191
& U_186 != U_193
& U_186 != U_195
& in(U_186,U_189) ) )
& ! [U_194,U_192,U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ( U_185 != U_190
& U_185 != U_192
& U_185 != U_194 ) )
& ! [U_184] :
( U_184 = U_190
| U_184 = U_192
| U_184 = U_194
| ~ in(U_184,U_188) ) )
| U_188 != unordered_triple(U_194,U_192,U_190) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_195,U_193,U_191,U_189] :
( U_189 = unordered_triple(U_195,U_193,U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ( U_187 = U_191
| U_187 = U_193
| U_187 = U_195 ) )
| ( sK27(U_195,U_193,U_191,U_189) != U_191
& sK27(U_195,U_193,U_191,U_189) != U_193
& sK27(U_195,U_193,U_191,U_189) != U_195
& in(sK27(U_195,U_193,U_191,U_189),U_189) ) )
& ! [U_194,U_192,U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ( U_185 != U_190
& U_185 != U_192
& U_185 != U_194 ) )
& ! [U_184] :
( U_184 = U_190
| U_184 = U_192
| U_184 = U_194
| ~ in(U_184,U_188) ) )
| U_188 != unordered_triple(U_194,U_192,U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_186,sK27(U_195,U_193,U_191,U_189))],[f_49_3]) ).
fof(f_49_5,plain,
( ! [U_195,U_193,U_191,U_189] :
( U_189 = unordered_triple(U_195,U_193,U_191)
| ( ~ in(sK28(U_195,U_193,U_191,U_189),U_189)
& ( sK28(U_195,U_193,U_191,U_189) = U_191
| sK28(U_195,U_193,U_191,U_189) = U_193
| sK28(U_195,U_193,U_191,U_189) = U_195 ) )
| ( sK27(U_195,U_193,U_191,U_189) != U_191
& sK27(U_195,U_193,U_191,U_189) != U_193
& sK27(U_195,U_193,U_191,U_189) != U_195
& in(sK27(U_195,U_193,U_191,U_189),U_189) ) )
& ! [U_194,U_192,U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ( U_185 != U_190
& U_185 != U_192
& U_185 != U_194 ) )
& ! [U_184] :
( U_184 = U_190
| U_184 = U_192
| U_184 = U_194
| ~ in(U_184,U_188) ) )
| U_188 != unordered_triple(U_194,U_192,U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_187,sK28(U_195,U_193,U_191,U_189))],[f_49_4]) ).
cnf(f_49_6,plain,
( U_184 = U_190
| U_184 = U_192
| U_184 = U_194
| ~ in(U_184,U_188)
| U_188 != unordered_triple(U_194,U_192,U_190) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_7,plain,
( U_185 != U_194
| in(U_185,U_188)
| U_188 != unordered_triple(U_194,U_192,U_190) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_8,plain,
( U_185 != U_192
| in(U_185,U_188)
| U_188 != unordered_triple(U_194,U_192,U_190) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_9,plain,
( U_185 != U_190
| in(U_185,U_188)
| U_188 != unordered_triple(U_194,U_192,U_190) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_10,plain,
( sK28(U_195,U_193,U_191,U_189) = U_191
| sK28(U_195,U_193,U_191,U_189) = U_193
| sK28(U_195,U_193,U_191,U_189) = U_195
| in(sK27(U_195,U_193,U_191,U_189),U_189)
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_11,plain,
( ~ in(sK28(U_195,U_193,U_191,U_189),U_189)
| in(sK27(U_195,U_193,U_191,U_189),U_189)
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_12,plain,
( sK27(U_195,U_193,U_191,U_189) != U_195
| sK28(U_195,U_193,U_191,U_189) = U_191
| sK28(U_195,U_193,U_191,U_189) = U_193
| sK28(U_195,U_193,U_191,U_189) = U_195
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_13,plain,
( sK27(U_195,U_193,U_191,U_189) != U_193
| sK28(U_195,U_193,U_191,U_189) = U_191
| sK28(U_195,U_193,U_191,U_189) = U_193
| sK28(U_195,U_193,U_191,U_189) = U_195
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_14,plain,
( sK27(U_195,U_193,U_191,U_189) != U_191
| sK28(U_195,U_193,U_191,U_189) = U_191
| sK28(U_195,U_193,U_191,U_189) = U_193
| sK28(U_195,U_193,U_191,U_189) = U_195
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_15,plain,
( sK27(U_195,U_193,U_191,U_189) != U_195
| ~ in(sK28(U_195,U_193,U_191,U_189),U_189)
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_16,plain,
( sK27(U_195,U_193,U_191,U_189) != U_193
| ~ in(sK28(U_195,U_193,U_191,U_189),U_189)
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_17,plain,
( sK27(U_195,U_193,U_191,U_189) != U_191
| ~ in(sK28(U_195,U_193,U_191,U_189),U_189)
| U_189 = unordered_triple(U_195,U_193,U_191) ),
inference(clausify,[status(thm)],[f_49_5]) ).
fof(f_50_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_50_2,plain,
! [U_198] :
( ( finite(U_198)
| ! [U_197] :
( ~ in(relation_dom(U_197),omega)
| relation_rng(U_197) != U_198
| ~ function(U_197)
| ~ relation(U_197) ) )
& ( ? [U_196] :
( in(relation_dom(U_196),omega)
& relation_rng(U_196) = U_198
& function(U_196)
& relation(U_196) )
| ~ finite(U_198) ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ! [U_200] :
( finite(U_200)
| ! [U_197] :
( ~ in(relation_dom(U_197),omega)
| relation_rng(U_197) != U_200
| ~ function(U_197)
| ~ relation(U_197) ) )
& ! [U_199] :
( ? [U_196] :
( in(relation_dom(U_196),omega)
& relation_rng(U_196) = U_199
& function(U_196)
& relation(U_196) )
| ~ finite(U_199) ) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
( ! [U_200] :
( finite(U_200)
| ! [U_197] :
( ~ in(relation_dom(U_197),omega)
| relation_rng(U_197) != U_200
| ~ function(U_197)
| ~ relation(U_197) ) )
& ! [U_199] :
( ( in(relation_dom(sK29(U_199)),omega)
& relation_rng(sK29(U_199)) = U_199
& function(sK29(U_199))
& relation(sK29(U_199)) )
| ~ finite(U_199) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_196,sK29(U_199))],[f_50_3]) ).
cnf(f_50_5,plain,
( relation(sK29(U_199))
| ~ finite(U_199) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_6,plain,
( function(sK29(U_199))
| ~ finite(U_199) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_7,plain,
( relation_rng(sK29(U_199)) = U_199
| ~ finite(U_199) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_8,plain,
( in(relation_dom(sK29(U_199)),omega)
| ~ finite(U_199) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_9,plain,
( finite(U_200)
| ~ in(relation_dom(U_197),omega)
| relation_rng(U_197) != U_200
| ~ function(U_197)
| ~ relation(U_197) ),
inference(clausify,[status(thm)],[f_50_4]) ).
fof(f_51_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_51_2,plain,
! [U_207] :
( ( function(U_207)
| ? [U_206,U_205,U_204] :
( U_205 != U_204
& in(ordered_pair(U_206,U_204),U_207)
& in(ordered_pair(U_206,U_205),U_207) ) )
& ( ! [U_203,U_202,U_201] :
( U_202 = U_201
| ~ in(ordered_pair(U_203,U_201),U_207)
| ~ in(ordered_pair(U_203,U_202),U_207) )
| ~ function(U_207) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_209] :
( function(U_209)
| ? [U_206,U_205,U_204] :
( U_205 != U_204
& in(ordered_pair(U_206,U_204),U_209)
& in(ordered_pair(U_206,U_205),U_209) ) )
& ! [U_208] :
( ! [U_203,U_202,U_201] :
( U_202 = U_201
| ~ in(ordered_pair(U_203,U_201),U_208)
| ~ in(ordered_pair(U_203,U_202),U_208) )
| ~ function(U_208) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_209] :
( function(U_209)
| ? [U_205,U_204] :
( U_205 != U_204
& in(ordered_pair(sK30(U_209),U_204),U_209)
& in(ordered_pair(sK30(U_209),U_205),U_209) ) )
& ! [U_208] :
( ! [U_203,U_202,U_201] :
( U_202 = U_201
| ~ in(ordered_pair(U_203,U_201),U_208)
| ~ in(ordered_pair(U_203,U_202),U_208) )
| ~ function(U_208) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_206,sK30(U_209))],[f_51_3]) ).
fof(f_51_5,plain,
( ! [U_209] :
( function(U_209)
| ? [U_204] :
( sK31(U_209) != U_204
& in(ordered_pair(sK30(U_209),U_204),U_209)
& in(ordered_pair(sK30(U_209),sK31(U_209)),U_209) ) )
& ! [U_208] :
( ! [U_203,U_202,U_201] :
( U_202 = U_201
| ~ in(ordered_pair(U_203,U_201),U_208)
| ~ in(ordered_pair(U_203,U_202),U_208) )
| ~ function(U_208) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_205,sK31(U_209))],[f_51_4]) ).
fof(f_51_6,plain,
( ! [U_209] :
( function(U_209)
| ( sK31(U_209) != sK32(U_209)
& in(ordered_pair(sK30(U_209),sK32(U_209)),U_209)
& in(ordered_pair(sK30(U_209),sK31(U_209)),U_209) ) )
& ! [U_208] :
( ! [U_203,U_202,U_201] :
( U_202 = U_201
| ~ in(ordered_pair(U_203,U_201),U_208)
| ~ in(ordered_pair(U_203,U_202),U_208) )
| ~ function(U_208) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_204,sK32(U_209))],[f_51_5]) ).
cnf(f_51_7,plain,
( U_202 = U_201
| ~ in(ordered_pair(U_203,U_201),U_208)
| ~ in(ordered_pair(U_203,U_202),U_208)
| ~ function(U_208) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_8,plain,
( in(ordered_pair(sK30(U_209),sK31(U_209)),U_209)
| function(U_209) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_9,plain,
( in(ordered_pair(sK30(U_209),sK32(U_209)),U_209)
| function(U_209) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_10,plain,
( sK31(U_209) != sK32(U_209)
| function(U_209) ),
inference(clausify,[status(thm)],[f_51_6]) ).
fof(f_52_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_52_2,plain,
! [U_212,U_211,U_210] :
( ( ( ( ( quasi_total(U_210,U_212,U_211)
| U_210 != empty_set )
& ( U_210 = empty_set
| ~ quasi_total(U_210,U_212,U_211) ) )
| U_212 = empty_set
| U_211 != empty_set )
& ( ( ( quasi_total(U_210,U_212,U_211)
| U_212 != relation_dom_as_subset(U_212,U_211,U_210) )
& ( U_212 = relation_dom_as_subset(U_212,U_211,U_210)
| ~ quasi_total(U_210,U_212,U_211) ) )
| ( U_212 != empty_set
& U_211 = empty_set ) ) )
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( U_212 = relation_dom_as_subset(U_212,U_211,U_210)
| ~ quasi_total(U_210,U_212,U_211)
| U_211 = empty_set
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( quasi_total(U_210,U_212,U_211)
| U_212 != relation_dom_as_subset(U_212,U_211,U_210)
| U_211 = empty_set
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_5,plain,
( U_212 = relation_dom_as_subset(U_212,U_211,U_210)
| ~ quasi_total(U_210,U_212,U_211)
| U_212 != empty_set
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_6,plain,
( quasi_total(U_210,U_212,U_211)
| U_212 != relation_dom_as_subset(U_212,U_211,U_210)
| U_212 != empty_set
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_7,plain,
( U_210 = empty_set
| ~ quasi_total(U_210,U_212,U_211)
| U_212 = empty_set
| U_211 != empty_set
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_8,plain,
( quasi_total(U_210,U_212,U_211)
| U_210 != empty_set
| U_212 = empty_set
| U_211 != empty_set
| ~ relation_of2_as_subset(U_210,U_212,U_211) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_215] :
( ! [U_214] :
( ! [U_213] :
( join(U_215,U_214,U_213) = apply_binary_as_element(the_carrier(U_215),the_carrier(U_215),the_carrier(U_215),the_L_join(U_215),U_214,U_213)
| ~ element(U_213,the_carrier(U_215)) )
| ~ element(U_214,the_carrier(U_215)) )
| ~ join_semilatt_str(U_215)
| empty_carrier(U_215) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( join(U_215,U_214,U_213) = apply_binary_as_element(the_carrier(U_215),the_carrier(U_215),the_carrier(U_215),the_L_join(U_215),U_214,U_213)
| ~ element(U_213,the_carrier(U_215))
| ~ element(U_214,the_carrier(U_215))
| ~ join_semilatt_str(U_215)
| empty_carrier(U_215) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_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_54_2,plain,
! [U_223] :
( ! [U_222] :
( ( U_222 = pair_first(U_223)
| ? [U_221,U_220] :
( U_222 != U_221
& U_223 = ordered_pair(U_221,U_220) ) )
& ( ! [U_219,U_218] :
( U_222 = U_219
| U_223 != ordered_pair(U_219,U_218) )
| U_222 != pair_first(U_223) ) )
| ! [U_217,U_216] : U_223 != ordered_pair(U_217,U_216) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_223] :
( ( ! [U_225] :
( U_225 = pair_first(U_223)
| ? [U_221] :
( ? [U_220] : U_223 = ordered_pair(U_221,U_220)
& U_225 != U_221 ) )
& ! [U_224] :
( ! [U_219] :
( ! [U_218] : U_223 != ordered_pair(U_219,U_218)
| U_224 = U_219 )
| U_224 != pair_first(U_223) ) )
| ! [U_217,U_216] : U_223 != ordered_pair(U_217,U_216) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_223] :
( ( ! [U_225] :
( U_225 = pair_first(U_223)
| ( ? [U_220] : U_223 = ordered_pair(sK33(U_223,U_225),U_220)
& U_225 != sK33(U_223,U_225) ) )
& ! [U_224] :
( ! [U_219] :
( ! [U_218] : U_223 != ordered_pair(U_219,U_218)
| U_224 = U_219 )
| U_224 != pair_first(U_223) ) )
| ! [U_217,U_216] : U_223 != ordered_pair(U_217,U_216) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_221,sK33(U_223,U_225))],[f_54_3]) ).
fof(f_54_5,plain,
! [U_223] :
( ( ! [U_225] :
( U_225 = pair_first(U_223)
| ( U_223 = ordered_pair(sK33(U_223,U_225),sK34(U_223,U_225))
& U_225 != sK33(U_223,U_225) ) )
& ! [U_224] :
( ! [U_219] :
( ! [U_218] : U_223 != ordered_pair(U_219,U_218)
| U_224 = U_219 )
| U_224 != pair_first(U_223) ) )
| ! [U_217,U_216] : U_223 != ordered_pair(U_217,U_216) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_220,sK34(U_223,U_225))],[f_54_4]) ).
cnf(f_54_6,plain,
( U_223 != ordered_pair(U_219,U_218)
| U_224 = U_219
| U_224 != pair_first(U_223)
| U_223 != ordered_pair(U_217,U_216) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_7,plain,
( U_225 != sK33(U_223,U_225)
| U_225 = pair_first(U_223)
| U_223 != ordered_pair(U_217,U_216) ),
inference(clausify,[status(thm)],[f_54_5]) ).
cnf(f_54_8,plain,
( U_223 = ordered_pair(sK33(U_223,U_225),sK34(U_223,U_225))
| U_225 = pair_first(U_223)
| U_223 != ordered_pair(U_217,U_216) ),
inference(clausify,[status(thm)],[f_54_5]) ).
fof(f_55_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_55_2,plain,
! [U_226] : succ(U_226) = set_union2(U_226,singleton(U_226)),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
succ(U_226) = set_union2(U_226,singleton(U_226)),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_233] :
( ( relation(U_233)
| ? [U_232] :
( ! [U_231,U_230] : U_232 != ordered_pair(U_231,U_230)
& in(U_232,U_233) ) )
& ( ! [U_229] :
( ? [U_228,U_227] : U_229 = ordered_pair(U_228,U_227)
| ~ in(U_229,U_233) )
| ~ relation(U_233) ) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_235] :
( relation(U_235)
| ? [U_232] :
( ! [U_231,U_230] : U_232 != ordered_pair(U_231,U_230)
& in(U_232,U_235) ) )
& ! [U_234] :
( ! [U_229] :
( ? [U_228,U_227] : U_229 = ordered_pair(U_228,U_227)
| ~ in(U_229,U_234) )
| ~ relation(U_234) ) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
( ! [U_235] :
( relation(U_235)
| ? [U_232] :
( ! [U_231,U_230] : U_232 != ordered_pair(U_231,U_230)
& in(U_232,U_235) ) )
& ! [U_234] :
( ! [U_229] :
( ? [U_227] : U_229 = ordered_pair(sK35(U_234,U_229),U_227)
| ~ in(U_229,U_234) )
| ~ relation(U_234) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_228,sK35(U_234,U_229))],[f_56_3]) ).
fof(f_56_5,plain,
( ! [U_235] :
( relation(U_235)
| ? [U_232] :
( ! [U_231,U_230] : U_232 != ordered_pair(U_231,U_230)
& in(U_232,U_235) ) )
& ! [U_234] :
( ! [U_229] :
( U_229 = ordered_pair(sK35(U_234,U_229),sK36(U_234,U_229))
| ~ in(U_229,U_234) )
| ~ relation(U_234) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_227,sK36(U_234,U_229))],[f_56_4]) ).
fof(f_56_6,plain,
( ! [U_235] :
( relation(U_235)
| ( ! [U_231,U_230] : sK37(U_235) != ordered_pair(U_231,U_230)
& in(sK37(U_235),U_235) ) )
& ! [U_234] :
( ! [U_229] :
( U_229 = ordered_pair(sK35(U_234,U_229),sK36(U_234,U_229))
| ~ in(U_229,U_234) )
| ~ relation(U_234) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_232,sK37(U_235))],[f_56_5]) ).
cnf(f_56_7,plain,
( U_229 = ordered_pair(sK35(U_234,U_229),sK36(U_234,U_229))
| ~ in(U_229,U_234)
| ~ relation(U_234) ),
inference(clausify,[status(thm)],[f_56_6]) ).
cnf(f_56_8,plain,
( in(sK37(U_235),U_235)
| relation(U_235) ),
inference(clausify,[status(thm)],[f_56_6]) ).
cnf(f_56_9,plain,
( sK37(U_235) != ordered_pair(U_231,U_230)
| relation(U_235) ),
inference(clausify,[status(thm)],[f_56_6]) ).
fof(f_57_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_57_2,plain,
! [U_239] :
( ! [U_238] :
( ( is_reflexive_in(U_239,U_238)
| ? [U_237] :
( ~ in(ordered_pair(U_237,U_237),U_239)
& in(U_237,U_238) ) )
& ( ! [U_236] :
( in(ordered_pair(U_236,U_236),U_239)
| ~ in(U_236,U_238) )
| ~ is_reflexive_in(U_239,U_238) ) )
| ~ relation(U_239) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_239] :
( ( ! [U_241] :
( is_reflexive_in(U_239,U_241)
| ? [U_237] :
( ~ in(ordered_pair(U_237,U_237),U_239)
& in(U_237,U_241) ) )
& ! [U_240] :
( ! [U_236] :
( in(ordered_pair(U_236,U_236),U_239)
| ~ in(U_236,U_240) )
| ~ is_reflexive_in(U_239,U_240) ) )
| ~ relation(U_239) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
! [U_239] :
( ( ! [U_241] :
( is_reflexive_in(U_239,U_241)
| ( ~ in(ordered_pair(sK38(U_239,U_241),sK38(U_239,U_241)),U_239)
& in(sK38(U_239,U_241),U_241) ) )
& ! [U_240] :
( ! [U_236] :
( in(ordered_pair(U_236,U_236),U_239)
| ~ in(U_236,U_240) )
| ~ is_reflexive_in(U_239,U_240) ) )
| ~ relation(U_239) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_237,sK38(U_239,U_241))],[f_57_3]) ).
cnf(f_57_5,plain,
( in(ordered_pair(U_236,U_236),U_239)
| ~ in(U_236,U_240)
| ~ is_reflexive_in(U_239,U_240)
| ~ relation(U_239) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_6,plain,
( in(sK38(U_239,U_241),U_241)
| is_reflexive_in(U_239,U_241)
| ~ relation(U_239) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_7,plain,
( ~ in(ordered_pair(sK38(U_239,U_241),sK38(U_239,U_241)),U_239)
| is_reflexive_in(U_239,U_241)
| ~ relation(U_239) ),
inference(clausify,[status(thm)],[f_57_4]) ).
fof(f_58_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_58_2,plain,
! [U_244,U_243,U_242] :
( ( relation_of2(U_242,U_244,U_243)
| ~ subset(U_242,cartesian_product2(U_244,U_243)) )
& ( subset(U_242,cartesian_product2(U_244,U_243))
| ~ relation_of2(U_242,U_244,U_243) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_250,U_248,U_246] :
( relation_of2(U_246,U_250,U_248)
| ~ subset(U_246,cartesian_product2(U_250,U_248)) )
& ! [U_249,U_247,U_245] :
( subset(U_245,cartesian_product2(U_249,U_247))
| ~ relation_of2(U_245,U_249,U_247) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( subset(U_245,cartesian_product2(U_249,U_247))
| ~ relation_of2(U_245,U_249,U_247) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( relation_of2(U_246,U_250,U_248)
| ~ subset(U_246,cartesian_product2(U_250,U_248)) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
! [U_258,U_257] :
( ( ( ( U_257 = set_meet(U_258)
| U_257 != empty_set )
& ( U_257 = empty_set
| U_257 != set_meet(U_258) ) )
| U_258 != empty_set )
& ( ( ( U_257 = set_meet(U_258)
| ? [U_256] :
( ( ~ in(U_256,U_257)
& ! [U_255] :
( in(U_256,U_255)
| ~ in(U_255,U_258) ) )
| ( ? [U_254] :
( ~ in(U_256,U_254)
& in(U_254,U_258) )
& in(U_256,U_257) ) ) )
& ( ! [U_253] :
( ( in(U_253,U_257)
| ? [U_252] :
( ~ in(U_253,U_252)
& in(U_252,U_258) ) )
& ( ! [U_251] :
( in(U_253,U_251)
| ~ in(U_251,U_258) )
| ~ in(U_253,U_257) ) )
| U_257 != set_meet(U_258) ) )
| U_258 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_270] :
( ( ! [U_268] :
( U_268 = set_meet(U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != set_meet(U_270) ) )
| U_270 != empty_set )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = set_meet(U_269)
| ? [U_262] :
( ~ in(U_262,U_266)
& ! [U_255] :
( in(U_262,U_255)
| ~ in(U_255,U_269) ) )
| ? [U_261] :
( ? [U_254] :
( ~ in(U_261,U_254)
& in(U_254,U_269) )
& in(U_261,U_266) ) )
& ! [U_265] :
( ( ! [U_260] :
( in(U_260,U_265)
| ? [U_252] :
( ~ in(U_260,U_252)
& in(U_252,U_269) ) )
& ! [U_259] :
( ! [U_251] :
( in(U_259,U_251)
| ~ in(U_251,U_269) )
| ~ in(U_259,U_265) ) )
| U_265 != set_meet(U_269) ) )
| U_269 = empty_set ) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
( ! [U_270] :
( ( ! [U_268] :
( U_268 = set_meet(U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != set_meet(U_270) ) )
| U_270 != empty_set )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = set_meet(U_269)
| ? [U_262] :
( ~ in(U_262,U_266)
& ! [U_255] :
( in(U_262,U_255)
| ~ in(U_255,U_269) ) )
| ? [U_261] :
( ? [U_254] :
( ~ in(U_261,U_254)
& in(U_254,U_269) )
& in(U_261,U_266) ) )
& ! [U_265] :
( ( ! [U_260] :
( in(U_260,U_265)
| ( ~ in(U_260,sK39(U_269,U_265,U_260))
& in(sK39(U_269,U_265,U_260),U_269) ) )
& ! [U_259] :
( ! [U_251] :
( in(U_259,U_251)
| ~ in(U_251,U_269) )
| ~ in(U_259,U_265) ) )
| U_265 != set_meet(U_269) ) )
| U_269 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_252,sK39(U_269,U_265,U_260))],[f_59_3]) ).
fof(f_59_5,plain,
( ! [U_270] :
( ( ! [U_268] :
( U_268 = set_meet(U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != set_meet(U_270) ) )
| U_270 != empty_set )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = set_meet(U_269)
| ? [U_262] :
( ~ in(U_262,U_266)
& ! [U_255] :
( in(U_262,U_255)
| ~ in(U_255,U_269) ) )
| ( ? [U_254] :
( ~ in(sK40(U_269,U_266),U_254)
& in(U_254,U_269) )
& in(sK40(U_269,U_266),U_266) ) )
& ! [U_265] :
( ( ! [U_260] :
( in(U_260,U_265)
| ( ~ in(U_260,sK39(U_269,U_265,U_260))
& in(sK39(U_269,U_265,U_260),U_269) ) )
& ! [U_259] :
( ! [U_251] :
( in(U_259,U_251)
| ~ in(U_251,U_269) )
| ~ in(U_259,U_265) ) )
| U_265 != set_meet(U_269) ) )
| U_269 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_261,sK40(U_269,U_266))],[f_59_4]) ).
fof(f_59_6,plain,
( ! [U_270] :
( ( ! [U_268] :
( U_268 = set_meet(U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != set_meet(U_270) ) )
| U_270 != empty_set )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = set_meet(U_269)
| ? [U_262] :
( ~ in(U_262,U_266)
& ! [U_255] :
( in(U_262,U_255)
| ~ in(U_255,U_269) ) )
| ( ~ in(sK40(U_269,U_266),sK41(U_269,U_266))
& in(sK41(U_269,U_266),U_269)
& in(sK40(U_269,U_266),U_266) ) )
& ! [U_265] :
( ( ! [U_260] :
( in(U_260,U_265)
| ( ~ in(U_260,sK39(U_269,U_265,U_260))
& in(sK39(U_269,U_265,U_260),U_269) ) )
& ! [U_259] :
( ! [U_251] :
( in(U_259,U_251)
| ~ in(U_251,U_269) )
| ~ in(U_259,U_265) ) )
| U_265 != set_meet(U_269) ) )
| U_269 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_254,sK41(U_269,U_266))],[f_59_5]) ).
fof(f_59_7,plain,
( ! [U_270] :
( ( ! [U_268] :
( U_268 = set_meet(U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != set_meet(U_270) ) )
| U_270 != empty_set )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = set_meet(U_269)
| ( ~ in(sK42(U_269,U_266),U_266)
& ! [U_255] :
( in(sK42(U_269,U_266),U_255)
| ~ in(U_255,U_269) ) )
| ( ~ in(sK40(U_269,U_266),sK41(U_269,U_266))
& in(sK41(U_269,U_266),U_269)
& in(sK40(U_269,U_266),U_266) ) )
& ! [U_265] :
( ( ! [U_260] :
( in(U_260,U_265)
| ( ~ in(U_260,sK39(U_269,U_265,U_260))
& in(sK39(U_269,U_265,U_260),U_269) ) )
& ! [U_259] :
( ! [U_251] :
( in(U_259,U_251)
| ~ in(U_251,U_269) )
| ~ in(U_259,U_265) ) )
| U_265 != set_meet(U_269) ) )
| U_269 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_262,sK42(U_269,U_266))],[f_59_6]) ).
cnf(f_59_8,plain,
( in(U_259,U_251)
| ~ in(U_251,U_269)
| ~ in(U_259,U_265)
| U_265 != set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_9,plain,
( in(sK39(U_269,U_265,U_260),U_269)
| in(U_260,U_265)
| U_265 != set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_10,plain,
( ~ in(U_260,sK39(U_269,U_265,U_260))
| in(U_260,U_265)
| U_265 != set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_11,plain,
( in(sK42(U_269,U_266),U_255)
| ~ in(U_255,U_269)
| in(sK40(U_269,U_266),U_266)
| U_266 = set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_12,plain,
( ~ in(sK42(U_269,U_266),U_266)
| in(sK40(U_269,U_266),U_266)
| U_266 = set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_13,plain,
( in(sK41(U_269,U_266),U_269)
| in(sK42(U_269,U_266),U_255)
| ~ in(U_255,U_269)
| U_266 = set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_14,plain,
( ~ in(sK40(U_269,U_266),sK41(U_269,U_266))
| in(sK42(U_269,U_266),U_255)
| ~ in(U_255,U_269)
| U_266 = set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_15,plain,
( in(sK41(U_269,U_266),U_269)
| ~ in(sK42(U_269,U_266),U_266)
| U_266 = set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_16,plain,
( ~ in(sK40(U_269,U_266),sK41(U_269,U_266))
| ~ in(sK42(U_269,U_266),U_266)
| U_266 = set_meet(U_269)
| U_269 = empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_17,plain,
( U_267 = empty_set
| U_267 != set_meet(U_270)
| U_270 != empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_18,plain,
( U_268 = set_meet(U_270)
| U_268 != empty_set
| U_270 != empty_set ),
inference(clausify,[status(thm)],[f_59_7]) ).
fof(f_60_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_60_2,plain,
! [U_274,U_273] :
( ( U_273 = singleton(U_274)
| ? [U_272] :
( ( ~ in(U_272,U_273)
& U_272 = U_274 )
| ( U_272 != U_274
& in(U_272,U_273) ) ) )
& ( ! [U_271] :
( ( in(U_271,U_273)
| U_271 != U_274 )
& ( U_271 = U_274
| ~ in(U_271,U_273) ) )
| U_273 != singleton(U_274) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ! [U_282,U_280] :
( U_280 = singleton(U_282)
| ? [U_278] :
( ~ in(U_278,U_280)
& U_278 = U_282 )
| ? [U_277] :
( U_277 != U_282
& in(U_277,U_280) ) )
& ! [U_281,U_279] :
( ( ! [U_276] :
( in(U_276,U_279)
| U_276 != U_281 )
& ! [U_275] :
( U_275 = U_281
| ~ in(U_275,U_279) ) )
| U_279 != singleton(U_281) ) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
fof(f_60_4,plain,
( ! [U_282,U_280] :
( U_280 = singleton(U_282)
| ? [U_278] :
( ~ in(U_278,U_280)
& U_278 = U_282 )
| ( sK43(U_282,U_280) != U_282
& in(sK43(U_282,U_280),U_280) ) )
& ! [U_281,U_279] :
( ( ! [U_276] :
( in(U_276,U_279)
| U_276 != U_281 )
& ! [U_275] :
( U_275 = U_281
| ~ in(U_275,U_279) ) )
| U_279 != singleton(U_281) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_277,sK43(U_282,U_280))],[f_60_3]) ).
fof(f_60_5,plain,
( ! [U_282,U_280] :
( U_280 = singleton(U_282)
| ( ~ in(sK44(U_282,U_280),U_280)
& sK44(U_282,U_280) = U_282 )
| ( sK43(U_282,U_280) != U_282
& in(sK43(U_282,U_280),U_280) ) )
& ! [U_281,U_279] :
( ( ! [U_276] :
( in(U_276,U_279)
| U_276 != U_281 )
& ! [U_275] :
( U_275 = U_281
| ~ in(U_275,U_279) ) )
| U_279 != singleton(U_281) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_278,sK44(U_282,U_280))],[f_60_4]) ).
cnf(f_60_6,plain,
( U_275 = U_281
| ~ in(U_275,U_279)
| U_279 != singleton(U_281) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_7,plain,
( in(U_276,U_279)
| U_276 != U_281
| U_279 != singleton(U_281) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_8,plain,
( sK44(U_282,U_280) = U_282
| in(sK43(U_282,U_280),U_280)
| U_280 = singleton(U_282) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_9,plain,
( ~ in(sK44(U_282,U_280),U_280)
| in(sK43(U_282,U_280),U_280)
| U_280 = singleton(U_282) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_10,plain,
( sK44(U_282,U_280) = U_282
| sK43(U_282,U_280) != U_282
| U_280 = singleton(U_282) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_11,plain,
( ~ in(sK44(U_282,U_280),U_280)
| sK43(U_282,U_280) != U_282
| U_280 = singleton(U_282) ),
inference(clausify,[status(thm)],[f_60_5]) ).
fof(f_61_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_61_2,plain,
! [U_287] :
( ! [U_286,U_285] :
( ( U_285 = fiber(U_287,U_286)
| ? [U_284] :
( ( ~ in(U_284,U_285)
& in(ordered_pair(U_284,U_286),U_287)
& U_284 != U_286 )
| ( ( ~ in(ordered_pair(U_284,U_286),U_287)
| U_284 = U_286 )
& in(U_284,U_285) ) ) )
& ( ! [U_283] :
( ( in(U_283,U_285)
| ~ in(ordered_pair(U_283,U_286),U_287)
| U_283 = U_286 )
& ( ( in(ordered_pair(U_283,U_286),U_287)
& U_283 != U_286 )
| ~ in(U_283,U_285) ) )
| U_285 != fiber(U_287,U_286) ) )
| ~ relation(U_287) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_287] :
( ( ! [U_295,U_293] :
( U_293 = fiber(U_287,U_295)
| ? [U_291] :
( ~ in(U_291,U_293)
& in(ordered_pair(U_291,U_295),U_287)
& U_291 != U_295 )
| ? [U_290] :
( ( ~ in(ordered_pair(U_290,U_295),U_287)
| U_290 = U_295 )
& in(U_290,U_293) ) )
& ! [U_294,U_292] :
( ( ! [U_289] :
( in(U_289,U_292)
| ~ in(ordered_pair(U_289,U_294),U_287)
| U_289 = U_294 )
& ! [U_288] :
( ( in(ordered_pair(U_288,U_294),U_287)
& U_288 != U_294 )
| ~ in(U_288,U_292) ) )
| U_292 != fiber(U_287,U_294) ) )
| ~ relation(U_287) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
! [U_287] :
( ( ! [U_295,U_293] :
( U_293 = fiber(U_287,U_295)
| ? [U_291] :
( ~ in(U_291,U_293)
& in(ordered_pair(U_291,U_295),U_287)
& U_291 != U_295 )
| ( ( ~ in(ordered_pair(sK45(U_287,U_295,U_293),U_295),U_287)
| sK45(U_287,U_295,U_293) = U_295 )
& in(sK45(U_287,U_295,U_293),U_293) ) )
& ! [U_294,U_292] :
( ( ! [U_289] :
( in(U_289,U_292)
| ~ in(ordered_pair(U_289,U_294),U_287)
| U_289 = U_294 )
& ! [U_288] :
( ( in(ordered_pair(U_288,U_294),U_287)
& U_288 != U_294 )
| ~ in(U_288,U_292) ) )
| U_292 != fiber(U_287,U_294) ) )
| ~ relation(U_287) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_290,sK45(U_287,U_295,U_293))],[f_61_3]) ).
fof(f_61_5,plain,
! [U_287] :
( ( ! [U_295,U_293] :
( U_293 = fiber(U_287,U_295)
| ( ~ in(sK46(U_287,U_295,U_293),U_293)
& in(ordered_pair(sK46(U_287,U_295,U_293),U_295),U_287)
& sK46(U_287,U_295,U_293) != U_295 )
| ( ( ~ in(ordered_pair(sK45(U_287,U_295,U_293),U_295),U_287)
| sK45(U_287,U_295,U_293) = U_295 )
& in(sK45(U_287,U_295,U_293),U_293) ) )
& ! [U_294,U_292] :
( ( ! [U_289] :
( in(U_289,U_292)
| ~ in(ordered_pair(U_289,U_294),U_287)
| U_289 = U_294 )
& ! [U_288] :
( ( in(ordered_pair(U_288,U_294),U_287)
& U_288 != U_294 )
| ~ in(U_288,U_292) ) )
| U_292 != fiber(U_287,U_294) ) )
| ~ relation(U_287) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_291,sK46(U_287,U_295,U_293))],[f_61_4]) ).
cnf(f_61_6,plain,
( U_288 != U_294
| ~ in(U_288,U_292)
| U_292 != fiber(U_287,U_294)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_7,plain,
( in(ordered_pair(U_288,U_294),U_287)
| ~ in(U_288,U_292)
| U_292 != fiber(U_287,U_294)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_8,plain,
( in(U_289,U_292)
| ~ in(ordered_pair(U_289,U_294),U_287)
| U_289 = U_294
| U_292 != fiber(U_287,U_294)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_9,plain,
( sK46(U_287,U_295,U_293) != U_295
| in(sK45(U_287,U_295,U_293),U_293)
| U_293 = fiber(U_287,U_295)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_10,plain,
( in(ordered_pair(sK46(U_287,U_295,U_293),U_295),U_287)
| in(sK45(U_287,U_295,U_293),U_293)
| U_293 = fiber(U_287,U_295)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_11,plain,
( ~ in(sK46(U_287,U_295,U_293),U_293)
| in(sK45(U_287,U_295,U_293),U_293)
| U_293 = fiber(U_287,U_295)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_12,plain,
( sK46(U_287,U_295,U_293) != U_295
| ~ in(ordered_pair(sK45(U_287,U_295,U_293),U_295),U_287)
| sK45(U_287,U_295,U_293) = U_295
| U_293 = fiber(U_287,U_295)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_13,plain,
( in(ordered_pair(sK46(U_287,U_295,U_293),U_295),U_287)
| ~ in(ordered_pair(sK45(U_287,U_295,U_293),U_295),U_287)
| sK45(U_287,U_295,U_293) = U_295
| U_293 = fiber(U_287,U_295)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
cnf(f_61_14,plain,
( ~ in(sK46(U_287,U_295,U_293),U_293)
| ~ in(ordered_pair(sK45(U_287,U_295,U_293),U_295),U_287)
| sK45(U_287,U_295,U_293) = U_295
| U_293 = fiber(U_287,U_295)
| ~ relation(U_287) ),
inference(clausify,[status(thm)],[f_61_5]) ).
fof(f_62_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_62_2,plain,
! [U_301,U_300] :
( ( ( U_300 = inclusion_relation(U_301)
| ? [U_299,U_298] :
( ( ( ~ in(ordered_pair(U_299,U_298),U_300)
& subset(U_299,U_298) )
| ( ~ subset(U_299,U_298)
& in(ordered_pair(U_299,U_298),U_300) ) )
& in(U_298,U_301)
& in(U_299,U_301) )
| relation_field(U_300) != U_301 )
& ( ( ! [U_297,U_296] :
( ( ( in(ordered_pair(U_297,U_296),U_300)
| ~ subset(U_297,U_296) )
& ( subset(U_297,U_296)
| ~ in(ordered_pair(U_297,U_296),U_300) ) )
| ~ in(U_296,U_301)
| ~ in(U_297,U_301) )
& relation_field(U_300) = U_301 )
| U_300 != inclusion_relation(U_301) ) )
| ~ relation(U_300) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_301,U_300] :
( ( ( U_300 = inclusion_relation(U_301)
| ? [U_298] :
( ( ( ~ in(ordered_pair(sK47(U_301,U_300),U_298),U_300)
& subset(sK47(U_301,U_300),U_298) )
| ( ~ subset(sK47(U_301,U_300),U_298)
& in(ordered_pair(sK47(U_301,U_300),U_298),U_300) ) )
& in(U_298,U_301)
& in(sK47(U_301,U_300),U_301) )
| relation_field(U_300) != U_301 )
& ( ( ! [U_297,U_296] :
( ( ( in(ordered_pair(U_297,U_296),U_300)
| ~ subset(U_297,U_296) )
& ( subset(U_297,U_296)
| ~ in(ordered_pair(U_297,U_296),U_300) ) )
| ~ in(U_296,U_301)
| ~ in(U_297,U_301) )
& relation_field(U_300) = U_301 )
| U_300 != inclusion_relation(U_301) ) )
| ~ relation(U_300) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_299,sK47(U_301,U_300))],[f_62_2]) ).
fof(f_62_4,plain,
! [U_301,U_300] :
( ( ( U_300 = inclusion_relation(U_301)
| ( ( ( ~ in(ordered_pair(sK47(U_301,U_300),sK48(U_301,U_300)),U_300)
& subset(sK47(U_301,U_300),sK48(U_301,U_300)) )
| ( ~ subset(sK47(U_301,U_300),sK48(U_301,U_300))
& in(ordered_pair(sK47(U_301,U_300),sK48(U_301,U_300)),U_300) ) )
& in(sK48(U_301,U_300),U_301)
& in(sK47(U_301,U_300),U_301) )
| relation_field(U_300) != U_301 )
& ( ( ! [U_297,U_296] :
( ( ( in(ordered_pair(U_297,U_296),U_300)
| ~ subset(U_297,U_296) )
& ( subset(U_297,U_296)
| ~ in(ordered_pair(U_297,U_296),U_300) ) )
| ~ in(U_296,U_301)
| ~ in(U_297,U_301) )
& relation_field(U_300) = U_301 )
| U_300 != inclusion_relation(U_301) ) )
| ~ relation(U_300) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_298,sK48(U_301,U_300))],[f_62_3]) ).
cnf(f_62_5,plain,
( relation_field(U_300) = U_301
| U_300 != inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_6,plain,
( subset(U_297,U_296)
| ~ in(ordered_pair(U_297,U_296),U_300)
| ~ in(U_296,U_301)
| ~ in(U_297,U_301)
| U_300 != inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_7,plain,
( in(ordered_pair(U_297,U_296),U_300)
| ~ subset(U_297,U_296)
| ~ in(U_296,U_301)
| ~ in(U_297,U_301)
| U_300 != inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_8,plain,
( in(sK47(U_301,U_300),U_301)
| relation_field(U_300) != U_301
| U_300 = inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_9,plain,
( in(sK48(U_301,U_300),U_301)
| relation_field(U_300) != U_301
| U_300 = inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_10,plain,
( subset(sK47(U_301,U_300),sK48(U_301,U_300))
| in(ordered_pair(sK47(U_301,U_300),sK48(U_301,U_300)),U_300)
| relation_field(U_300) != U_301
| U_300 = inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_11,plain,
( ~ in(ordered_pair(sK47(U_301,U_300),sK48(U_301,U_300)),U_300)
| in(ordered_pair(sK47(U_301,U_300),sK48(U_301,U_300)),U_300)
| relation_field(U_300) != U_301
| U_300 = inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_12,plain,
( subset(sK47(U_301,U_300),sK48(U_301,U_300))
| ~ subset(sK47(U_301,U_300),sK48(U_301,U_300))
| relation_field(U_300) != U_301
| U_300 = inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_13,plain,
( ~ in(ordered_pair(sK47(U_301,U_300),sK48(U_301,U_300)),U_300)
| ~ subset(sK47(U_301,U_300),sK48(U_301,U_300))
| relation_field(U_300) != U_301
| U_300 = inclusion_relation(U_301)
| ~ relation(U_300) ),
inference(clausify,[status(thm)],[f_62_4]) ).
fof(f_63_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_63_2,plain,
! [U_304] :
( ( U_304 = empty_set
| ? [U_303] : in(U_303,U_304) )
& ( ! [U_302] : ~ in(U_302,U_304)
| U_304 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_306] :
( U_306 = empty_set
| ? [U_303] : in(U_303,U_306) )
& ! [U_305] :
( ! [U_302] : ~ in(U_302,U_305)
| U_305 != empty_set ) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
fof(f_63_4,plain,
( ! [U_306] :
( U_306 = empty_set
| in(sK49(U_306),U_306) )
& ! [U_305] :
( ! [U_302] : ~ in(U_302,U_305)
| U_305 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_303,sK49(U_306))],[f_63_3]) ).
cnf(f_63_5,plain,
( ~ in(U_302,U_305)
| U_305 != empty_set ),
inference(clausify,[status(thm)],[f_63_4]) ).
cnf(f_63_6,plain,
( U_306 = empty_set
| in(sK49(U_306),U_306) ),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_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_64_2,plain,
! [U_310,U_309] :
( ( U_309 = powerset(U_310)
| ? [U_308] :
( ( ~ in(U_308,U_309)
& subset(U_308,U_310) )
| ( ~ subset(U_308,U_310)
& in(U_308,U_309) ) ) )
& ( ! [U_307] :
( ( in(U_307,U_309)
| ~ subset(U_307,U_310) )
& ( subset(U_307,U_310)
| ~ in(U_307,U_309) ) )
| U_309 != powerset(U_310) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_318,U_316] :
( U_316 = powerset(U_318)
| ? [U_314] :
( ~ in(U_314,U_316)
& subset(U_314,U_318) )
| ? [U_313] :
( ~ subset(U_313,U_318)
& in(U_313,U_316) ) )
& ! [U_317,U_315] :
( ( ! [U_312] :
( in(U_312,U_315)
| ~ subset(U_312,U_317) )
& ! [U_311] :
( subset(U_311,U_317)
| ~ in(U_311,U_315) ) )
| U_315 != powerset(U_317) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
( ! [U_318,U_316] :
( U_316 = powerset(U_318)
| ? [U_314] :
( ~ in(U_314,U_316)
& subset(U_314,U_318) )
| ( ~ subset(sK50(U_318,U_316),U_318)
& in(sK50(U_318,U_316),U_316) ) )
& ! [U_317,U_315] :
( ( ! [U_312] :
( in(U_312,U_315)
| ~ subset(U_312,U_317) )
& ! [U_311] :
( subset(U_311,U_317)
| ~ in(U_311,U_315) ) )
| U_315 != powerset(U_317) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_313,sK50(U_318,U_316))],[f_64_3]) ).
fof(f_64_5,plain,
( ! [U_318,U_316] :
( U_316 = powerset(U_318)
| ( ~ in(sK51(U_318,U_316),U_316)
& subset(sK51(U_318,U_316),U_318) )
| ( ~ subset(sK50(U_318,U_316),U_318)
& in(sK50(U_318,U_316),U_316) ) )
& ! [U_317,U_315] :
( ( ! [U_312] :
( in(U_312,U_315)
| ~ subset(U_312,U_317) )
& ! [U_311] :
( subset(U_311,U_317)
| ~ in(U_311,U_315) ) )
| U_315 != powerset(U_317) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_314,sK51(U_318,U_316))],[f_64_4]) ).
cnf(f_64_6,plain,
( subset(U_311,U_317)
| ~ in(U_311,U_315)
| U_315 != powerset(U_317) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_7,plain,
( in(U_312,U_315)
| ~ subset(U_312,U_317)
| U_315 != powerset(U_317) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_8,plain,
( subset(sK51(U_318,U_316),U_318)
| in(sK50(U_318,U_316),U_316)
| U_316 = powerset(U_318) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_9,plain,
( ~ in(sK51(U_318,U_316),U_316)
| in(sK50(U_318,U_316),U_316)
| U_316 = powerset(U_318) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_10,plain,
( subset(sK51(U_318,U_316),U_318)
| ~ subset(sK50(U_318,U_316),U_318)
| U_316 = powerset(U_318) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_11,plain,
( ~ in(sK51(U_318,U_316),U_316)
| ~ subset(sK50(U_318,U_316),U_318)
| U_316 = powerset(U_318) ),
inference(clausify,[status(thm)],[f_64_5]) ).
fof(f_65_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_65_2,plain,
! [U_321] :
( ! [U_320] :
( ! [U_319] :
( meet(U_321,U_320,U_319) = apply_binary_as_element(the_carrier(U_321),the_carrier(U_321),the_carrier(U_321),the_L_meet(U_321),U_320,U_319)
| ~ element(U_319,the_carrier(U_321)) )
| ~ element(U_320,the_carrier(U_321)) )
| ~ meet_semilatt_str(U_321)
| empty_carrier(U_321) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( meet(U_321,U_320,U_319) = apply_binary_as_element(the_carrier(U_321),the_carrier(U_321),the_carrier(U_321),the_L_meet(U_321),U_320,U_319)
| ~ element(U_319,the_carrier(U_321))
| ~ element(U_320,the_carrier(U_321))
| ~ meet_semilatt_str(U_321)
| empty_carrier(U_321) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_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_66_2,plain,
! [U_329] :
( ! [U_328] :
( ( U_328 = pair_second(U_329)
| ? [U_327,U_326] :
( U_328 != U_326
& U_329 = ordered_pair(U_327,U_326) ) )
& ( ! [U_325,U_324] :
( U_328 = U_324
| U_329 != ordered_pair(U_325,U_324) )
| U_328 != pair_second(U_329) ) )
| ! [U_323,U_322] : U_329 != ordered_pair(U_323,U_322) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_329] :
( ( ! [U_331] :
( U_331 = pair_second(U_329)
| ? [U_327,U_326] :
( U_331 != U_326
& U_329 = ordered_pair(U_327,U_326) ) )
& ! [U_330] :
( ! [U_325,U_324] :
( U_330 = U_324
| U_329 != ordered_pair(U_325,U_324) )
| U_330 != pair_second(U_329) ) )
| ! [U_323,U_322] : U_329 != ordered_pair(U_323,U_322) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
! [U_329] :
( ( ! [U_331] :
( U_331 = pair_second(U_329)
| ? [U_326] :
( U_331 != U_326
& U_329 = ordered_pair(sK52(U_329,U_331),U_326) ) )
& ! [U_330] :
( ! [U_325,U_324] :
( U_330 = U_324
| U_329 != ordered_pair(U_325,U_324) )
| U_330 != pair_second(U_329) ) )
| ! [U_323,U_322] : U_329 != ordered_pair(U_323,U_322) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_327,sK52(U_329,U_331))],[f_66_3]) ).
fof(f_66_5,plain,
! [U_329] :
( ( ! [U_331] :
( U_331 = pair_second(U_329)
| ( U_331 != sK53(U_329,U_331)
& U_329 = ordered_pair(sK52(U_329,U_331),sK53(U_329,U_331)) ) )
& ! [U_330] :
( ! [U_325,U_324] :
( U_330 = U_324
| U_329 != ordered_pair(U_325,U_324) )
| U_330 != pair_second(U_329) ) )
| ! [U_323,U_322] : U_329 != ordered_pair(U_323,U_322) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_326,sK53(U_329,U_331))],[f_66_4]) ).
cnf(f_66_6,plain,
( U_330 = U_324
| U_329 != ordered_pair(U_325,U_324)
| U_330 != pair_second(U_329)
| U_329 != ordered_pair(U_323,U_322) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_7,plain,
( U_329 = ordered_pair(sK52(U_329,U_331),sK53(U_329,U_331))
| U_331 = pair_second(U_329)
| U_329 != ordered_pair(U_323,U_322) ),
inference(clausify,[status(thm)],[f_66_5]) ).
cnf(f_66_8,plain,
( U_331 != sK53(U_329,U_331)
| U_331 = pair_second(U_329)
| U_329 != ordered_pair(U_323,U_322) ),
inference(clausify,[status(thm)],[f_66_5]) ).
fof(f_67_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_67_2,plain,
! [U_334] :
( ( epsilon_transitive(U_334)
| ? [U_333] :
( ~ subset(U_333,U_334)
& in(U_333,U_334) ) )
& ( ! [U_332] :
( subset(U_332,U_334)
| ~ in(U_332,U_334) )
| ~ epsilon_transitive(U_334) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_336] :
( epsilon_transitive(U_336)
| ? [U_333] :
( ~ subset(U_333,U_336)
& in(U_333,U_336) ) )
& ! [U_335] :
( ! [U_332] :
( subset(U_332,U_335)
| ~ in(U_332,U_335) )
| ~ epsilon_transitive(U_335) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
( ! [U_336] :
( epsilon_transitive(U_336)
| ( ~ subset(sK54(U_336),U_336)
& in(sK54(U_336),U_336) ) )
& ! [U_335] :
( ! [U_332] :
( subset(U_332,U_335)
| ~ in(U_332,U_335) )
| ~ epsilon_transitive(U_335) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_333,sK54(U_336))],[f_67_3]) ).
cnf(f_67_5,plain,
( subset(U_332,U_335)
| ~ in(U_332,U_335)
| ~ epsilon_transitive(U_335) ),
inference(clausify,[status(thm)],[f_67_4]) ).
cnf(f_67_6,plain,
( in(sK54(U_336),U_336)
| epsilon_transitive(U_336) ),
inference(clausify,[status(thm)],[f_67_4]) ).
cnf(f_67_7,plain,
( ~ subset(sK54(U_336),U_336)
| epsilon_transitive(U_336) ),
inference(clausify,[status(thm)],[f_67_4]) ).
fof(f_68_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_68_2,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_342 = U_341
| ? [U_340,U_339] :
( ( ~ in(ordered_pair(U_340,U_339),U_342)
& in(ordered_pair(U_340,U_339),U_341) )
| ( ~ in(ordered_pair(U_340,U_339),U_341)
& in(ordered_pair(U_340,U_339),U_342) ) ) )
& ( ! [U_338,U_337] :
( ( in(ordered_pair(U_338,U_337),U_342)
| ~ in(ordered_pair(U_338,U_337),U_341) )
& ( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_338,U_337),U_342) ) )
| U_342 != U_341 ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_342 = U_341
| ? [U_350,U_348] :
( ~ in(ordered_pair(U_350,U_348),U_342)
& in(ordered_pair(U_350,U_348),U_341) )
| ? [U_349,U_347] :
( ~ in(ordered_pair(U_349,U_347),U_341)
& in(ordered_pair(U_349,U_347),U_342) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_342)
| ~ in(ordered_pair(U_346,U_344),U_341) )
& ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_341)
| ~ in(ordered_pair(U_345,U_343),U_342) ) )
| U_342 != U_341 ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_342 = U_341
| ? [U_350,U_348] :
( ~ in(ordered_pair(U_350,U_348),U_342)
& in(ordered_pair(U_350,U_348),U_341) )
| ? [U_347] :
( ~ in(ordered_pair(sK55(U_342,U_341),U_347),U_341)
& in(ordered_pair(sK55(U_342,U_341),U_347),U_342) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_342)
| ~ in(ordered_pair(U_346,U_344),U_341) )
& ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_341)
| ~ in(ordered_pair(U_345,U_343),U_342) ) )
| U_342 != U_341 ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_349,sK55(U_342,U_341))],[f_68_3]) ).
fof(f_68_5,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_342 = U_341
| ? [U_350,U_348] :
( ~ in(ordered_pair(U_350,U_348),U_342)
& in(ordered_pair(U_350,U_348),U_341) )
| ( ~ in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_341)
& in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_342) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_342)
| ~ in(ordered_pair(U_346,U_344),U_341) )
& ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_341)
| ~ in(ordered_pair(U_345,U_343),U_342) ) )
| U_342 != U_341 ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_347,sK56(U_342,U_341))],[f_68_4]) ).
fof(f_68_6,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_342 = U_341
| ? [U_348] :
( ~ in(ordered_pair(sK57(U_342,U_341),U_348),U_342)
& in(ordered_pair(sK57(U_342,U_341),U_348),U_341) )
| ( ~ in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_341)
& in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_342) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_342)
| ~ in(ordered_pair(U_346,U_344),U_341) )
& ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_341)
| ~ in(ordered_pair(U_345,U_343),U_342) ) )
| U_342 != U_341 ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_350,sK57(U_342,U_341))],[f_68_5]) ).
fof(f_68_7,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_342 = U_341
| ( ~ in(ordered_pair(sK57(U_342,U_341),sK58(U_342,U_341)),U_342)
& in(ordered_pair(sK57(U_342,U_341),sK58(U_342,U_341)),U_341) )
| ( ~ in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_341)
& in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_342) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_342)
| ~ in(ordered_pair(U_346,U_344),U_341) )
& ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_341)
| ~ in(ordered_pair(U_345,U_343),U_342) ) )
| U_342 != U_341 ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_348,sK58(U_342,U_341))],[f_68_6]) ).
cnf(f_68_8,plain,
( in(ordered_pair(U_345,U_343),U_341)
| ~ in(ordered_pair(U_345,U_343),U_342)
| U_342 != U_341
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_9,plain,
( in(ordered_pair(U_346,U_344),U_342)
| ~ in(ordered_pair(U_346,U_344),U_341)
| U_342 != U_341
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_10,plain,
( in(ordered_pair(sK57(U_342,U_341),sK58(U_342,U_341)),U_341)
| in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_342)
| U_342 = U_341
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_11,plain,
( ~ in(ordered_pair(sK57(U_342,U_341),sK58(U_342,U_341)),U_342)
| in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_342)
| U_342 = U_341
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_12,plain,
( in(ordered_pair(sK57(U_342,U_341),sK58(U_342,U_341)),U_341)
| ~ in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_341)
| U_342 = U_341
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_13,plain,
( ~ in(ordered_pair(sK57(U_342,U_341),sK58(U_342,U_341)),U_342)
| ~ in(ordered_pair(sK55(U_342,U_341),sK56(U_342,U_341)),U_341)
| U_342 = U_341
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_68_7]) ).
fof(f_69_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_69_2,plain,
! [U_352,U_351] :
( ( ( ( element(U_351,U_352)
| ~ empty(U_351) )
& ( empty(U_351)
| ~ element(U_351,U_352) ) )
| ~ empty(U_352) )
& ( ( ( element(U_351,U_352)
| ~ in(U_351,U_352) )
& ( in(U_351,U_352)
| ~ element(U_351,U_352) ) )
| empty(U_352) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_360] :
( ( ! [U_358] :
( element(U_358,U_360)
| ~ empty(U_358) )
& ! [U_357] :
( empty(U_357)
| ~ element(U_357,U_360) ) )
| ~ empty(U_360) )
& ! [U_359] :
( ( ! [U_356] :
( element(U_356,U_359)
| ~ in(U_356,U_359) )
& ! [U_355] :
( in(U_355,U_359)
| ~ element(U_355,U_359) ) )
| empty(U_359) ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
cnf(f_69_4,plain,
( in(U_355,U_359)
| ~ element(U_355,U_359)
| empty(U_359) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_5,plain,
( element(U_356,U_359)
| ~ in(U_356,U_359)
| empty(U_359) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_6,plain,
( empty(U_357)
| ~ element(U_357,U_360)
| ~ empty(U_360) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_7,plain,
( element(U_358,U_360)
| ~ empty(U_358)
| ~ empty(U_360) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_365,U_364,U_363] :
( ( U_363 = unordered_pair(U_365,U_364)
| ? [U_362] :
( ( ~ in(U_362,U_363)
& ( U_362 = U_364
| U_362 = U_365 ) )
| ( U_362 != U_364
& U_362 != U_365
& in(U_362,U_363) ) ) )
& ( ! [U_361] :
( ( in(U_361,U_363)
| ( U_361 != U_364
& U_361 != U_365 ) )
& ( U_361 = U_364
| U_361 = U_365
| ~ in(U_361,U_363) ) )
| U_363 != unordered_pair(U_365,U_364) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_375,U_373,U_371] :
( U_371 = unordered_pair(U_375,U_373)
| ? [U_369] :
( ~ in(U_369,U_371)
& ( U_369 = U_373
| U_369 = U_375 ) )
| ? [U_368] :
( U_368 != U_373
& U_368 != U_375
& in(U_368,U_371) ) )
& ! [U_374,U_372,U_370] :
( ( ! [U_367] :
( in(U_367,U_370)
| ( U_367 != U_372
& U_367 != U_374 ) )
& ! [U_366] :
( U_366 = U_372
| U_366 = U_374
| ~ in(U_366,U_370) ) )
| U_370 != unordered_pair(U_374,U_372) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
fof(f_70_4,plain,
( ! [U_375,U_373,U_371] :
( U_371 = unordered_pair(U_375,U_373)
| ? [U_369] :
( ~ in(U_369,U_371)
& ( U_369 = U_373
| U_369 = U_375 ) )
| ( sK59(U_375,U_373,U_371) != U_373
& sK59(U_375,U_373,U_371) != U_375
& in(sK59(U_375,U_373,U_371),U_371) ) )
& ! [U_374,U_372,U_370] :
( ( ! [U_367] :
( in(U_367,U_370)
| ( U_367 != U_372
& U_367 != U_374 ) )
& ! [U_366] :
( U_366 = U_372
| U_366 = U_374
| ~ in(U_366,U_370) ) )
| U_370 != unordered_pair(U_374,U_372) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_368,sK59(U_375,U_373,U_371))],[f_70_3]) ).
fof(f_70_5,plain,
( ! [U_375,U_373,U_371] :
( U_371 = unordered_pair(U_375,U_373)
| ( ~ in(sK60(U_375,U_373,U_371),U_371)
& ( sK60(U_375,U_373,U_371) = U_373
| sK60(U_375,U_373,U_371) = U_375 ) )
| ( sK59(U_375,U_373,U_371) != U_373
& sK59(U_375,U_373,U_371) != U_375
& in(sK59(U_375,U_373,U_371),U_371) ) )
& ! [U_374,U_372,U_370] :
( ( ! [U_367] :
( in(U_367,U_370)
| ( U_367 != U_372
& U_367 != U_374 ) )
& ! [U_366] :
( U_366 = U_372
| U_366 = U_374
| ~ in(U_366,U_370) ) )
| U_370 != unordered_pair(U_374,U_372) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_369,sK60(U_375,U_373,U_371))],[f_70_4]) ).
cnf(f_70_6,plain,
( U_366 = U_372
| U_366 = U_374
| ~ in(U_366,U_370)
| U_370 != unordered_pair(U_374,U_372) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_7,plain,
( U_367 != U_374
| in(U_367,U_370)
| U_370 != unordered_pair(U_374,U_372) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_8,plain,
( U_367 != U_372
| in(U_367,U_370)
| U_370 != unordered_pair(U_374,U_372) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_9,plain,
( sK60(U_375,U_373,U_371) = U_373
| sK60(U_375,U_373,U_371) = U_375
| in(sK59(U_375,U_373,U_371),U_371)
| U_371 = unordered_pair(U_375,U_373) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_10,plain,
( ~ in(sK60(U_375,U_373,U_371),U_371)
| in(sK59(U_375,U_373,U_371),U_371)
| U_371 = unordered_pair(U_375,U_373) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_11,plain,
( sK59(U_375,U_373,U_371) != U_375
| sK60(U_375,U_373,U_371) = U_373
| sK60(U_375,U_373,U_371) = U_375
| U_371 = unordered_pair(U_375,U_373) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_12,plain,
( sK59(U_375,U_373,U_371) != U_373
| sK60(U_375,U_373,U_371) = U_373
| sK60(U_375,U_373,U_371) = U_375
| U_371 = unordered_pair(U_375,U_373) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_13,plain,
( sK59(U_375,U_373,U_371) != U_375
| ~ in(sK60(U_375,U_373,U_371),U_371)
| U_371 = unordered_pair(U_375,U_373) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_14,plain,
( sK59(U_375,U_373,U_371) != U_373
| ~ in(sK60(U_375,U_373,U_371),U_371)
| U_371 = unordered_pair(U_375,U_373) ),
inference(clausify,[status(thm)],[f_70_5]) ).
fof(f_71_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_71_2,plain,
! [U_380] :
( ( ( well_founded_relation(U_380)
| ? [U_379] :
( ! [U_378] :
( ~ disjoint(fiber(U_380,U_378),U_379)
| ~ in(U_378,U_379) )
& U_379 != empty_set
& subset(U_379,relation_field(U_380)) ) )
& ( ! [U_377] :
( ? [U_376] :
( disjoint(fiber(U_380,U_376),U_377)
& in(U_376,U_377) )
| U_377 = empty_set
| ~ subset(U_377,relation_field(U_380)) )
| ~ well_founded_relation(U_380) ) )
| ~ relation(U_380) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_380] :
( ( ( well_founded_relation(U_380)
| ? [U_379] :
( ! [U_378] :
( ~ disjoint(fiber(U_380,U_378),U_379)
| ~ in(U_378,U_379) )
& U_379 != empty_set
& subset(U_379,relation_field(U_380)) ) )
& ( ! [U_377] :
( ( disjoint(fiber(U_380,sK61(U_380,U_377)),U_377)
& in(sK61(U_380,U_377),U_377) )
| U_377 = empty_set
| ~ subset(U_377,relation_field(U_380)) )
| ~ well_founded_relation(U_380) ) )
| ~ relation(U_380) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_376,sK61(U_380,U_377))],[f_71_2]) ).
fof(f_71_4,plain,
! [U_380] :
( ( ( well_founded_relation(U_380)
| ( ! [U_378] :
( ~ disjoint(fiber(U_380,U_378),sK62(U_380))
| ~ in(U_378,sK62(U_380)) )
& sK62(U_380) != empty_set
& subset(sK62(U_380),relation_field(U_380)) ) )
& ( ! [U_377] :
( ( disjoint(fiber(U_380,sK61(U_380,U_377)),U_377)
& in(sK61(U_380,U_377),U_377) )
| U_377 = empty_set
| ~ subset(U_377,relation_field(U_380)) )
| ~ well_founded_relation(U_380) ) )
| ~ relation(U_380) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_379,sK62(U_380))],[f_71_3]) ).
cnf(f_71_5,plain,
( in(sK61(U_380,U_377),U_377)
| U_377 = empty_set
| ~ subset(U_377,relation_field(U_380))
| ~ well_founded_relation(U_380)
| ~ relation(U_380) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_6,plain,
( disjoint(fiber(U_380,sK61(U_380,U_377)),U_377)
| U_377 = empty_set
| ~ subset(U_377,relation_field(U_380))
| ~ well_founded_relation(U_380)
| ~ relation(U_380) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_7,plain,
( subset(sK62(U_380),relation_field(U_380))
| well_founded_relation(U_380)
| ~ relation(U_380) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_8,plain,
( sK62(U_380) != empty_set
| well_founded_relation(U_380)
| ~ relation(U_380) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_9,plain,
( ~ disjoint(fiber(U_380,U_378),sK62(U_380))
| ~ in(U_378,sK62(U_380))
| well_founded_relation(U_380)
| ~ relation(U_380) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_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_72_2,plain,
! [U_385,U_384,U_383] :
( ( U_383 = set_union2(U_385,U_384)
| ? [U_382] :
( ( ~ in(U_382,U_383)
& ( in(U_382,U_384)
| in(U_382,U_385) ) )
| ( ~ in(U_382,U_384)
& ~ in(U_382,U_385)
& in(U_382,U_383) ) ) )
& ( ! [U_381] :
( ( in(U_381,U_383)
| ( ~ in(U_381,U_384)
& ~ in(U_381,U_385) ) )
& ( in(U_381,U_384)
| in(U_381,U_385)
| ~ in(U_381,U_383) ) )
| U_383 != set_union2(U_385,U_384) ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_395,U_393,U_391] :
( U_391 = set_union2(U_395,U_393)
| ? [U_389] :
( ~ in(U_389,U_391)
& ( in(U_389,U_393)
| in(U_389,U_395) ) )
| ? [U_388] :
( ~ in(U_388,U_393)
& ~ in(U_388,U_395)
& in(U_388,U_391) ) )
& ! [U_394,U_392,U_390] :
( ( ! [U_387] :
( in(U_387,U_390)
| ( ~ in(U_387,U_392)
& ~ in(U_387,U_394) ) )
& ! [U_386] :
( in(U_386,U_392)
| in(U_386,U_394)
| ~ in(U_386,U_390) ) )
| U_390 != set_union2(U_394,U_392) ) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
( ! [U_395,U_393,U_391] :
( U_391 = set_union2(U_395,U_393)
| ? [U_389] :
( ~ in(U_389,U_391)
& ( in(U_389,U_393)
| in(U_389,U_395) ) )
| ( ~ in(sK63(U_395,U_393,U_391),U_393)
& ~ in(sK63(U_395,U_393,U_391),U_395)
& in(sK63(U_395,U_393,U_391),U_391) ) )
& ! [U_394,U_392,U_390] :
( ( ! [U_387] :
( in(U_387,U_390)
| ( ~ in(U_387,U_392)
& ~ in(U_387,U_394) ) )
& ! [U_386] :
( in(U_386,U_392)
| in(U_386,U_394)
| ~ in(U_386,U_390) ) )
| U_390 != set_union2(U_394,U_392) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_388,sK63(U_395,U_393,U_391))],[f_72_3]) ).
fof(f_72_5,plain,
( ! [U_395,U_393,U_391] :
( U_391 = set_union2(U_395,U_393)
| ( ~ in(sK64(U_395,U_393,U_391),U_391)
& ( in(sK64(U_395,U_393,U_391),U_393)
| in(sK64(U_395,U_393,U_391),U_395) ) )
| ( ~ in(sK63(U_395,U_393,U_391),U_393)
& ~ in(sK63(U_395,U_393,U_391),U_395)
& in(sK63(U_395,U_393,U_391),U_391) ) )
& ! [U_394,U_392,U_390] :
( ( ! [U_387] :
( in(U_387,U_390)
| ( ~ in(U_387,U_392)
& ~ in(U_387,U_394) ) )
& ! [U_386] :
( in(U_386,U_392)
| in(U_386,U_394)
| ~ in(U_386,U_390) ) )
| U_390 != set_union2(U_394,U_392) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_389,sK64(U_395,U_393,U_391))],[f_72_4]) ).
cnf(f_72_6,plain,
( in(U_386,U_392)
| in(U_386,U_394)
| ~ in(U_386,U_390)
| U_390 != set_union2(U_394,U_392) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_7,plain,
( ~ in(U_387,U_394)
| in(U_387,U_390)
| U_390 != set_union2(U_394,U_392) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_8,plain,
( ~ in(U_387,U_392)
| in(U_387,U_390)
| U_390 != set_union2(U_394,U_392) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_9,plain,
( in(sK64(U_395,U_393,U_391),U_393)
| in(sK64(U_395,U_393,U_391),U_395)
| in(sK63(U_395,U_393,U_391),U_391)
| U_391 = set_union2(U_395,U_393) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_10,plain,
( ~ in(sK64(U_395,U_393,U_391),U_391)
| in(sK63(U_395,U_393,U_391),U_391)
| U_391 = set_union2(U_395,U_393) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_11,plain,
( ~ in(sK63(U_395,U_393,U_391),U_395)
| in(sK64(U_395,U_393,U_391),U_393)
| in(sK64(U_395,U_393,U_391),U_395)
| U_391 = set_union2(U_395,U_393) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_12,plain,
( ~ in(sK63(U_395,U_393,U_391),U_393)
| in(sK64(U_395,U_393,U_391),U_393)
| in(sK64(U_395,U_393,U_391),U_395)
| U_391 = set_union2(U_395,U_393) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_13,plain,
( ~ in(sK63(U_395,U_393,U_391),U_395)
| ~ in(sK64(U_395,U_393,U_391),U_391)
| U_391 = set_union2(U_395,U_393) ),
inference(clausify,[status(thm)],[f_72_5]) ).
cnf(f_72_14,plain,
( ~ in(sK63(U_395,U_393,U_391),U_393)
| ~ in(sK64(U_395,U_393,U_391),U_391)
| U_391 = set_union2(U_395,U_393) ),
inference(clausify,[status(thm)],[f_72_5]) ).
fof(f_73_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_73_2,plain,
! [U_408,U_407,U_406] :
( ( U_406 = cartesian_product2(U_408,U_407)
| ? [U_405] :
( ( ~ in(U_405,U_406)
& ? [U_404,U_403] :
( U_405 = ordered_pair(U_404,U_403)
& in(U_403,U_407)
& in(U_404,U_408) ) )
| ( ! [U_402,U_401] :
( U_405 != ordered_pair(U_402,U_401)
| ~ in(U_401,U_407)
| ~ in(U_402,U_408) )
& in(U_405,U_406) ) ) )
& ( ! [U_400] :
( ( in(U_400,U_406)
| ! [U_399,U_398] :
( U_400 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_407)
| ~ in(U_399,U_408) ) )
& ( ? [U_397,U_396] :
( U_400 = ordered_pair(U_397,U_396)
& in(U_396,U_407)
& in(U_397,U_408) )
| ~ in(U_400,U_406) ) )
| U_406 != cartesian_product2(U_408,U_407) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ? [U_412] :
( ~ in(U_412,U_414)
& ? [U_404] :
( ? [U_403] :
( U_412 = ordered_pair(U_404,U_403)
& in(U_403,U_416) )
& in(U_404,U_418) ) )
| ? [U_411] :
( ! [U_402] :
( ! [U_401] :
( U_411 != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(U_411,U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ? [U_397] :
( ? [U_396] :
( U_409 = ordered_pair(U_397,U_396)
& in(U_396,U_415) )
& in(U_397,U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ? [U_412] :
( ~ in(U_412,U_414)
& ? [U_404] :
( ? [U_403] :
( U_412 = ordered_pair(U_404,U_403)
& in(U_403,U_416) )
& in(U_404,U_418) ) )
| ? [U_411] :
( ! [U_402] :
( ! [U_401] :
( U_411 != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(U_411,U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ( ? [U_396] :
( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),U_396)
& in(U_396,U_415) )
& in(sK65(U_417,U_415,U_413,U_409),U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_397,sK65(U_417,U_415,U_413,U_409))],[f_73_3]) ).
fof(f_73_5,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ? [U_412] :
( ~ in(U_412,U_414)
& ? [U_404] :
( ? [U_403] :
( U_412 = ordered_pair(U_404,U_403)
& in(U_403,U_416) )
& in(U_404,U_418) ) )
| ? [U_411] :
( ! [U_402] :
( ! [U_401] :
( U_411 != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(U_411,U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),sK66(U_417,U_415,U_413,U_409))
& in(sK66(U_417,U_415,U_413,U_409),U_415)
& in(sK65(U_417,U_415,U_413,U_409),U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_396,sK66(U_417,U_415,U_413,U_409))],[f_73_4]) ).
fof(f_73_6,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ? [U_412] :
( ~ in(U_412,U_414)
& ? [U_404] :
( ? [U_403] :
( U_412 = ordered_pair(U_404,U_403)
& in(U_403,U_416) )
& in(U_404,U_418) ) )
| ( ! [U_402] :
( ! [U_401] :
( sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(sK67(U_418,U_416,U_414),U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),sK66(U_417,U_415,U_413,U_409))
& in(sK66(U_417,U_415,U_413,U_409),U_415)
& in(sK65(U_417,U_415,U_413,U_409),U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_411,sK67(U_418,U_416,U_414))],[f_73_5]) ).
fof(f_73_7,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ( ~ in(sK68(U_418,U_416,U_414),U_414)
& ? [U_404] :
( ? [U_403] :
( sK68(U_418,U_416,U_414) = ordered_pair(U_404,U_403)
& in(U_403,U_416) )
& in(U_404,U_418) ) )
| ( ! [U_402] :
( ! [U_401] :
( sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(sK67(U_418,U_416,U_414),U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),sK66(U_417,U_415,U_413,U_409))
& in(sK66(U_417,U_415,U_413,U_409),U_415)
& in(sK65(U_417,U_415,U_413,U_409),U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_412,sK68(U_418,U_416,U_414))],[f_73_6]) ).
fof(f_73_8,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ( ~ in(sK68(U_418,U_416,U_414),U_414)
& ? [U_403] :
( sK68(U_418,U_416,U_414) = ordered_pair(sK69(U_418,U_416,U_414),U_403)
& in(U_403,U_416) )
& in(sK69(U_418,U_416,U_414),U_418) )
| ( ! [U_402] :
( ! [U_401] :
( sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(sK67(U_418,U_416,U_414),U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),sK66(U_417,U_415,U_413,U_409))
& in(sK66(U_417,U_415,U_413,U_409),U_415)
& in(sK65(U_417,U_415,U_413,U_409),U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_404,sK69(U_418,U_416,U_414))],[f_73_7]) ).
fof(f_73_9,plain,
( ! [U_418,U_416,U_414] :
( U_414 = cartesian_product2(U_418,U_416)
| ( ~ in(sK68(U_418,U_416,U_414),U_414)
& sK68(U_418,U_416,U_414) = ordered_pair(sK69(U_418,U_416,U_414),sK70(U_418,U_416,U_414))
& in(sK70(U_418,U_416,U_414),U_416)
& in(sK69(U_418,U_416,U_414),U_418) )
| ( ! [U_402] :
( ! [U_401] :
( sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416) )
| ~ in(U_402,U_418) )
& in(sK67(U_418,U_416,U_414),U_414) ) )
& ! [U_417,U_415,U_413] :
( ( ! [U_410] :
( in(U_410,U_413)
| ! [U_399] :
( ! [U_398] :
( U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415) )
| ~ in(U_399,U_417) ) )
& ! [U_409] :
( ( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),sK66(U_417,U_415,U_413,U_409))
& in(sK66(U_417,U_415,U_413,U_409),U_415)
& in(sK65(U_417,U_415,U_413,U_409),U_417) )
| ~ in(U_409,U_413) ) )
| U_413 != cartesian_product2(U_417,U_415) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_403,sK70(U_418,U_416,U_414))],[f_73_8]) ).
cnf(f_73_10,plain,
( in(sK65(U_417,U_415,U_413,U_409),U_417)
| ~ in(U_409,U_413)
| U_413 != cartesian_product2(U_417,U_415) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_11,plain,
( in(sK66(U_417,U_415,U_413,U_409),U_415)
| ~ in(U_409,U_413)
| U_413 != cartesian_product2(U_417,U_415) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_12,plain,
( U_409 = ordered_pair(sK65(U_417,U_415,U_413,U_409),sK66(U_417,U_415,U_413,U_409))
| ~ in(U_409,U_413)
| U_413 != cartesian_product2(U_417,U_415) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_13,plain,
( in(U_410,U_413)
| U_410 != ordered_pair(U_399,U_398)
| ~ in(U_398,U_415)
| ~ in(U_399,U_417)
| U_413 != cartesian_product2(U_417,U_415) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_14,plain,
( in(sK69(U_418,U_416,U_414),U_418)
| in(sK67(U_418,U_416,U_414),U_414)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_15,plain,
( in(sK70(U_418,U_416,U_414),U_416)
| in(sK67(U_418,U_416,U_414),U_414)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_16,plain,
( sK68(U_418,U_416,U_414) = ordered_pair(sK69(U_418,U_416,U_414),sK70(U_418,U_416,U_414))
| in(sK67(U_418,U_416,U_414),U_414)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_17,plain,
( ~ in(sK68(U_418,U_416,U_414),U_414)
| in(sK67(U_418,U_416,U_414),U_414)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_18,plain,
( in(sK69(U_418,U_416,U_414),U_418)
| sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416)
| ~ in(U_402,U_418)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_19,plain,
( in(sK70(U_418,U_416,U_414),U_416)
| sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416)
| ~ in(U_402,U_418)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_20,plain,
( sK68(U_418,U_416,U_414) = ordered_pair(sK69(U_418,U_416,U_414),sK70(U_418,U_416,U_414))
| sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416)
| ~ in(U_402,U_418)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
cnf(f_73_21,plain,
( ~ in(sK68(U_418,U_416,U_414),U_414)
| sK67(U_418,U_416,U_414) != ordered_pair(U_402,U_401)
| ~ in(U_401,U_416)
| ~ in(U_402,U_418)
| U_414 = cartesian_product2(U_418,U_416) ),
inference(clausify,[status(thm)],[f_73_9]) ).
fof(f_74_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_74_2,plain,
! [U_421] :
( ! [U_420] :
( ! [U_419] :
( ( ( below(U_421,U_420,U_419)
| join(U_421,U_420,U_419) != U_419 )
& ( join(U_421,U_420,U_419) = U_419
| ~ below(U_421,U_420,U_419) ) )
| ~ element(U_419,the_carrier(U_421)) )
| ~ element(U_420,the_carrier(U_421)) )
| ~ join_semilatt_str(U_421)
| empty_carrier(U_421) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( join(U_421,U_420,U_419) = U_419
| ~ below(U_421,U_420,U_419)
| ~ element(U_419,the_carrier(U_421))
| ~ element(U_420,the_carrier(U_421))
| ~ join_semilatt_str(U_421)
| empty_carrier(U_421) ),
inference(clausify,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( below(U_421,U_420,U_419)
| join(U_421,U_420,U_419) != U_419
| ~ element(U_419,the_carrier(U_421))
| ~ element(U_420,the_carrier(U_421))
| ~ join_semilatt_str(U_421)
| empty_carrier(U_421) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_426] :
( ( epsilon_connected(U_426)
| ? [U_425,U_424] :
( ~ in(U_424,U_425)
& U_425 != U_424
& ~ in(U_425,U_424)
& in(U_424,U_426)
& in(U_425,U_426) ) )
& ( ! [U_423,U_422] :
( in(U_422,U_423)
| U_423 = U_422
| in(U_423,U_422)
| ~ in(U_422,U_426)
| ~ in(U_423,U_426) )
| ~ epsilon_connected(U_426) ) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_428] :
( epsilon_connected(U_428)
| ? [U_425] :
( ? [U_424] :
( ~ in(U_424,U_425)
& U_425 != U_424
& ~ in(U_425,U_424)
& in(U_424,U_428) )
& in(U_425,U_428) ) )
& ! [U_427] :
( ! [U_423] :
( ! [U_422] :
( in(U_422,U_423)
| U_423 = U_422
| in(U_423,U_422)
| ~ in(U_422,U_427) )
| ~ in(U_423,U_427) )
| ~ epsilon_connected(U_427) ) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
fof(f_75_4,plain,
( ! [U_428] :
( epsilon_connected(U_428)
| ( ? [U_424] :
( ~ in(U_424,sK71(U_428))
& sK71(U_428) != U_424
& ~ in(sK71(U_428),U_424)
& in(U_424,U_428) )
& in(sK71(U_428),U_428) ) )
& ! [U_427] :
( ! [U_423] :
( ! [U_422] :
( in(U_422,U_423)
| U_423 = U_422
| in(U_423,U_422)
| ~ in(U_422,U_427) )
| ~ in(U_423,U_427) )
| ~ epsilon_connected(U_427) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_425,sK71(U_428))],[f_75_3]) ).
fof(f_75_5,plain,
( ! [U_428] :
( epsilon_connected(U_428)
| ( ~ in(sK72(U_428),sK71(U_428))
& sK71(U_428) != sK72(U_428)
& ~ in(sK71(U_428),sK72(U_428))
& in(sK72(U_428),U_428)
& in(sK71(U_428),U_428) ) )
& ! [U_427] :
( ! [U_423] :
( ! [U_422] :
( in(U_422,U_423)
| U_423 = U_422
| in(U_423,U_422)
| ~ in(U_422,U_427) )
| ~ in(U_423,U_427) )
| ~ epsilon_connected(U_427) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_424,sK72(U_428))],[f_75_4]) ).
cnf(f_75_6,plain,
( in(U_422,U_423)
| U_423 = U_422
| in(U_423,U_422)
| ~ in(U_422,U_427)
| ~ in(U_423,U_427)
| ~ epsilon_connected(U_427) ),
inference(clausify,[status(thm)],[f_75_5]) ).
cnf(f_75_7,plain,
( in(sK71(U_428),U_428)
| epsilon_connected(U_428) ),
inference(clausify,[status(thm)],[f_75_5]) ).
cnf(f_75_8,plain,
( in(sK72(U_428),U_428)
| epsilon_connected(U_428) ),
inference(clausify,[status(thm)],[f_75_5]) ).
cnf(f_75_9,plain,
( ~ in(sK71(U_428),sK72(U_428))
| epsilon_connected(U_428) ),
inference(clausify,[status(thm)],[f_75_5]) ).
cnf(f_75_10,plain,
( sK71(U_428) != sK72(U_428)
| epsilon_connected(U_428) ),
inference(clausify,[status(thm)],[f_75_5]) ).
cnf(f_75_11,plain,
( ~ in(sK72(U_428),sK71(U_428))
| epsilon_connected(U_428) ),
inference(clausify,[status(thm)],[f_75_5]) ).
fof(f_76_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_76_2,plain,
! [U_429] :
( cast_as_carrier_subset(U_429) = the_carrier(U_429)
| ~ one_sorted_str(U_429) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( cast_as_carrier_subset(U_429) = the_carrier(U_429)
| ~ one_sorted_str(U_429) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_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_77_2,plain,
! [U_435] :
( ! [U_434] :
( ( ( subset(U_435,U_434)
| ? [U_433,U_432] :
( ~ in(ordered_pair(U_433,U_432),U_434)
& in(ordered_pair(U_433,U_432),U_435) ) )
& ( ! [U_431,U_430] :
( in(ordered_pair(U_431,U_430),U_434)
| ~ in(ordered_pair(U_431,U_430),U_435) )
| ~ subset(U_435,U_434) ) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_435] :
( ! [U_434] :
( ( ( subset(U_435,U_434)
| ? [U_432] :
( ~ in(ordered_pair(sK73(U_435,U_434),U_432),U_434)
& in(ordered_pair(sK73(U_435,U_434),U_432),U_435) ) )
& ( ! [U_431,U_430] :
( in(ordered_pair(U_431,U_430),U_434)
| ~ in(ordered_pair(U_431,U_430),U_435) )
| ~ subset(U_435,U_434) ) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_433,sK73(U_435,U_434))],[f_77_2]) ).
fof(f_77_4,plain,
! [U_435] :
( ! [U_434] :
( ( ( subset(U_435,U_434)
| ( ~ in(ordered_pair(sK73(U_435,U_434),sK74(U_435,U_434)),U_434)
& in(ordered_pair(sK73(U_435,U_434),sK74(U_435,U_434)),U_435) ) )
& ( ! [U_431,U_430] :
( in(ordered_pair(U_431,U_430),U_434)
| ~ in(ordered_pair(U_431,U_430),U_435) )
| ~ subset(U_435,U_434) ) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_432,sK74(U_435,U_434))],[f_77_3]) ).
cnf(f_77_5,plain,
( in(ordered_pair(U_431,U_430),U_434)
| ~ in(ordered_pair(U_431,U_430),U_435)
| ~ subset(U_435,U_434)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_6,plain,
( in(ordered_pair(sK73(U_435,U_434),sK74(U_435,U_434)),U_435)
| subset(U_435,U_434)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_7,plain,
( ~ in(ordered_pair(sK73(U_435,U_434),sK74(U_435,U_434)),U_434)
| subset(U_435,U_434)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_77_4]) ).
fof(f_78_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_78_2,plain,
! [U_439,U_438] :
( ( subset(U_439,U_438)
| ? [U_437] :
( ~ in(U_437,U_438)
& in(U_437,U_439) ) )
& ( ! [U_436] :
( in(U_436,U_438)
| ~ in(U_436,U_439) )
| ~ subset(U_439,U_438) ) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_443,U_441] :
( subset(U_443,U_441)
| ? [U_437] :
( ~ in(U_437,U_441)
& in(U_437,U_443) ) )
& ! [U_442,U_440] :
( ! [U_436] :
( in(U_436,U_440)
| ~ in(U_436,U_442) )
| ~ subset(U_442,U_440) ) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
( ! [U_443,U_441] :
( subset(U_443,U_441)
| ( ~ in(sK75(U_443,U_441),U_441)
& in(sK75(U_443,U_441),U_443) ) )
& ! [U_442,U_440] :
( ! [U_436] :
( in(U_436,U_440)
| ~ in(U_436,U_442) )
| ~ subset(U_442,U_440) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_437,sK75(U_443,U_441))],[f_78_3]) ).
cnf(f_78_5,plain,
( in(U_436,U_440)
| ~ in(U_436,U_442)
| ~ subset(U_442,U_440) ),
inference(clausify,[status(thm)],[f_78_4]) ).
cnf(f_78_6,plain,
( in(sK75(U_443,U_441),U_443)
| subset(U_443,U_441) ),
inference(clausify,[status(thm)],[f_78_4]) ).
cnf(f_78_7,plain,
( ~ in(sK75(U_443,U_441),U_441)
| subset(U_443,U_441) ),
inference(clausify,[status(thm)],[f_78_4]) ).
fof(f_79_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_79_2,plain,
! [U_449] :
( ! [U_448] :
( ( is_well_founded_in(U_449,U_448)
| ? [U_447] :
( ! [U_446] :
( ~ disjoint(fiber(U_449,U_446),U_447)
| ~ in(U_446,U_447) )
& U_447 != empty_set
& subset(U_447,U_448) ) )
& ( ! [U_445] :
( ? [U_444] :
( disjoint(fiber(U_449,U_444),U_445)
& in(U_444,U_445) )
| U_445 = empty_set
| ~ subset(U_445,U_448) )
| ~ is_well_founded_in(U_449,U_448) ) )
| ~ relation(U_449) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_449] :
( ( ! [U_451] :
( is_well_founded_in(U_449,U_451)
| ? [U_447] :
( ! [U_446] :
( ~ disjoint(fiber(U_449,U_446),U_447)
| ~ in(U_446,U_447) )
& U_447 != empty_set
& subset(U_447,U_451) ) )
& ! [U_450] :
( ! [U_445] :
( ? [U_444] :
( disjoint(fiber(U_449,U_444),U_445)
& in(U_444,U_445) )
| U_445 = empty_set
| ~ subset(U_445,U_450) )
| ~ is_well_founded_in(U_449,U_450) ) )
| ~ relation(U_449) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
fof(f_79_4,plain,
! [U_449] :
( ( ! [U_451] :
( is_well_founded_in(U_449,U_451)
| ? [U_447] :
( ! [U_446] :
( ~ disjoint(fiber(U_449,U_446),U_447)
| ~ in(U_446,U_447) )
& U_447 != empty_set
& subset(U_447,U_451) ) )
& ! [U_450] :
( ! [U_445] :
( ( disjoint(fiber(U_449,sK76(U_449,U_450,U_445)),U_445)
& in(sK76(U_449,U_450,U_445),U_445) )
| U_445 = empty_set
| ~ subset(U_445,U_450) )
| ~ is_well_founded_in(U_449,U_450) ) )
| ~ relation(U_449) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_444,sK76(U_449,U_450,U_445))],[f_79_3]) ).
fof(f_79_5,plain,
! [U_449] :
( ( ! [U_451] :
( is_well_founded_in(U_449,U_451)
| ( ! [U_446] :
( ~ disjoint(fiber(U_449,U_446),sK77(U_449,U_451))
| ~ in(U_446,sK77(U_449,U_451)) )
& sK77(U_449,U_451) != empty_set
& subset(sK77(U_449,U_451),U_451) ) )
& ! [U_450] :
( ! [U_445] :
( ( disjoint(fiber(U_449,sK76(U_449,U_450,U_445)),U_445)
& in(sK76(U_449,U_450,U_445),U_445) )
| U_445 = empty_set
| ~ subset(U_445,U_450) )
| ~ is_well_founded_in(U_449,U_450) ) )
| ~ relation(U_449) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_447,sK77(U_449,U_451))],[f_79_4]) ).
cnf(f_79_6,plain,
( in(sK76(U_449,U_450,U_445),U_445)
| U_445 = empty_set
| ~ subset(U_445,U_450)
| ~ is_well_founded_in(U_449,U_450)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_7,plain,
( disjoint(fiber(U_449,sK76(U_449,U_450,U_445)),U_445)
| U_445 = empty_set
| ~ subset(U_445,U_450)
| ~ is_well_founded_in(U_449,U_450)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_8,plain,
( subset(sK77(U_449,U_451),U_451)
| is_well_founded_in(U_449,U_451)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_9,plain,
( sK77(U_449,U_451) != empty_set
| is_well_founded_in(U_449,U_451)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_10,plain,
( ~ disjoint(fiber(U_449,U_446),sK77(U_449,U_451))
| ~ in(U_446,sK77(U_449,U_451))
| is_well_founded_in(U_449,U_451)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_79_5]) ).
fof(f_80_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_80_2,plain,
! [U_456,U_455,U_454] :
( ( U_454 = set_intersection2(U_456,U_455)
| ? [U_453] :
( ( ~ in(U_453,U_454)
& in(U_453,U_455)
& in(U_453,U_456) )
| ( ( ~ in(U_453,U_455)
| ~ in(U_453,U_456) )
& in(U_453,U_454) ) ) )
& ( ! [U_452] :
( ( in(U_452,U_454)
| ~ in(U_452,U_455)
| ~ in(U_452,U_456) )
& ( ( in(U_452,U_455)
& in(U_452,U_456) )
| ~ in(U_452,U_454) ) )
| U_454 != set_intersection2(U_456,U_455) ) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_466,U_464,U_462] :
( U_462 = set_intersection2(U_466,U_464)
| ? [U_460] :
( ~ in(U_460,U_462)
& in(U_460,U_464)
& in(U_460,U_466) )
| ? [U_459] :
( ( ~ in(U_459,U_464)
| ~ in(U_459,U_466) )
& in(U_459,U_462) ) )
& ! [U_465,U_463,U_461] :
( ( ! [U_458] :
( in(U_458,U_461)
| ~ in(U_458,U_463)
| ~ in(U_458,U_465) )
& ! [U_457] :
( ( in(U_457,U_463)
& in(U_457,U_465) )
| ~ in(U_457,U_461) ) )
| U_461 != set_intersection2(U_465,U_463) ) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
fof(f_80_4,plain,
( ! [U_466,U_464,U_462] :
( U_462 = set_intersection2(U_466,U_464)
| ? [U_460] :
( ~ in(U_460,U_462)
& in(U_460,U_464)
& in(U_460,U_466) )
| ( ( ~ in(sK78(U_466,U_464,U_462),U_464)
| ~ in(sK78(U_466,U_464,U_462),U_466) )
& in(sK78(U_466,U_464,U_462),U_462) ) )
& ! [U_465,U_463,U_461] :
( ( ! [U_458] :
( in(U_458,U_461)
| ~ in(U_458,U_463)
| ~ in(U_458,U_465) )
& ! [U_457] :
( ( in(U_457,U_463)
& in(U_457,U_465) )
| ~ in(U_457,U_461) ) )
| U_461 != set_intersection2(U_465,U_463) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_459,sK78(U_466,U_464,U_462))],[f_80_3]) ).
fof(f_80_5,plain,
( ! [U_466,U_464,U_462] :
( U_462 = set_intersection2(U_466,U_464)
| ( ~ in(sK79(U_466,U_464,U_462),U_462)
& in(sK79(U_466,U_464,U_462),U_464)
& in(sK79(U_466,U_464,U_462),U_466) )
| ( ( ~ in(sK78(U_466,U_464,U_462),U_464)
| ~ in(sK78(U_466,U_464,U_462),U_466) )
& in(sK78(U_466,U_464,U_462),U_462) ) )
& ! [U_465,U_463,U_461] :
( ( ! [U_458] :
( in(U_458,U_461)
| ~ in(U_458,U_463)
| ~ in(U_458,U_465) )
& ! [U_457] :
( ( in(U_457,U_463)
& in(U_457,U_465) )
| ~ in(U_457,U_461) ) )
| U_461 != set_intersection2(U_465,U_463) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_460,sK79(U_466,U_464,U_462))],[f_80_4]) ).
cnf(f_80_6,plain,
( in(U_457,U_465)
| ~ in(U_457,U_461)
| U_461 != set_intersection2(U_465,U_463) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_7,plain,
( in(U_457,U_463)
| ~ in(U_457,U_461)
| U_461 != set_intersection2(U_465,U_463) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_8,plain,
( in(U_458,U_461)
| ~ in(U_458,U_463)
| ~ in(U_458,U_465)
| U_461 != set_intersection2(U_465,U_463) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_9,plain,
( in(sK79(U_466,U_464,U_462),U_466)
| in(sK78(U_466,U_464,U_462),U_462)
| U_462 = set_intersection2(U_466,U_464) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_10,plain,
( in(sK79(U_466,U_464,U_462),U_464)
| in(sK78(U_466,U_464,U_462),U_462)
| U_462 = set_intersection2(U_466,U_464) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_11,plain,
( ~ in(sK79(U_466,U_464,U_462),U_462)
| in(sK78(U_466,U_464,U_462),U_462)
| U_462 = set_intersection2(U_466,U_464) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_12,plain,
( in(sK79(U_466,U_464,U_462),U_466)
| ~ in(sK78(U_466,U_464,U_462),U_464)
| ~ in(sK78(U_466,U_464,U_462),U_466)
| U_462 = set_intersection2(U_466,U_464) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_13,plain,
( in(sK79(U_466,U_464,U_462),U_464)
| ~ in(sK78(U_466,U_464,U_462),U_464)
| ~ in(sK78(U_466,U_464,U_462),U_466)
| U_462 = set_intersection2(U_466,U_464) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_14,plain,
( ~ in(sK79(U_466,U_464,U_462),U_462)
| ~ in(sK78(U_466,U_464,U_462),U_464)
| ~ in(sK78(U_466,U_464,U_462),U_466)
| U_462 = set_intersection2(U_466,U_464) ),
inference(clausify,[status(thm)],[f_80_5]) ).
fof(f_81_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_81_2,plain,
! [U_469] :
( ! [U_468,U_467] :
( ( ( ( U_467 = apply(U_469,U_468)
| U_467 != empty_set )
& ( U_467 = empty_set
| U_467 != apply(U_469,U_468) ) )
| in(U_468,relation_dom(U_469)) )
& ( ( ( U_467 = apply(U_469,U_468)
| ~ in(ordered_pair(U_468,U_467),U_469) )
& ( in(ordered_pair(U_468,U_467),U_469)
| U_467 != apply(U_469,U_468) ) )
| ~ in(U_468,relation_dom(U_469)) ) )
| ~ function(U_469)
| ~ relation(U_469) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_469] :
( ( ! [U_477] :
( ( ! [U_475] :
( U_475 = apply(U_469,U_477)
| U_475 != empty_set )
& ! [U_474] :
( U_474 = empty_set
| U_474 != apply(U_469,U_477) ) )
| in(U_477,relation_dom(U_469)) )
& ! [U_476] :
( ( ! [U_473] :
( U_473 = apply(U_469,U_476)
| ~ in(ordered_pair(U_476,U_473),U_469) )
& ! [U_472] :
( in(ordered_pair(U_476,U_472),U_469)
| U_472 != apply(U_469,U_476) ) )
| ~ in(U_476,relation_dom(U_469)) ) )
| ~ function(U_469)
| ~ relation(U_469) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( in(ordered_pair(U_476,U_472),U_469)
| U_472 != apply(U_469,U_476)
| ~ in(U_476,relation_dom(U_469))
| ~ function(U_469)
| ~ relation(U_469) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_5,plain,
( U_473 = apply(U_469,U_476)
| ~ in(ordered_pair(U_476,U_473),U_469)
| ~ in(U_476,relation_dom(U_469))
| ~ function(U_469)
| ~ relation(U_469) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_6,plain,
( U_474 = empty_set
| U_474 != apply(U_469,U_477)
| in(U_477,relation_dom(U_469))
| ~ function(U_469)
| ~ relation(U_469) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_7,plain,
( U_475 = apply(U_469,U_477)
| U_475 != empty_set
| in(U_477,relation_dom(U_469))
| ~ function(U_469)
| ~ relation(U_469) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_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_82_2,plain,
! [U_478] :
( ( ordinal(U_478)
| ~ epsilon_connected(U_478)
| ~ epsilon_transitive(U_478) )
& ( ( epsilon_connected(U_478)
& epsilon_transitive(U_478) )
| ~ ordinal(U_478) ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_480] :
( ordinal(U_480)
| ~ epsilon_connected(U_480)
| ~ epsilon_transitive(U_480) )
& ! [U_479] :
( ( epsilon_connected(U_479)
& epsilon_transitive(U_479) )
| ~ ordinal(U_479) ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( epsilon_transitive(U_479)
| ~ ordinal(U_479) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_5,plain,
( epsilon_connected(U_479)
| ~ ordinal(U_479) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_6,plain,
( ordinal(U_480)
| ~ epsilon_connected(U_480)
| ~ epsilon_transitive(U_480) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_488] :
( ! [U_487] :
( ( U_487 = relation_dom(U_488)
| ? [U_486] :
( ( ~ in(U_486,U_487)
& ? [U_485] : in(ordered_pair(U_486,U_485),U_488) )
| ( ! [U_484] : ~ in(ordered_pair(U_486,U_484),U_488)
& in(U_486,U_487) ) ) )
& ( ! [U_483] :
( ( in(U_483,U_487)
| ! [U_482] : ~ in(ordered_pair(U_483,U_482),U_488) )
& ( ? [U_481] : in(ordered_pair(U_483,U_481),U_488)
| ~ in(U_483,U_487) ) )
| U_487 != relation_dom(U_488) ) )
| ~ relation(U_488) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_488] :
( ( ! [U_494] :
( U_494 = relation_dom(U_488)
| ? [U_492] :
( ~ in(U_492,U_494)
& ? [U_485] : in(ordered_pair(U_492,U_485),U_488) )
| ? [U_491] :
( ! [U_484] : ~ in(ordered_pair(U_491,U_484),U_488)
& in(U_491,U_494) ) )
& ! [U_493] :
( ( ! [U_490] :
( in(U_490,U_493)
| ! [U_482] : ~ in(ordered_pair(U_490,U_482),U_488) )
& ! [U_489] :
( ? [U_481] : in(ordered_pair(U_489,U_481),U_488)
| ~ in(U_489,U_493) ) )
| U_493 != relation_dom(U_488) ) )
| ~ relation(U_488) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
fof(f_83_4,plain,
! [U_488] :
( ( ! [U_494] :
( U_494 = relation_dom(U_488)
| ? [U_492] :
( ~ in(U_492,U_494)
& ? [U_485] : in(ordered_pair(U_492,U_485),U_488) )
| ? [U_491] :
( ! [U_484] : ~ in(ordered_pair(U_491,U_484),U_488)
& in(U_491,U_494) ) )
& ! [U_493] :
( ( ! [U_490] :
( in(U_490,U_493)
| ! [U_482] : ~ in(ordered_pair(U_490,U_482),U_488) )
& ! [U_489] :
( in(ordered_pair(U_489,sK80(U_488,U_493,U_489)),U_488)
| ~ in(U_489,U_493) ) )
| U_493 != relation_dom(U_488) ) )
| ~ relation(U_488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_481,sK80(U_488,U_493,U_489))],[f_83_3]) ).
fof(f_83_5,plain,
! [U_488] :
( ( ! [U_494] :
( U_494 = relation_dom(U_488)
| ? [U_492] :
( ~ in(U_492,U_494)
& ? [U_485] : in(ordered_pair(U_492,U_485),U_488) )
| ( ! [U_484] : ~ in(ordered_pair(sK81(U_488,U_494),U_484),U_488)
& in(sK81(U_488,U_494),U_494) ) )
& ! [U_493] :
( ( ! [U_490] :
( in(U_490,U_493)
| ! [U_482] : ~ in(ordered_pair(U_490,U_482),U_488) )
& ! [U_489] :
( in(ordered_pair(U_489,sK80(U_488,U_493,U_489)),U_488)
| ~ in(U_489,U_493) ) )
| U_493 != relation_dom(U_488) ) )
| ~ relation(U_488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_491,sK81(U_488,U_494))],[f_83_4]) ).
fof(f_83_6,plain,
! [U_488] :
( ( ! [U_494] :
( U_494 = relation_dom(U_488)
| ( ~ in(sK82(U_488,U_494),U_494)
& ? [U_485] : in(ordered_pair(sK82(U_488,U_494),U_485),U_488) )
| ( ! [U_484] : ~ in(ordered_pair(sK81(U_488,U_494),U_484),U_488)
& in(sK81(U_488,U_494),U_494) ) )
& ! [U_493] :
( ( ! [U_490] :
( in(U_490,U_493)
| ! [U_482] : ~ in(ordered_pair(U_490,U_482),U_488) )
& ! [U_489] :
( in(ordered_pair(U_489,sK80(U_488,U_493,U_489)),U_488)
| ~ in(U_489,U_493) ) )
| U_493 != relation_dom(U_488) ) )
| ~ relation(U_488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_492,sK82(U_488,U_494))],[f_83_5]) ).
fof(f_83_7,plain,
! [U_488] :
( ( ! [U_494] :
( U_494 = relation_dom(U_488)
| ( ~ in(sK82(U_488,U_494),U_494)
& in(ordered_pair(sK82(U_488,U_494),sK83(U_488,U_494)),U_488) )
| ( ! [U_484] : ~ in(ordered_pair(sK81(U_488,U_494),U_484),U_488)
& in(sK81(U_488,U_494),U_494) ) )
& ! [U_493] :
( ( ! [U_490] :
( in(U_490,U_493)
| ! [U_482] : ~ in(ordered_pair(U_490,U_482),U_488) )
& ! [U_489] :
( in(ordered_pair(U_489,sK80(U_488,U_493,U_489)),U_488)
| ~ in(U_489,U_493) ) )
| U_493 != relation_dom(U_488) ) )
| ~ relation(U_488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_485,sK83(U_488,U_494))],[f_83_6]) ).
cnf(f_83_8,plain,
( in(ordered_pair(U_489,sK80(U_488,U_493,U_489)),U_488)
| ~ in(U_489,U_493)
| U_493 != relation_dom(U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_83_7]) ).
cnf(f_83_9,plain,
( in(U_490,U_493)
| ~ in(ordered_pair(U_490,U_482),U_488)
| U_493 != relation_dom(U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_83_7]) ).
cnf(f_83_10,plain,
( in(ordered_pair(sK82(U_488,U_494),sK83(U_488,U_494)),U_488)
| in(sK81(U_488,U_494),U_494)
| U_494 = relation_dom(U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_83_7]) ).
cnf(f_83_11,plain,
( ~ in(sK82(U_488,U_494),U_494)
| in(sK81(U_488,U_494),U_494)
| U_494 = relation_dom(U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_83_7]) ).
cnf(f_83_12,plain,
( in(ordered_pair(sK82(U_488,U_494),sK83(U_488,U_494)),U_488)
| ~ in(ordered_pair(sK81(U_488,U_494),U_484),U_488)
| U_494 = relation_dom(U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_83_7]) ).
cnf(f_83_13,plain,
( ~ in(sK82(U_488,U_494),U_494)
| ~ in(ordered_pair(sK81(U_488,U_494),U_484),U_488)
| U_494 = relation_dom(U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_83_7]) ).
fof(f_84_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_84_2,plain,
! [U_500] :
( ! [U_499] :
( ( is_antisymmetric_in(U_500,U_499)
| ? [U_498,U_497] :
( U_498 != U_497
& in(ordered_pair(U_497,U_498),U_500)
& in(ordered_pair(U_498,U_497),U_500)
& in(U_497,U_499)
& in(U_498,U_499) ) )
& ( ! [U_496,U_495] :
( U_496 = U_495
| ~ in(ordered_pair(U_495,U_496),U_500)
| ~ in(ordered_pair(U_496,U_495),U_500)
| ~ in(U_495,U_499)
| ~ in(U_496,U_499) )
| ~ is_antisymmetric_in(U_500,U_499) ) )
| ~ relation(U_500) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_500] :
( ( ! [U_502] :
( is_antisymmetric_in(U_500,U_502)
| ? [U_498,U_497] :
( U_498 != U_497
& in(ordered_pair(U_497,U_498),U_500)
& in(ordered_pair(U_498,U_497),U_500)
& in(U_497,U_502)
& in(U_498,U_502) ) )
& ! [U_501] :
( ! [U_496,U_495] :
( U_496 = U_495
| ~ in(ordered_pair(U_495,U_496),U_500)
| ~ in(ordered_pair(U_496,U_495),U_500)
| ~ in(U_495,U_501)
| ~ in(U_496,U_501) )
| ~ is_antisymmetric_in(U_500,U_501) ) )
| ~ relation(U_500) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
fof(f_84_4,plain,
! [U_500] :
( ( ! [U_502] :
( is_antisymmetric_in(U_500,U_502)
| ? [U_497] :
( sK84(U_500,U_502) != U_497
& in(ordered_pair(U_497,sK84(U_500,U_502)),U_500)
& in(ordered_pair(sK84(U_500,U_502),U_497),U_500)
& in(U_497,U_502)
& in(sK84(U_500,U_502),U_502) ) )
& ! [U_501] :
( ! [U_496,U_495] :
( U_496 = U_495
| ~ in(ordered_pair(U_495,U_496),U_500)
| ~ in(ordered_pair(U_496,U_495),U_500)
| ~ in(U_495,U_501)
| ~ in(U_496,U_501) )
| ~ is_antisymmetric_in(U_500,U_501) ) )
| ~ relation(U_500) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_498,sK84(U_500,U_502))],[f_84_3]) ).
fof(f_84_5,plain,
! [U_500] :
( ( ! [U_502] :
( is_antisymmetric_in(U_500,U_502)
| ( sK84(U_500,U_502) != sK85(U_500,U_502)
& in(ordered_pair(sK85(U_500,U_502),sK84(U_500,U_502)),U_500)
& in(ordered_pair(sK84(U_500,U_502),sK85(U_500,U_502)),U_500)
& in(sK85(U_500,U_502),U_502)
& in(sK84(U_500,U_502),U_502) ) )
& ! [U_501] :
( ! [U_496,U_495] :
( U_496 = U_495
| ~ in(ordered_pair(U_495,U_496),U_500)
| ~ in(ordered_pair(U_496,U_495),U_500)
| ~ in(U_495,U_501)
| ~ in(U_496,U_501) )
| ~ is_antisymmetric_in(U_500,U_501) ) )
| ~ relation(U_500) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_497,sK85(U_500,U_502))],[f_84_4]) ).
cnf(f_84_6,plain,
( U_496 = U_495
| ~ in(ordered_pair(U_495,U_496),U_500)
| ~ in(ordered_pair(U_496,U_495),U_500)
| ~ in(U_495,U_501)
| ~ in(U_496,U_501)
| ~ is_antisymmetric_in(U_500,U_501)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_84_5]) ).
cnf(f_84_7,plain,
( in(sK84(U_500,U_502),U_502)
| is_antisymmetric_in(U_500,U_502)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_84_5]) ).
cnf(f_84_8,plain,
( in(sK85(U_500,U_502),U_502)
| is_antisymmetric_in(U_500,U_502)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_84_5]) ).
cnf(f_84_9,plain,
( in(ordered_pair(sK84(U_500,U_502),sK85(U_500,U_502)),U_500)
| is_antisymmetric_in(U_500,U_502)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_84_5]) ).
cnf(f_84_10,plain,
( in(ordered_pair(sK85(U_500,U_502),sK84(U_500,U_502)),U_500)
| is_antisymmetric_in(U_500,U_502)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_84_5]) ).
cnf(f_84_11,plain,
( sK84(U_500,U_502) != sK85(U_500,U_502)
| is_antisymmetric_in(U_500,U_502)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_84_5]) ).
fof(f_85_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_85_2,plain,
! [U_503] : cast_to_subset(U_503) = U_503,
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
cast_to_subset(U_503) = U_503,
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_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_86_2,plain,
! [U_511,U_510] :
( ( U_510 = union(U_511)
| ? [U_509] :
( ( ~ in(U_509,U_510)
& ? [U_508] :
( in(U_508,U_511)
& in(U_509,U_508) ) )
| ( ! [U_507] :
( ~ in(U_507,U_511)
| ~ in(U_509,U_507) )
& in(U_509,U_510) ) ) )
& ( ! [U_506] :
( ( in(U_506,U_510)
| ! [U_505] :
( ~ in(U_505,U_511)
| ~ in(U_506,U_505) ) )
& ( ? [U_504] :
( in(U_504,U_511)
& in(U_506,U_504) )
| ~ in(U_506,U_510) ) )
| U_510 != union(U_511) ) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
( ! [U_519,U_517] :
( U_517 = union(U_519)
| ? [U_515] :
( ~ in(U_515,U_517)
& ? [U_508] :
( in(U_508,U_519)
& in(U_515,U_508) ) )
| ? [U_514] :
( ! [U_507] :
( ~ in(U_507,U_519)
| ~ in(U_514,U_507) )
& in(U_514,U_517) ) )
& ! [U_518,U_516] :
( ( ! [U_513] :
( in(U_513,U_516)
| ! [U_505] :
( ~ in(U_505,U_518)
| ~ in(U_513,U_505) ) )
& ! [U_512] :
( ? [U_504] :
( in(U_504,U_518)
& in(U_512,U_504) )
| ~ in(U_512,U_516) ) )
| U_516 != union(U_518) ) ),
inference(miniscope,[status(thm)],[f_86_2]) ).
fof(f_86_4,plain,
( ! [U_519,U_517] :
( U_517 = union(U_519)
| ? [U_515] :
( ~ in(U_515,U_517)
& ? [U_508] :
( in(U_508,U_519)
& in(U_515,U_508) ) )
| ? [U_514] :
( ! [U_507] :
( ~ in(U_507,U_519)
| ~ in(U_514,U_507) )
& in(U_514,U_517) ) )
& ! [U_518,U_516] :
( ( ! [U_513] :
( in(U_513,U_516)
| ! [U_505] :
( ~ in(U_505,U_518)
| ~ in(U_513,U_505) ) )
& ! [U_512] :
( ( in(sK86(U_518,U_516,U_512),U_518)
& in(U_512,sK86(U_518,U_516,U_512)) )
| ~ in(U_512,U_516) ) )
| U_516 != union(U_518) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_504,sK86(U_518,U_516,U_512))],[f_86_3]) ).
fof(f_86_5,plain,
( ! [U_519,U_517] :
( U_517 = union(U_519)
| ? [U_515] :
( ~ in(U_515,U_517)
& ? [U_508] :
( in(U_508,U_519)
& in(U_515,U_508) ) )
| ( ! [U_507] :
( ~ in(U_507,U_519)
| ~ in(sK87(U_519,U_517),U_507) )
& in(sK87(U_519,U_517),U_517) ) )
& ! [U_518,U_516] :
( ( ! [U_513] :
( in(U_513,U_516)
| ! [U_505] :
( ~ in(U_505,U_518)
| ~ in(U_513,U_505) ) )
& ! [U_512] :
( ( in(sK86(U_518,U_516,U_512),U_518)
& in(U_512,sK86(U_518,U_516,U_512)) )
| ~ in(U_512,U_516) ) )
| U_516 != union(U_518) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_514,sK87(U_519,U_517))],[f_86_4]) ).
fof(f_86_6,plain,
( ! [U_519,U_517] :
( U_517 = union(U_519)
| ( ~ in(sK88(U_519,U_517),U_517)
& ? [U_508] :
( in(U_508,U_519)
& in(sK88(U_519,U_517),U_508) ) )
| ( ! [U_507] :
( ~ in(U_507,U_519)
| ~ in(sK87(U_519,U_517),U_507) )
& in(sK87(U_519,U_517),U_517) ) )
& ! [U_518,U_516] :
( ( ! [U_513] :
( in(U_513,U_516)
| ! [U_505] :
( ~ in(U_505,U_518)
| ~ in(U_513,U_505) ) )
& ! [U_512] :
( ( in(sK86(U_518,U_516,U_512),U_518)
& in(U_512,sK86(U_518,U_516,U_512)) )
| ~ in(U_512,U_516) ) )
| U_516 != union(U_518) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_515,sK88(U_519,U_517))],[f_86_5]) ).
fof(f_86_7,plain,
( ! [U_519,U_517] :
( U_517 = union(U_519)
| ( ~ in(sK88(U_519,U_517),U_517)
& in(sK89(U_519,U_517),U_519)
& in(sK88(U_519,U_517),sK89(U_519,U_517)) )
| ( ! [U_507] :
( ~ in(U_507,U_519)
| ~ in(sK87(U_519,U_517),U_507) )
& in(sK87(U_519,U_517),U_517) ) )
& ! [U_518,U_516] :
( ( ! [U_513] :
( in(U_513,U_516)
| ! [U_505] :
( ~ in(U_505,U_518)
| ~ in(U_513,U_505) ) )
& ! [U_512] :
( ( in(sK86(U_518,U_516,U_512),U_518)
& in(U_512,sK86(U_518,U_516,U_512)) )
| ~ in(U_512,U_516) ) )
| U_516 != union(U_518) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_508,sK89(U_519,U_517))],[f_86_6]) ).
cnf(f_86_8,plain,
( in(U_512,sK86(U_518,U_516,U_512))
| ~ in(U_512,U_516)
| U_516 != union(U_518) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_9,plain,
( in(sK86(U_518,U_516,U_512),U_518)
| ~ in(U_512,U_516)
| U_516 != union(U_518) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_10,plain,
( in(U_513,U_516)
| ~ in(U_505,U_518)
| ~ in(U_513,U_505)
| U_516 != union(U_518) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_11,plain,
( in(sK88(U_519,U_517),sK89(U_519,U_517))
| in(sK87(U_519,U_517),U_517)
| U_517 = union(U_519) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_12,plain,
( in(sK89(U_519,U_517),U_519)
| in(sK87(U_519,U_517),U_517)
| U_517 = union(U_519) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_13,plain,
( ~ in(sK88(U_519,U_517),U_517)
| in(sK87(U_519,U_517),U_517)
| U_517 = union(U_519) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_14,plain,
( in(sK88(U_519,U_517),sK89(U_519,U_517))
| ~ in(U_507,U_519)
| ~ in(sK87(U_519,U_517),U_507)
| U_517 = union(U_519) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_15,plain,
( in(sK89(U_519,U_517),U_519)
| ~ in(U_507,U_519)
| ~ in(sK87(U_519,U_517),U_507)
| U_517 = union(U_519) ),
inference(clausify,[status(thm)],[f_86_7]) ).
cnf(f_86_16,plain,
( ~ in(sK88(U_519,U_517),U_517)
| ~ in(U_507,U_519)
| ~ in(sK87(U_519,U_517),U_507)
| U_517 = union(U_519) ),
inference(clausify,[status(thm)],[f_86_7]) ).
fof(f_87_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_87_2,plain,
! [U_520] :
( ( ( well_ordering(U_520)
| ~ well_founded_relation(U_520)
| ~ connected(U_520)
| ~ antisymmetric(U_520)
| ~ transitive(U_520)
| ~ reflexive(U_520) )
& ( ( well_founded_relation(U_520)
& connected(U_520)
& antisymmetric(U_520)
& transitive(U_520)
& reflexive(U_520) )
| ~ well_ordering(U_520) ) )
| ~ relation(U_520) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( reflexive(U_520)
| ~ well_ordering(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_87_2]) ).
cnf(f_87_4,plain,
( transitive(U_520)
| ~ well_ordering(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_87_2]) ).
cnf(f_87_5,plain,
( antisymmetric(U_520)
| ~ well_ordering(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_87_2]) ).
cnf(f_87_6,plain,
( connected(U_520)
| ~ well_ordering(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_87_2]) ).
cnf(f_87_7,plain,
( well_founded_relation(U_520)
| ~ well_ordering(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_87_2]) ).
cnf(f_87_8,plain,
( well_ordering(U_520)
| ~ well_founded_relation(U_520)
| ~ connected(U_520)
| ~ antisymmetric(U_520)
| ~ transitive(U_520)
| ~ reflexive(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_88_2,plain,
! [U_524,U_523] :
( ( equipotent(U_524,U_523)
| ! [U_522] :
( relation_rng(U_522) != U_523
| relation_dom(U_522) != U_524
| ~ one_to_one(U_522)
| ~ function(U_522)
| ~ relation(U_522) ) )
& ( ? [U_521] :
( relation_rng(U_521) = U_523
& relation_dom(U_521) = U_524
& one_to_one(U_521)
& function(U_521)
& relation(U_521) )
| ~ equipotent(U_524,U_523) ) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
( ! [U_528,U_526] :
( equipotent(U_528,U_526)
| ! [U_522] :
( relation_rng(U_522) != U_526
| relation_dom(U_522) != U_528
| ~ one_to_one(U_522)
| ~ function(U_522)
| ~ relation(U_522) ) )
& ! [U_527,U_525] :
( ? [U_521] :
( relation_rng(U_521) = U_525
& relation_dom(U_521) = U_527
& one_to_one(U_521)
& function(U_521)
& relation(U_521) )
| ~ equipotent(U_527,U_525) ) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
fof(f_88_4,plain,
( ! [U_528,U_526] :
( equipotent(U_528,U_526)
| ! [U_522] :
( relation_rng(U_522) != U_526
| relation_dom(U_522) != U_528
| ~ one_to_one(U_522)
| ~ function(U_522)
| ~ relation(U_522) ) )
& ! [U_527,U_525] :
( ( relation_rng(sK90(U_527,U_525)) = U_525
& relation_dom(sK90(U_527,U_525)) = U_527
& one_to_one(sK90(U_527,U_525))
& function(sK90(U_527,U_525))
& relation(sK90(U_527,U_525)) )
| ~ equipotent(U_527,U_525) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_521,sK90(U_527,U_525))],[f_88_3]) ).
cnf(f_88_5,plain,
( relation(sK90(U_527,U_525))
| ~ equipotent(U_527,U_525) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_88_6,plain,
( function(sK90(U_527,U_525))
| ~ equipotent(U_527,U_525) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_88_7,plain,
( one_to_one(sK90(U_527,U_525))
| ~ equipotent(U_527,U_525) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_88_8,plain,
( relation_dom(sK90(U_527,U_525)) = U_527
| ~ equipotent(U_527,U_525) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_88_9,plain,
( relation_rng(sK90(U_527,U_525)) = U_525
| ~ equipotent(U_527,U_525) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_88_10,plain,
( equipotent(U_528,U_526)
| relation_rng(U_522) != U_526
| relation_dom(U_522) != U_528
| ~ one_to_one(U_522)
| ~ function(U_522)
| ~ relation(U_522) ),
inference(clausify,[status(thm)],[f_88_4]) ).
fof(f_89_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_89_2,plain,
! [U_533,U_532,U_531] :
( ( U_531 = set_difference(U_533,U_532)
| ? [U_530] :
( ( ~ in(U_530,U_531)
& ~ in(U_530,U_532)
& in(U_530,U_533) )
| ( ( in(U_530,U_532)
| ~ in(U_530,U_533) )
& in(U_530,U_531) ) ) )
& ( ! [U_529] :
( ( in(U_529,U_531)
| in(U_529,U_532)
| ~ in(U_529,U_533) )
& ( ( ~ in(U_529,U_532)
& in(U_529,U_533) )
| ~ in(U_529,U_531) ) )
| U_531 != set_difference(U_533,U_532) ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_543,U_541,U_539] :
( U_539 = set_difference(U_543,U_541)
| ? [U_537] :
( ~ in(U_537,U_539)
& ~ in(U_537,U_541)
& in(U_537,U_543) )
| ? [U_536] :
( ( in(U_536,U_541)
| ~ in(U_536,U_543) )
& in(U_536,U_539) ) )
& ! [U_542,U_540,U_538] :
( ( ! [U_535] :
( in(U_535,U_538)
| in(U_535,U_540)
| ~ in(U_535,U_542) )
& ! [U_534] :
( ( ~ in(U_534,U_540)
& in(U_534,U_542) )
| ~ in(U_534,U_538) ) )
| U_538 != set_difference(U_542,U_540) ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
fof(f_89_4,plain,
( ! [U_543,U_541,U_539] :
( U_539 = set_difference(U_543,U_541)
| ? [U_537] :
( ~ in(U_537,U_539)
& ~ in(U_537,U_541)
& in(U_537,U_543) )
| ( ( in(sK91(U_543,U_541,U_539),U_541)
| ~ in(sK91(U_543,U_541,U_539),U_543) )
& in(sK91(U_543,U_541,U_539),U_539) ) )
& ! [U_542,U_540,U_538] :
( ( ! [U_535] :
( in(U_535,U_538)
| in(U_535,U_540)
| ~ in(U_535,U_542) )
& ! [U_534] :
( ( ~ in(U_534,U_540)
& in(U_534,U_542) )
| ~ in(U_534,U_538) ) )
| U_538 != set_difference(U_542,U_540) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_536,sK91(U_543,U_541,U_539))],[f_89_3]) ).
fof(f_89_5,plain,
( ! [U_543,U_541,U_539] :
( U_539 = set_difference(U_543,U_541)
| ( ~ in(sK92(U_543,U_541,U_539),U_539)
& ~ in(sK92(U_543,U_541,U_539),U_541)
& in(sK92(U_543,U_541,U_539),U_543) )
| ( ( in(sK91(U_543,U_541,U_539),U_541)
| ~ in(sK91(U_543,U_541,U_539),U_543) )
& in(sK91(U_543,U_541,U_539),U_539) ) )
& ! [U_542,U_540,U_538] :
( ( ! [U_535] :
( in(U_535,U_538)
| in(U_535,U_540)
| ~ in(U_535,U_542) )
& ! [U_534] :
( ( ~ in(U_534,U_540)
& in(U_534,U_542) )
| ~ in(U_534,U_538) ) )
| U_538 != set_difference(U_542,U_540) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_537,sK92(U_543,U_541,U_539))],[f_89_4]) ).
cnf(f_89_6,plain,
( in(U_534,U_542)
| ~ in(U_534,U_538)
| U_538 != set_difference(U_542,U_540) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_7,plain,
( ~ in(U_534,U_540)
| ~ in(U_534,U_538)
| U_538 != set_difference(U_542,U_540) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_8,plain,
( in(U_535,U_538)
| in(U_535,U_540)
| ~ in(U_535,U_542)
| U_538 != set_difference(U_542,U_540) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_9,plain,
( in(sK92(U_543,U_541,U_539),U_543)
| in(sK91(U_543,U_541,U_539),U_539)
| U_539 = set_difference(U_543,U_541) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_10,plain,
( ~ in(sK92(U_543,U_541,U_539),U_541)
| in(sK91(U_543,U_541,U_539),U_539)
| U_539 = set_difference(U_543,U_541) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_11,plain,
( ~ in(sK92(U_543,U_541,U_539),U_539)
| in(sK91(U_543,U_541,U_539),U_539)
| U_539 = set_difference(U_543,U_541) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_12,plain,
( in(sK92(U_543,U_541,U_539),U_543)
| in(sK91(U_543,U_541,U_539),U_541)
| ~ in(sK91(U_543,U_541,U_539),U_543)
| U_539 = set_difference(U_543,U_541) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_13,plain,
( ~ in(sK92(U_543,U_541,U_539),U_541)
| in(sK91(U_543,U_541,U_539),U_541)
| ~ in(sK91(U_543,U_541,U_539),U_543)
| U_539 = set_difference(U_543,U_541) ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_14,plain,
( ~ in(sK92(U_543,U_541,U_539),U_539)
| in(sK91(U_543,U_541,U_539),U_541)
| ~ in(sK91(U_543,U_541,U_539),U_543)
| U_539 = set_difference(U_543,U_541) ),
inference(clausify,[status(thm)],[f_89_5]) ).
fof(f_90_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_90_2,plain,
! [U_551] :
( ! [U_550] :
( ( U_550 = relation_rng(U_551)
| ? [U_549] :
( ( ~ in(U_549,U_550)
& ? [U_548] :
( U_549 = apply(U_551,U_548)
& in(U_548,relation_dom(U_551)) ) )
| ( ! [U_547] :
( U_549 != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551)) )
& in(U_549,U_550) ) ) )
& ( ! [U_546] :
( ( in(U_546,U_550)
| ! [U_545] :
( U_546 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551)) ) )
& ( ? [U_544] :
( U_546 = apply(U_551,U_544)
& in(U_544,relation_dom(U_551)) )
| ~ in(U_546,U_550) ) )
| U_550 != relation_rng(U_551) ) )
| ~ function(U_551)
| ~ relation(U_551) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_551] :
( ( ! [U_557] :
( U_557 = relation_rng(U_551)
| ? [U_555] :
( ~ in(U_555,U_557)
& ? [U_548] :
( U_555 = apply(U_551,U_548)
& in(U_548,relation_dom(U_551)) ) )
| ? [U_554] :
( ! [U_547] :
( U_554 != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551)) )
& in(U_554,U_557) ) )
& ! [U_556] :
( ( ! [U_553] :
( in(U_553,U_556)
| ! [U_545] :
( U_553 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551)) ) )
& ! [U_552] :
( ? [U_544] :
( U_552 = apply(U_551,U_544)
& in(U_544,relation_dom(U_551)) )
| ~ in(U_552,U_556) ) )
| U_556 != relation_rng(U_551) ) )
| ~ function(U_551)
| ~ relation(U_551) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
fof(f_90_4,plain,
! [U_551] :
( ( ! [U_557] :
( U_557 = relation_rng(U_551)
| ? [U_555] :
( ~ in(U_555,U_557)
& ? [U_548] :
( U_555 = apply(U_551,U_548)
& in(U_548,relation_dom(U_551)) ) )
| ? [U_554] :
( ! [U_547] :
( U_554 != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551)) )
& in(U_554,U_557) ) )
& ! [U_556] :
( ( ! [U_553] :
( in(U_553,U_556)
| ! [U_545] :
( U_553 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551)) ) )
& ! [U_552] :
( ( U_552 = apply(U_551,sK93(U_551,U_556,U_552))
& in(sK93(U_551,U_556,U_552),relation_dom(U_551)) )
| ~ in(U_552,U_556) ) )
| U_556 != relation_rng(U_551) ) )
| ~ function(U_551)
| ~ relation(U_551) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_544,sK93(U_551,U_556,U_552))],[f_90_3]) ).
fof(f_90_5,plain,
! [U_551] :
( ( ! [U_557] :
( U_557 = relation_rng(U_551)
| ? [U_555] :
( ~ in(U_555,U_557)
& ? [U_548] :
( U_555 = apply(U_551,U_548)
& in(U_548,relation_dom(U_551)) ) )
| ( ! [U_547] :
( sK94(U_551,U_557) != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551)) )
& in(sK94(U_551,U_557),U_557) ) )
& ! [U_556] :
( ( ! [U_553] :
( in(U_553,U_556)
| ! [U_545] :
( U_553 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551)) ) )
& ! [U_552] :
( ( U_552 = apply(U_551,sK93(U_551,U_556,U_552))
& in(sK93(U_551,U_556,U_552),relation_dom(U_551)) )
| ~ in(U_552,U_556) ) )
| U_556 != relation_rng(U_551) ) )
| ~ function(U_551)
| ~ relation(U_551) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_554,sK94(U_551,U_557))],[f_90_4]) ).
fof(f_90_6,plain,
! [U_551] :
( ( ! [U_557] :
( U_557 = relation_rng(U_551)
| ( ~ in(sK95(U_551,U_557),U_557)
& ? [U_548] :
( sK95(U_551,U_557) = apply(U_551,U_548)
& in(U_548,relation_dom(U_551)) ) )
| ( ! [U_547] :
( sK94(U_551,U_557) != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551)) )
& in(sK94(U_551,U_557),U_557) ) )
& ! [U_556] :
( ( ! [U_553] :
( in(U_553,U_556)
| ! [U_545] :
( U_553 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551)) ) )
& ! [U_552] :
( ( U_552 = apply(U_551,sK93(U_551,U_556,U_552))
& in(sK93(U_551,U_556,U_552),relation_dom(U_551)) )
| ~ in(U_552,U_556) ) )
| U_556 != relation_rng(U_551) ) )
| ~ function(U_551)
| ~ relation(U_551) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_555,sK95(U_551,U_557))],[f_90_5]) ).
fof(f_90_7,plain,
! [U_551] :
( ( ! [U_557] :
( U_557 = relation_rng(U_551)
| ( ~ in(sK95(U_551,U_557),U_557)
& sK95(U_551,U_557) = apply(U_551,sK96(U_551,U_557))
& in(sK96(U_551,U_557),relation_dom(U_551)) )
| ( ! [U_547] :
( sK94(U_551,U_557) != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551)) )
& in(sK94(U_551,U_557),U_557) ) )
& ! [U_556] :
( ( ! [U_553] :
( in(U_553,U_556)
| ! [U_545] :
( U_553 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551)) ) )
& ! [U_552] :
( ( U_552 = apply(U_551,sK93(U_551,U_556,U_552))
& in(sK93(U_551,U_556,U_552),relation_dom(U_551)) )
| ~ in(U_552,U_556) ) )
| U_556 != relation_rng(U_551) ) )
| ~ function(U_551)
| ~ relation(U_551) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_548,sK96(U_551,U_557))],[f_90_6]) ).
cnf(f_90_8,plain,
( in(sK93(U_551,U_556,U_552),relation_dom(U_551))
| ~ in(U_552,U_556)
| U_556 != relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_9,plain,
( U_552 = apply(U_551,sK93(U_551,U_556,U_552))
| ~ in(U_552,U_556)
| U_556 != relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_10,plain,
( in(U_553,U_556)
| U_553 != apply(U_551,U_545)
| ~ in(U_545,relation_dom(U_551))
| U_556 != relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_11,plain,
( in(sK96(U_551,U_557),relation_dom(U_551))
| in(sK94(U_551,U_557),U_557)
| U_557 = relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_12,plain,
( sK95(U_551,U_557) = apply(U_551,sK96(U_551,U_557))
| in(sK94(U_551,U_557),U_557)
| U_557 = relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_13,plain,
( ~ in(sK95(U_551,U_557),U_557)
| in(sK94(U_551,U_557),U_557)
| U_557 = relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_14,plain,
( in(sK96(U_551,U_557),relation_dom(U_551))
| sK94(U_551,U_557) != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551))
| U_557 = relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_15,plain,
( sK95(U_551,U_557) = apply(U_551,sK96(U_551,U_557))
| sK94(U_551,U_557) != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551))
| U_557 = relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
cnf(f_90_16,plain,
( ~ in(sK95(U_551,U_557),U_557)
| sK94(U_551,U_557) != apply(U_551,U_547)
| ~ in(U_547,relation_dom(U_551))
| U_557 = relation_rng(U_551)
| ~ function(U_551)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_90_7]) ).
fof(f_91_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_91_2,plain,
! [U_560] :
( ( U_560 = omega
| ? [U_559] :
( ~ subset(U_560,U_559)
& being_limit_ordinal(U_559)
& in(empty_set,U_559)
& ordinal(U_559) )
| ~ ordinal(U_560)
| ~ being_limit_ordinal(U_560)
| ~ in(empty_set,U_560) )
& ( ( ! [U_558] :
( subset(U_560,U_558)
| ~ being_limit_ordinal(U_558)
| ~ in(empty_set,U_558)
| ~ ordinal(U_558) )
& ordinal(U_560)
& being_limit_ordinal(U_560)
& in(empty_set,U_560) )
| U_560 != omega ) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( ! [U_562] :
( U_562 = omega
| ? [U_559] :
( ~ subset(U_562,U_559)
& being_limit_ordinal(U_559)
& in(empty_set,U_559)
& ordinal(U_559) )
| ~ ordinal(U_562)
| ~ being_limit_ordinal(U_562)
| ~ in(empty_set,U_562) )
& ! [U_561] :
( ( ! [U_558] :
( subset(U_561,U_558)
| ~ being_limit_ordinal(U_558)
| ~ in(empty_set,U_558)
| ~ ordinal(U_558) )
& ordinal(U_561)
& being_limit_ordinal(U_561)
& in(empty_set,U_561) )
| U_561 != omega ) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
fof(f_91_4,plain,
( ! [U_562] :
( U_562 = omega
| ( ~ subset(U_562,sK97(U_562))
& being_limit_ordinal(sK97(U_562))
& in(empty_set,sK97(U_562))
& ordinal(sK97(U_562)) )
| ~ ordinal(U_562)
| ~ being_limit_ordinal(U_562)
| ~ in(empty_set,U_562) )
& ! [U_561] :
( ( ! [U_558] :
( subset(U_561,U_558)
| ~ being_limit_ordinal(U_558)
| ~ in(empty_set,U_558)
| ~ ordinal(U_558) )
& ordinal(U_561)
& being_limit_ordinal(U_561)
& in(empty_set,U_561) )
| U_561 != omega ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_559,sK97(U_562))],[f_91_3]) ).
cnf(f_91_5,plain,
( in(empty_set,U_561)
| U_561 != omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_6,plain,
( being_limit_ordinal(U_561)
| U_561 != omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_7,plain,
( ordinal(U_561)
| U_561 != omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_8,plain,
( subset(U_561,U_558)
| ~ being_limit_ordinal(U_558)
| ~ in(empty_set,U_558)
| ~ ordinal(U_558)
| U_561 != omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_9,plain,
( ordinal(sK97(U_562))
| ~ ordinal(U_562)
| ~ being_limit_ordinal(U_562)
| ~ in(empty_set,U_562)
| U_562 = omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_10,plain,
( in(empty_set,sK97(U_562))
| ~ ordinal(U_562)
| ~ being_limit_ordinal(U_562)
| ~ in(empty_set,U_562)
| U_562 = omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_11,plain,
( being_limit_ordinal(sK97(U_562))
| ~ ordinal(U_562)
| ~ being_limit_ordinal(U_562)
| ~ in(empty_set,U_562)
| U_562 = omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_12,plain,
( ~ subset(U_562,sK97(U_562))
| ~ ordinal(U_562)
| ~ being_limit_ordinal(U_562)
| ~ in(empty_set,U_562)
| U_562 = omega ),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_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_92_2,plain,
! [U_570] :
( ! [U_569] :
( ( U_569 = relation_rng(U_570)
| ? [U_568] :
( ( ~ in(U_568,U_569)
& ? [U_567] : in(ordered_pair(U_567,U_568),U_570) )
| ( ! [U_566] : ~ in(ordered_pair(U_566,U_568),U_570)
& in(U_568,U_569) ) ) )
& ( ! [U_565] :
( ( in(U_565,U_569)
| ! [U_564] : ~ in(ordered_pair(U_564,U_565),U_570) )
& ( ? [U_563] : in(ordered_pair(U_563,U_565),U_570)
| ~ in(U_565,U_569) ) )
| U_569 != relation_rng(U_570) ) )
| ~ relation(U_570) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_570] :
( ( ! [U_576] :
( U_576 = relation_rng(U_570)
| ? [U_574] :
( ~ in(U_574,U_576)
& ? [U_567] : in(ordered_pair(U_567,U_574),U_570) )
| ? [U_573] :
( ! [U_566] : ~ in(ordered_pair(U_566,U_573),U_570)
& in(U_573,U_576) ) )
& ! [U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ! [U_564] : ~ in(ordered_pair(U_564,U_572),U_570) )
& ! [U_571] :
( ? [U_563] : in(ordered_pair(U_563,U_571),U_570)
| ~ in(U_571,U_575) ) )
| U_575 != relation_rng(U_570) ) )
| ~ relation(U_570) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
fof(f_92_4,plain,
! [U_570] :
( ( ! [U_576] :
( U_576 = relation_rng(U_570)
| ? [U_574] :
( ~ in(U_574,U_576)
& ? [U_567] : in(ordered_pair(U_567,U_574),U_570) )
| ? [U_573] :
( ! [U_566] : ~ in(ordered_pair(U_566,U_573),U_570)
& in(U_573,U_576) ) )
& ! [U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ! [U_564] : ~ in(ordered_pair(U_564,U_572),U_570) )
& ! [U_571] :
( in(ordered_pair(sK98(U_570,U_575,U_571),U_571),U_570)
| ~ in(U_571,U_575) ) )
| U_575 != relation_rng(U_570) ) )
| ~ relation(U_570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_563,sK98(U_570,U_575,U_571))],[f_92_3]) ).
fof(f_92_5,plain,
! [U_570] :
( ( ! [U_576] :
( U_576 = relation_rng(U_570)
| ? [U_574] :
( ~ in(U_574,U_576)
& ? [U_567] : in(ordered_pair(U_567,U_574),U_570) )
| ( ! [U_566] : ~ in(ordered_pair(U_566,sK99(U_570,U_576)),U_570)
& in(sK99(U_570,U_576),U_576) ) )
& ! [U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ! [U_564] : ~ in(ordered_pair(U_564,U_572),U_570) )
& ! [U_571] :
( in(ordered_pair(sK98(U_570,U_575,U_571),U_571),U_570)
| ~ in(U_571,U_575) ) )
| U_575 != relation_rng(U_570) ) )
| ~ relation(U_570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_573,sK99(U_570,U_576))],[f_92_4]) ).
fof(f_92_6,plain,
! [U_570] :
( ( ! [U_576] :
( U_576 = relation_rng(U_570)
| ( ~ in(sK100(U_570,U_576),U_576)
& ? [U_567] : in(ordered_pair(U_567,sK100(U_570,U_576)),U_570) )
| ( ! [U_566] : ~ in(ordered_pair(U_566,sK99(U_570,U_576)),U_570)
& in(sK99(U_570,U_576),U_576) ) )
& ! [U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ! [U_564] : ~ in(ordered_pair(U_564,U_572),U_570) )
& ! [U_571] :
( in(ordered_pair(sK98(U_570,U_575,U_571),U_571),U_570)
| ~ in(U_571,U_575) ) )
| U_575 != relation_rng(U_570) ) )
| ~ relation(U_570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_574,sK100(U_570,U_576))],[f_92_5]) ).
fof(f_92_7,plain,
! [U_570] :
( ( ! [U_576] :
( U_576 = relation_rng(U_570)
| ( ~ in(sK100(U_570,U_576),U_576)
& in(ordered_pair(sK101(U_570,U_576),sK100(U_570,U_576)),U_570) )
| ( ! [U_566] : ~ in(ordered_pair(U_566,sK99(U_570,U_576)),U_570)
& in(sK99(U_570,U_576),U_576) ) )
& ! [U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ! [U_564] : ~ in(ordered_pair(U_564,U_572),U_570) )
& ! [U_571] :
( in(ordered_pair(sK98(U_570,U_575,U_571),U_571),U_570)
| ~ in(U_571,U_575) ) )
| U_575 != relation_rng(U_570) ) )
| ~ relation(U_570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_567,sK101(U_570,U_576))],[f_92_6]) ).
cnf(f_92_8,plain,
( in(ordered_pair(sK98(U_570,U_575,U_571),U_571),U_570)
| ~ in(U_571,U_575)
| U_575 != relation_rng(U_570)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_92_7]) ).
cnf(f_92_9,plain,
( in(U_572,U_575)
| ~ in(ordered_pair(U_564,U_572),U_570)
| U_575 != relation_rng(U_570)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_92_7]) ).
cnf(f_92_10,plain,
( in(ordered_pair(sK101(U_570,U_576),sK100(U_570,U_576)),U_570)
| in(sK99(U_570,U_576),U_576)
| U_576 = relation_rng(U_570)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_92_7]) ).
cnf(f_92_11,plain,
( ~ in(sK100(U_570,U_576),U_576)
| in(sK99(U_570,U_576),U_576)
| U_576 = relation_rng(U_570)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_92_7]) ).
cnf(f_92_12,plain,
( in(ordered_pair(sK101(U_570,U_576),sK100(U_570,U_576)),U_570)
| ~ in(ordered_pair(U_566,sK99(U_570,U_576)),U_570)
| U_576 = relation_rng(U_570)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_92_7]) ).
cnf(f_92_13,plain,
( ~ in(sK100(U_570,U_576),U_576)
| ~ in(ordered_pair(U_566,sK99(U_570,U_576)),U_570)
| U_576 = relation_rng(U_570)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_92_7]) ).
fof(f_93_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_93_2,plain,
! [U_578,U_577] :
( subset_complement(U_578,U_577) = set_difference(U_578,U_577)
| ~ element(U_577,powerset(U_578)) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( subset_complement(U_578,U_577) = set_difference(U_578,U_577)
| ~ element(U_577,powerset(U_578)) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_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_94_2,plain,
! [U_580,U_579] : ordered_pair(U_580,U_579) = unordered_pair(unordered_pair(U_580,U_579),singleton(U_580)),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
ordered_pair(U_580,U_579) = unordered_pair(unordered_pair(U_580,U_579),singleton(U_580)),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_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_95_2,plain,
! [U_582] :
( ! [U_581] :
( ( well_orders(U_582,U_581)
| ~ is_well_founded_in(U_582,U_581)
| ~ is_connected_in(U_582,U_581)
| ~ is_antisymmetric_in(U_582,U_581)
| ~ is_transitive_in(U_582,U_581)
| ~ is_reflexive_in(U_582,U_581) )
& ( ( is_well_founded_in(U_582,U_581)
& is_connected_in(U_582,U_581)
& is_antisymmetric_in(U_582,U_581)
& is_transitive_in(U_582,U_581)
& is_reflexive_in(U_582,U_581) )
| ~ well_orders(U_582,U_581) ) )
| ~ relation(U_582) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_582] :
( ( ! [U_584] :
( well_orders(U_582,U_584)
| ~ is_well_founded_in(U_582,U_584)
| ~ is_connected_in(U_582,U_584)
| ~ is_antisymmetric_in(U_582,U_584)
| ~ is_transitive_in(U_582,U_584)
| ~ is_reflexive_in(U_582,U_584) )
& ! [U_583] :
( ( is_well_founded_in(U_582,U_583)
& is_connected_in(U_582,U_583)
& is_antisymmetric_in(U_582,U_583)
& is_transitive_in(U_582,U_583)
& is_reflexive_in(U_582,U_583) )
| ~ well_orders(U_582,U_583) ) )
| ~ relation(U_582) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( is_reflexive_in(U_582,U_583)
| ~ well_orders(U_582,U_583)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( is_transitive_in(U_582,U_583)
| ~ well_orders(U_582,U_583)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_6,plain,
( is_antisymmetric_in(U_582,U_583)
| ~ well_orders(U_582,U_583)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_7,plain,
( is_connected_in(U_582,U_583)
| ~ well_orders(U_582,U_583)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_8,plain,
( is_well_founded_in(U_582,U_583)
| ~ well_orders(U_582,U_583)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_9,plain,
( well_orders(U_582,U_584)
| ~ is_well_founded_in(U_582,U_584)
| ~ is_connected_in(U_582,U_584)
| ~ is_antisymmetric_in(U_582,U_584)
| ~ is_transitive_in(U_582,U_584)
| ~ is_reflexive_in(U_582,U_584)
| ~ relation(U_582) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_585] :
( ( being_limit_ordinal(U_585)
| U_585 != union(U_585) )
& ( U_585 = union(U_585)
| ~ being_limit_ordinal(U_585) ) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
( ! [U_587] :
( being_limit_ordinal(U_587)
| U_587 != union(U_587) )
& ! [U_586] :
( U_586 = union(U_586)
| ~ being_limit_ordinal(U_586) ) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( U_586 = union(U_586)
| ~ being_limit_ordinal(U_586) ),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_5,plain,
( being_limit_ordinal(U_587)
| U_587 != union(U_587) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_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_97_2,plain,
! [U_588] :
( relation_field(U_588) = set_union2(relation_dom(U_588),relation_rng(U_588))
| ~ relation(U_588) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( relation_field(U_588) = set_union2(relation_dom(U_588),relation_rng(U_588))
| ~ relation(U_588) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_594] :
( ! [U_593] :
( ( is_connected_in(U_594,U_593)
| ? [U_592,U_591] :
( ~ in(ordered_pair(U_591,U_592),U_594)
& ~ in(ordered_pair(U_592,U_591),U_594)
& U_592 != U_591
& in(U_591,U_593)
& in(U_592,U_593) ) )
& ( ! [U_590,U_589] :
( in(ordered_pair(U_589,U_590),U_594)
| in(ordered_pair(U_590,U_589),U_594)
| U_590 = U_589
| ~ in(U_589,U_593)
| ~ in(U_590,U_593) )
| ~ is_connected_in(U_594,U_593) ) )
| ~ relation(U_594) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_594] :
( ( ! [U_596] :
( is_connected_in(U_594,U_596)
| ? [U_592] :
( ? [U_591] :
( ~ in(ordered_pair(U_591,U_592),U_594)
& ~ in(ordered_pair(U_592,U_591),U_594)
& U_592 != U_591
& in(U_591,U_596) )
& in(U_592,U_596) ) )
& ! [U_595] :
( ! [U_590] :
( ! [U_589] :
( in(ordered_pair(U_589,U_590),U_594)
| in(ordered_pair(U_590,U_589),U_594)
| U_590 = U_589
| ~ in(U_589,U_595) )
| ~ in(U_590,U_595) )
| ~ is_connected_in(U_594,U_595) ) )
| ~ relation(U_594) ),
inference(miniscope,[status(thm)],[f_98_2]) ).
fof(f_98_4,plain,
! [U_594] :
( ( ! [U_596] :
( is_connected_in(U_594,U_596)
| ( ? [U_591] :
( ~ in(ordered_pair(U_591,sK102(U_594,U_596)),U_594)
& ~ in(ordered_pair(sK102(U_594,U_596),U_591),U_594)
& sK102(U_594,U_596) != U_591
& in(U_591,U_596) )
& in(sK102(U_594,U_596),U_596) ) )
& ! [U_595] :
( ! [U_590] :
( ! [U_589] :
( in(ordered_pair(U_589,U_590),U_594)
| in(ordered_pair(U_590,U_589),U_594)
| U_590 = U_589
| ~ in(U_589,U_595) )
| ~ in(U_590,U_595) )
| ~ is_connected_in(U_594,U_595) ) )
| ~ relation(U_594) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_592,sK102(U_594,U_596))],[f_98_3]) ).
fof(f_98_5,plain,
! [U_594] :
( ( ! [U_596] :
( is_connected_in(U_594,U_596)
| ( ~ in(ordered_pair(sK103(U_594,U_596),sK102(U_594,U_596)),U_594)
& ~ in(ordered_pair(sK102(U_594,U_596),sK103(U_594,U_596)),U_594)
& sK102(U_594,U_596) != sK103(U_594,U_596)
& in(sK103(U_594,U_596),U_596)
& in(sK102(U_594,U_596),U_596) ) )
& ! [U_595] :
( ! [U_590] :
( ! [U_589] :
( in(ordered_pair(U_589,U_590),U_594)
| in(ordered_pair(U_590,U_589),U_594)
| U_590 = U_589
| ~ in(U_589,U_595) )
| ~ in(U_590,U_595) )
| ~ is_connected_in(U_594,U_595) ) )
| ~ relation(U_594) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_591,sK103(U_594,U_596))],[f_98_4]) ).
cnf(f_98_6,plain,
( in(ordered_pair(U_589,U_590),U_594)
| in(ordered_pair(U_590,U_589),U_594)
| U_590 = U_589
| ~ in(U_589,U_595)
| ~ in(U_590,U_595)
| ~ is_connected_in(U_594,U_595)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_98_5]) ).
cnf(f_98_7,plain,
( in(sK102(U_594,U_596),U_596)
| is_connected_in(U_594,U_596)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_98_5]) ).
cnf(f_98_8,plain,
( in(sK103(U_594,U_596),U_596)
| is_connected_in(U_594,U_596)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_98_5]) ).
cnf(f_98_9,plain,
( sK102(U_594,U_596) != sK103(U_594,U_596)
| is_connected_in(U_594,U_596)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_98_5]) ).
cnf(f_98_10,plain,
( ~ in(ordered_pair(sK102(U_594,U_596),sK103(U_594,U_596)),U_594)
| is_connected_in(U_594,U_596)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_98_5]) ).
cnf(f_98_11,plain,
( ~ in(ordered_pair(sK103(U_594,U_596),sK102(U_594,U_596)),U_594)
| is_connected_in(U_594,U_596)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_98_5]) ).
fof(f_99_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_99_2,plain,
! [U_598] :
( ! [U_597] : relation_restriction(U_598,U_597) = set_intersection2(U_598,cartesian_product2(U_597,U_597))
| ~ relation(U_598) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( relation_restriction(U_598,U_597) = set_intersection2(U_598,cartesian_product2(U_597,U_597))
| ~ relation(U_598) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_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_100_2,plain,
! [U_604] :
( ! [U_603] :
( ( ( U_603 = relation_inverse(U_604)
| ? [U_602,U_601] :
( ( ~ in(ordered_pair(U_602,U_601),U_603)
& in(ordered_pair(U_601,U_602),U_604) )
| ( ~ in(ordered_pair(U_601,U_602),U_604)
& in(ordered_pair(U_602,U_601),U_603) ) ) )
& ( ! [U_600,U_599] :
( ( in(ordered_pair(U_600,U_599),U_603)
| ~ in(ordered_pair(U_599,U_600),U_604) )
& ( in(ordered_pair(U_599,U_600),U_604)
| ~ in(ordered_pair(U_600,U_599),U_603) ) )
| U_603 != relation_inverse(U_604) ) )
| ~ relation(U_603) )
| ~ relation(U_604) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_604] :
( ! [U_603] :
( ( ( U_603 = relation_inverse(U_604)
| ? [U_612,U_610] :
( ~ in(ordered_pair(U_612,U_610),U_603)
& in(ordered_pair(U_610,U_612),U_604) )
| ? [U_611,U_609] :
( ~ in(ordered_pair(U_609,U_611),U_604)
& in(ordered_pair(U_611,U_609),U_603) ) )
& ( ( ! [U_608,U_606] :
( in(ordered_pair(U_608,U_606),U_603)
| ~ in(ordered_pair(U_606,U_608),U_604) )
& ! [U_607,U_605] :
( in(ordered_pair(U_605,U_607),U_604)
| ~ in(ordered_pair(U_607,U_605),U_603) ) )
| U_603 != relation_inverse(U_604) ) )
| ~ relation(U_603) )
| ~ relation(U_604) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
fof(f_100_4,plain,
! [U_604] :
( ! [U_603] :
( ( ( U_603 = relation_inverse(U_604)
| ? [U_612,U_610] :
( ~ in(ordered_pair(U_612,U_610),U_603)
& in(ordered_pair(U_610,U_612),U_604) )
| ? [U_609] :
( ~ in(ordered_pair(U_609,sK104(U_604,U_603)),U_604)
& in(ordered_pair(sK104(U_604,U_603),U_609),U_603) ) )
& ( ( ! [U_608,U_606] :
( in(ordered_pair(U_608,U_606),U_603)
| ~ in(ordered_pair(U_606,U_608),U_604) )
& ! [U_607,U_605] :
( in(ordered_pair(U_605,U_607),U_604)
| ~ in(ordered_pair(U_607,U_605),U_603) ) )
| U_603 != relation_inverse(U_604) ) )
| ~ relation(U_603) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_611,sK104(U_604,U_603))],[f_100_3]) ).
fof(f_100_5,plain,
! [U_604] :
( ! [U_603] :
( ( ( U_603 = relation_inverse(U_604)
| ? [U_612,U_610] :
( ~ in(ordered_pair(U_612,U_610),U_603)
& in(ordered_pair(U_610,U_612),U_604) )
| ( ~ in(ordered_pair(sK105(U_604,U_603),sK104(U_604,U_603)),U_604)
& in(ordered_pair(sK104(U_604,U_603),sK105(U_604,U_603)),U_603) ) )
& ( ( ! [U_608,U_606] :
( in(ordered_pair(U_608,U_606),U_603)
| ~ in(ordered_pair(U_606,U_608),U_604) )
& ! [U_607,U_605] :
( in(ordered_pair(U_605,U_607),U_604)
| ~ in(ordered_pair(U_607,U_605),U_603) ) )
| U_603 != relation_inverse(U_604) ) )
| ~ relation(U_603) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_609,sK105(U_604,U_603))],[f_100_4]) ).
fof(f_100_6,plain,
! [U_604] :
( ! [U_603] :
( ( ( U_603 = relation_inverse(U_604)
| ? [U_610] :
( ~ in(ordered_pair(sK106(U_604,U_603),U_610),U_603)
& in(ordered_pair(U_610,sK106(U_604,U_603)),U_604) )
| ( ~ in(ordered_pair(sK105(U_604,U_603),sK104(U_604,U_603)),U_604)
& in(ordered_pair(sK104(U_604,U_603),sK105(U_604,U_603)),U_603) ) )
& ( ( ! [U_608,U_606] :
( in(ordered_pair(U_608,U_606),U_603)
| ~ in(ordered_pair(U_606,U_608),U_604) )
& ! [U_607,U_605] :
( in(ordered_pair(U_605,U_607),U_604)
| ~ in(ordered_pair(U_607,U_605),U_603) ) )
| U_603 != relation_inverse(U_604) ) )
| ~ relation(U_603) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_612,sK106(U_604,U_603))],[f_100_5]) ).
fof(f_100_7,plain,
! [U_604] :
( ! [U_603] :
( ( ( U_603 = relation_inverse(U_604)
| ( ~ in(ordered_pair(sK106(U_604,U_603),sK107(U_604,U_603)),U_603)
& in(ordered_pair(sK107(U_604,U_603),sK106(U_604,U_603)),U_604) )
| ( ~ in(ordered_pair(sK105(U_604,U_603),sK104(U_604,U_603)),U_604)
& in(ordered_pair(sK104(U_604,U_603),sK105(U_604,U_603)),U_603) ) )
& ( ( ! [U_608,U_606] :
( in(ordered_pair(U_608,U_606),U_603)
| ~ in(ordered_pair(U_606,U_608),U_604) )
& ! [U_607,U_605] :
( in(ordered_pair(U_605,U_607),U_604)
| ~ in(ordered_pair(U_607,U_605),U_603) ) )
| U_603 != relation_inverse(U_604) ) )
| ~ relation(U_603) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_610,sK107(U_604,U_603))],[f_100_6]) ).
cnf(f_100_8,plain,
( in(ordered_pair(U_605,U_607),U_604)
| ~ in(ordered_pair(U_607,U_605),U_603)
| U_603 != relation_inverse(U_604)
| ~ relation(U_603)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_100_7]) ).
cnf(f_100_9,plain,
( in(ordered_pair(U_608,U_606),U_603)
| ~ in(ordered_pair(U_606,U_608),U_604)
| U_603 != relation_inverse(U_604)
| ~ relation(U_603)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_100_7]) ).
cnf(f_100_10,plain,
( in(ordered_pair(sK107(U_604,U_603),sK106(U_604,U_603)),U_604)
| in(ordered_pair(sK104(U_604,U_603),sK105(U_604,U_603)),U_603)
| U_603 = relation_inverse(U_604)
| ~ relation(U_603)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_100_7]) ).
cnf(f_100_11,plain,
( ~ in(ordered_pair(sK106(U_604,U_603),sK107(U_604,U_603)),U_603)
| in(ordered_pair(sK104(U_604,U_603),sK105(U_604,U_603)),U_603)
| U_603 = relation_inverse(U_604)
| ~ relation(U_603)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_100_7]) ).
cnf(f_100_12,plain,
( in(ordered_pair(sK107(U_604,U_603),sK106(U_604,U_603)),U_604)
| ~ in(ordered_pair(sK105(U_604,U_603),sK104(U_604,U_603)),U_604)
| U_603 = relation_inverse(U_604)
| ~ relation(U_603)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_100_7]) ).
cnf(f_100_13,plain,
( ~ in(ordered_pair(sK106(U_604,U_603),sK107(U_604,U_603)),U_603)
| ~ in(ordered_pair(sK105(U_604,U_603),sK104(U_604,U_603)),U_604)
| U_603 = relation_inverse(U_604)
| ~ relation(U_603)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_100_7]) ).
fof(f_101_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_101_2,plain,
! [U_619] :
( ! [U_618] :
( ! [U_617] :
( ( ( relation_isomorphism(U_619,U_618,U_617)
| ? [U_616,U_615] :
( ( ~ in(ordered_pair(U_616,U_615),U_619)
& in(ordered_pair(apply(U_617,U_616),apply(U_617,U_615)),U_618)
& in(U_615,relation_field(U_619))
& in(U_616,relation_field(U_619)) )
| ( ( ~ in(ordered_pair(apply(U_617,U_616),apply(U_617,U_615)),U_618)
| ~ in(U_615,relation_field(U_619))
| ~ in(U_616,relation_field(U_619)) )
& in(ordered_pair(U_616,U_615),U_619) ) )
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619) )
& ( ( ! [U_614,U_613] :
( ( in(ordered_pair(U_614,U_613),U_619)
| ~ in(ordered_pair(apply(U_617,U_614),apply(U_617,U_613)),U_618)
| ~ in(U_613,relation_field(U_619))
| ~ in(U_614,relation_field(U_619)) )
& ( ( in(ordered_pair(apply(U_617,U_614),apply(U_617,U_613)),U_618)
& in(U_613,relation_field(U_619))
& in(U_614,relation_field(U_619)) )
| ~ in(ordered_pair(U_614,U_613),U_619) ) )
& one_to_one(U_617)
& relation_rng(U_617) = relation_field(U_618)
& relation_dom(U_617) = relation_field(U_619) )
| ~ relation_isomorphism(U_619,U_618,U_617) ) )
| ~ function(U_617)
| ~ relation(U_617) )
| ~ relation(U_618) )
| ~ relation(U_619) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_619] :
( ! [U_618] :
( ! [U_617] :
( ( ( relation_isomorphism(U_619,U_618,U_617)
| ? [U_627,U_625] :
( ~ in(ordered_pair(U_627,U_625),U_619)
& in(ordered_pair(apply(U_617,U_627),apply(U_617,U_625)),U_618)
& in(U_625,relation_field(U_619))
& in(U_627,relation_field(U_619)) )
| ? [U_626,U_624] :
( ( ~ in(ordered_pair(apply(U_617,U_626),apply(U_617,U_624)),U_618)
| ~ in(U_624,relation_field(U_619))
| ~ in(U_626,relation_field(U_619)) )
& in(ordered_pair(U_626,U_624),U_619) )
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619) )
& ( ( ! [U_623,U_621] :
( in(ordered_pair(U_623,U_621),U_619)
| ~ in(ordered_pair(apply(U_617,U_623),apply(U_617,U_621)),U_618)
| ~ in(U_621,relation_field(U_619))
| ~ in(U_623,relation_field(U_619)) )
& ! [U_622,U_620] :
( ( in(ordered_pair(apply(U_617,U_622),apply(U_617,U_620)),U_618)
& in(U_620,relation_field(U_619))
& in(U_622,relation_field(U_619)) )
| ~ in(ordered_pair(U_622,U_620),U_619) )
& one_to_one(U_617)
& relation_rng(U_617) = relation_field(U_618)
& relation_dom(U_617) = relation_field(U_619) )
| ~ relation_isomorphism(U_619,U_618,U_617) ) )
| ~ function(U_617)
| ~ relation(U_617) )
| ~ relation(U_618) )
| ~ relation(U_619) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
! [U_619] :
( ! [U_618] :
( ! [U_617] :
( ( ( relation_isomorphism(U_619,U_618,U_617)
| ? [U_627,U_625] :
( ~ in(ordered_pair(U_627,U_625),U_619)
& in(ordered_pair(apply(U_617,U_627),apply(U_617,U_625)),U_618)
& in(U_625,relation_field(U_619))
& in(U_627,relation_field(U_619)) )
| ? [U_624] :
( ( ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,U_624)),U_618)
| ~ in(U_624,relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619)) )
& in(ordered_pair(sK108(U_619,U_618,U_617),U_624),U_619) )
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619) )
& ( ( ! [U_623,U_621] :
( in(ordered_pair(U_623,U_621),U_619)
| ~ in(ordered_pair(apply(U_617,U_623),apply(U_617,U_621)),U_618)
| ~ in(U_621,relation_field(U_619))
| ~ in(U_623,relation_field(U_619)) )
& ! [U_622,U_620] :
( ( in(ordered_pair(apply(U_617,U_622),apply(U_617,U_620)),U_618)
& in(U_620,relation_field(U_619))
& in(U_622,relation_field(U_619)) )
| ~ in(ordered_pair(U_622,U_620),U_619) )
& one_to_one(U_617)
& relation_rng(U_617) = relation_field(U_618)
& relation_dom(U_617) = relation_field(U_619) )
| ~ relation_isomorphism(U_619,U_618,U_617) ) )
| ~ function(U_617)
| ~ relation(U_617) )
| ~ relation(U_618) )
| ~ relation(U_619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_626,sK108(U_619,U_618,U_617))],[f_101_3]) ).
fof(f_101_5,plain,
! [U_619] :
( ! [U_618] :
( ! [U_617] :
( ( ( relation_isomorphism(U_619,U_618,U_617)
| ? [U_627,U_625] :
( ~ in(ordered_pair(U_627,U_625),U_619)
& in(ordered_pair(apply(U_617,U_627),apply(U_617,U_625)),U_618)
& in(U_625,relation_field(U_619))
& in(U_627,relation_field(U_619)) )
| ( ( ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619)) )
& in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619) )
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619) )
& ( ( ! [U_623,U_621] :
( in(ordered_pair(U_623,U_621),U_619)
| ~ in(ordered_pair(apply(U_617,U_623),apply(U_617,U_621)),U_618)
| ~ in(U_621,relation_field(U_619))
| ~ in(U_623,relation_field(U_619)) )
& ! [U_622,U_620] :
( ( in(ordered_pair(apply(U_617,U_622),apply(U_617,U_620)),U_618)
& in(U_620,relation_field(U_619))
& in(U_622,relation_field(U_619)) )
| ~ in(ordered_pair(U_622,U_620),U_619) )
& one_to_one(U_617)
& relation_rng(U_617) = relation_field(U_618)
& relation_dom(U_617) = relation_field(U_619) )
| ~ relation_isomorphism(U_619,U_618,U_617) ) )
| ~ function(U_617)
| ~ relation(U_617) )
| ~ relation(U_618) )
| ~ relation(U_619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_624,sK109(U_619,U_618,U_617))],[f_101_4]) ).
fof(f_101_6,plain,
! [U_619] :
( ! [U_618] :
( ! [U_617] :
( ( ( relation_isomorphism(U_619,U_618,U_617)
| ? [U_625] :
( ~ in(ordered_pair(sK110(U_619,U_618,U_617),U_625),U_619)
& in(ordered_pair(apply(U_617,sK110(U_619,U_618,U_617)),apply(U_617,U_625)),U_618)
& in(U_625,relation_field(U_619))
& in(sK110(U_619,U_618,U_617),relation_field(U_619)) )
| ( ( ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619)) )
& in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619) )
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619) )
& ( ( ! [U_623,U_621] :
( in(ordered_pair(U_623,U_621),U_619)
| ~ in(ordered_pair(apply(U_617,U_623),apply(U_617,U_621)),U_618)
| ~ in(U_621,relation_field(U_619))
| ~ in(U_623,relation_field(U_619)) )
& ! [U_622,U_620] :
( ( in(ordered_pair(apply(U_617,U_622),apply(U_617,U_620)),U_618)
& in(U_620,relation_field(U_619))
& in(U_622,relation_field(U_619)) )
| ~ in(ordered_pair(U_622,U_620),U_619) )
& one_to_one(U_617)
& relation_rng(U_617) = relation_field(U_618)
& relation_dom(U_617) = relation_field(U_619) )
| ~ relation_isomorphism(U_619,U_618,U_617) ) )
| ~ function(U_617)
| ~ relation(U_617) )
| ~ relation(U_618) )
| ~ relation(U_619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_627,sK110(U_619,U_618,U_617))],[f_101_5]) ).
fof(f_101_7,plain,
! [U_619] :
( ! [U_618] :
( ! [U_617] :
( ( ( relation_isomorphism(U_619,U_618,U_617)
| ( ~ in(ordered_pair(sK110(U_619,U_618,U_617),sK111(U_619,U_618,U_617)),U_619)
& in(ordered_pair(apply(U_617,sK110(U_619,U_618,U_617)),apply(U_617,sK111(U_619,U_618,U_617))),U_618)
& in(sK111(U_619,U_618,U_617),relation_field(U_619))
& in(sK110(U_619,U_618,U_617),relation_field(U_619)) )
| ( ( ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619)) )
& in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619) )
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619) )
& ( ( ! [U_623,U_621] :
( in(ordered_pair(U_623,U_621),U_619)
| ~ in(ordered_pair(apply(U_617,U_623),apply(U_617,U_621)),U_618)
| ~ in(U_621,relation_field(U_619))
| ~ in(U_623,relation_field(U_619)) )
& ! [U_622,U_620] :
( ( in(ordered_pair(apply(U_617,U_622),apply(U_617,U_620)),U_618)
& in(U_620,relation_field(U_619))
& in(U_622,relation_field(U_619)) )
| ~ in(ordered_pair(U_622,U_620),U_619) )
& one_to_one(U_617)
& relation_rng(U_617) = relation_field(U_618)
& relation_dom(U_617) = relation_field(U_619) )
| ~ relation_isomorphism(U_619,U_618,U_617) ) )
| ~ function(U_617)
| ~ relation(U_617) )
| ~ relation(U_618) )
| ~ relation(U_619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_625,sK111(U_619,U_618,U_617))],[f_101_6]) ).
cnf(f_101_8,plain,
( relation_dom(U_617) = relation_field(U_619)
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_9,plain,
( relation_rng(U_617) = relation_field(U_618)
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_10,plain,
( one_to_one(U_617)
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_11,plain,
( in(U_622,relation_field(U_619))
| ~ in(ordered_pair(U_622,U_620),U_619)
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_12,plain,
( in(U_620,relation_field(U_619))
| ~ in(ordered_pair(U_622,U_620),U_619)
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_13,plain,
( in(ordered_pair(apply(U_617,U_622),apply(U_617,U_620)),U_618)
| ~ in(ordered_pair(U_622,U_620),U_619)
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_14,plain,
( in(ordered_pair(U_623,U_621),U_619)
| ~ in(ordered_pair(apply(U_617,U_623),apply(U_617,U_621)),U_618)
| ~ in(U_621,relation_field(U_619))
| ~ in(U_623,relation_field(U_619))
| ~ relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_15,plain,
( in(sK110(U_619,U_618,U_617),relation_field(U_619))
| in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619)
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_16,plain,
( in(sK111(U_619,U_618,U_617),relation_field(U_619))
| in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619)
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_17,plain,
( in(ordered_pair(apply(U_617,sK110(U_619,U_618,U_617)),apply(U_617,sK111(U_619,U_618,U_617))),U_618)
| in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619)
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_18,plain,
( ~ in(ordered_pair(sK110(U_619,U_618,U_617),sK111(U_619,U_618,U_617)),U_619)
| in(ordered_pair(sK108(U_619,U_618,U_617),sK109(U_619,U_618,U_617)),U_619)
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_19,plain,
( in(sK110(U_619,U_618,U_617),relation_field(U_619))
| ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619))
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_20,plain,
( in(sK111(U_619,U_618,U_617),relation_field(U_619))
| ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619))
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_21,plain,
( in(ordered_pair(apply(U_617,sK110(U_619,U_618,U_617)),apply(U_617,sK111(U_619,U_618,U_617))),U_618)
| ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619))
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
cnf(f_101_22,plain,
( ~ in(ordered_pair(sK110(U_619,U_618,U_617),sK111(U_619,U_618,U_617)),U_619)
| ~ in(ordered_pair(apply(U_617,sK108(U_619,U_618,U_617)),apply(U_617,sK109(U_619,U_618,U_617))),U_618)
| ~ in(sK109(U_619,U_618,U_617),relation_field(U_619))
| ~ in(sK108(U_619,U_618,U_617),relation_field(U_619))
| ~ one_to_one(U_617)
| relation_rng(U_617) != relation_field(U_618)
| relation_dom(U_617) != relation_field(U_619)
| relation_isomorphism(U_619,U_618,U_617)
| ~ function(U_617)
| ~ relation(U_617)
| ~ relation(U_618)
| ~ relation(U_619) ),
inference(clausify,[status(thm)],[f_101_7]) ).
fof(f_102_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_102_2,plain,
! [U_629,U_628] :
( ( disjoint(U_629,U_628)
| set_intersection2(U_629,U_628) != empty_set )
& ( set_intersection2(U_629,U_628) = empty_set
| ~ disjoint(U_629,U_628) ) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( ! [U_633,U_631] :
( disjoint(U_633,U_631)
| set_intersection2(U_633,U_631) != empty_set )
& ! [U_632,U_630] :
( set_intersection2(U_632,U_630) = empty_set
| ~ disjoint(U_632,U_630) ) ),
inference(miniscope,[status(thm)],[f_102_2]) ).
cnf(f_102_4,plain,
( set_intersection2(U_632,U_630) = empty_set
| ~ disjoint(U_632,U_630) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( disjoint(U_633,U_631)
| set_intersection2(U_633,U_631) != empty_set ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_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_103_2,plain,
! [U_638] :
( ( ( one_to_one(U_638)
| ? [U_637,U_636] :
( U_637 != U_636
& apply(U_638,U_637) = apply(U_638,U_636)
& in(U_636,relation_dom(U_638))
& in(U_637,relation_dom(U_638)) ) )
& ( ! [U_635,U_634] :
( U_635 = U_634
| apply(U_638,U_635) != apply(U_638,U_634)
| ~ in(U_634,relation_dom(U_638))
| ~ in(U_635,relation_dom(U_638)) )
| ~ one_to_one(U_638) ) )
| ~ function(U_638)
| ~ relation(U_638) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_638] :
( ( ( one_to_one(U_638)
| ? [U_636] :
( sK112(U_638) != U_636
& apply(U_638,sK112(U_638)) = apply(U_638,U_636)
& in(U_636,relation_dom(U_638))
& in(sK112(U_638),relation_dom(U_638)) ) )
& ( ! [U_635,U_634] :
( U_635 = U_634
| apply(U_638,U_635) != apply(U_638,U_634)
| ~ in(U_634,relation_dom(U_638))
| ~ in(U_635,relation_dom(U_638)) )
| ~ one_to_one(U_638) ) )
| ~ function(U_638)
| ~ relation(U_638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_637,sK112(U_638))],[f_103_2]) ).
fof(f_103_4,plain,
! [U_638] :
( ( ( one_to_one(U_638)
| ( sK112(U_638) != sK113(U_638)
& apply(U_638,sK112(U_638)) = apply(U_638,sK113(U_638))
& in(sK113(U_638),relation_dom(U_638))
& in(sK112(U_638),relation_dom(U_638)) ) )
& ( ! [U_635,U_634] :
( U_635 = U_634
| apply(U_638,U_635) != apply(U_638,U_634)
| ~ in(U_634,relation_dom(U_638))
| ~ in(U_635,relation_dom(U_638)) )
| ~ one_to_one(U_638) ) )
| ~ function(U_638)
| ~ relation(U_638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_636,sK113(U_638))],[f_103_3]) ).
cnf(f_103_5,plain,
( U_635 = U_634
| apply(U_638,U_635) != apply(U_638,U_634)
| ~ in(U_634,relation_dom(U_638))
| ~ in(U_635,relation_dom(U_638))
| ~ one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_6,plain,
( in(sK112(U_638),relation_dom(U_638))
| one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_7,plain,
( in(sK113(U_638),relation_dom(U_638))
| one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_8,plain,
( apply(U_638,sK112(U_638)) = apply(U_638,sK113(U_638))
| one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_9,plain,
( sK112(U_638) != sK113(U_638)
| one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_103_4]) ).
fof(f_104_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_104_2,plain,
! [U_643] :
( ( ( meet_absorbing(U_643)
| ? [U_642] :
( ? [U_641] :
( join(U_643,meet(U_643,U_642,U_641),U_641) != U_641
& element(U_641,the_carrier(U_643)) )
& element(U_642,the_carrier(U_643)) ) )
& ( ! [U_640] :
( ! [U_639] :
( join(U_643,meet(U_643,U_640,U_639),U_639) = U_639
| ~ element(U_639,the_carrier(U_643)) )
| ~ element(U_640,the_carrier(U_643)) )
| ~ meet_absorbing(U_643) ) )
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_643] :
( ( ( meet_absorbing(U_643)
| ( ? [U_641] :
( join(U_643,meet(U_643,sK114(U_643),U_641),U_641) != U_641
& element(U_641,the_carrier(U_643)) )
& element(sK114(U_643),the_carrier(U_643)) ) )
& ( ! [U_640] :
( ! [U_639] :
( join(U_643,meet(U_643,U_640,U_639),U_639) = U_639
| ~ element(U_639,the_carrier(U_643)) )
| ~ element(U_640,the_carrier(U_643)) )
| ~ meet_absorbing(U_643) ) )
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_642,sK114(U_643))],[f_104_2]) ).
fof(f_104_4,plain,
! [U_643] :
( ( ( meet_absorbing(U_643)
| ( join(U_643,meet(U_643,sK114(U_643),sK115(U_643)),sK115(U_643)) != sK115(U_643)
& element(sK115(U_643),the_carrier(U_643))
& element(sK114(U_643),the_carrier(U_643)) ) )
& ( ! [U_640] :
( ! [U_639] :
( join(U_643,meet(U_643,U_640,U_639),U_639) = U_639
| ~ element(U_639,the_carrier(U_643)) )
| ~ element(U_640,the_carrier(U_643)) )
| ~ meet_absorbing(U_643) ) )
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_641,sK115(U_643))],[f_104_3]) ).
cnf(f_104_5,plain,
( join(U_643,meet(U_643,U_640,U_639),U_639) = U_639
| ~ element(U_639,the_carrier(U_643))
| ~ element(U_640,the_carrier(U_643))
| ~ meet_absorbing(U_643)
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(clausify,[status(thm)],[f_104_4]) ).
cnf(f_104_6,plain,
( element(sK114(U_643),the_carrier(U_643))
| meet_absorbing(U_643)
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(clausify,[status(thm)],[f_104_4]) ).
cnf(f_104_7,plain,
( element(sK115(U_643),the_carrier(U_643))
| meet_absorbing(U_643)
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(clausify,[status(thm)],[f_104_4]) ).
cnf(f_104_8,plain,
( join(U_643,meet(U_643,sK114(U_643),sK115(U_643)),sK115(U_643)) != sK115(U_643)
| meet_absorbing(U_643)
| ~ latt_str(U_643)
| empty_carrier(U_643) ),
inference(clausify,[status(thm)],[f_104_4]) ).
fof(f_105_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_105_2,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ? [U_651,U_650] :
( ( ~ in(ordered_pair(U_651,U_650),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,U_650),U_653)
& in(ordered_pair(U_651,U_649),U_654) ) )
| ( ! [U_648] :
( ~ in(ordered_pair(U_648,U_650),U_653)
| ~ in(ordered_pair(U_651,U_648),U_654) )
& in(ordered_pair(U_651,U_650),U_652) ) ) )
& ( ! [U_647,U_646] :
( ( in(ordered_pair(U_647,U_646),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_646),U_653)
| ~ in(ordered_pair(U_647,U_645),U_654) ) )
& ( ? [U_644] :
( in(ordered_pair(U_644,U_646),U_653)
& in(ordered_pair(U_647,U_644),U_654) )
| ~ in(ordered_pair(U_647,U_646),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ? [U_662,U_660] :
( ~ in(ordered_pair(U_662,U_660),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,U_660),U_653)
& in(ordered_pair(U_662,U_649),U_654) ) )
| ? [U_661,U_659] :
( ! [U_648] :
( ~ in(ordered_pair(U_648,U_659),U_653)
| ~ in(ordered_pair(U_661,U_648),U_654) )
& in(ordered_pair(U_661,U_659),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ? [U_644] :
( in(ordered_pair(U_644,U_655),U_653)
& in(ordered_pair(U_657,U_644),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(miniscope,[status(thm)],[f_105_2]) ).
fof(f_105_4,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ? [U_662,U_660] :
( ~ in(ordered_pair(U_662,U_660),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,U_660),U_653)
& in(ordered_pair(U_662,U_649),U_654) ) )
| ? [U_661,U_659] :
( ! [U_648] :
( ~ in(ordered_pair(U_648,U_659),U_653)
| ~ in(ordered_pair(U_661,U_648),U_654) )
& in(ordered_pair(U_661,U_659),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
& in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_644,sK116(U_654,U_653,U_652,U_657,U_655))],[f_105_3]) ).
fof(f_105_5,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ? [U_662,U_660] :
( ~ in(ordered_pair(U_662,U_660),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,U_660),U_653)
& in(ordered_pair(U_662,U_649),U_654) ) )
| ? [U_659] :
( ! [U_648] :
( ~ in(ordered_pair(U_648,U_659),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654) )
& in(ordered_pair(sK117(U_654,U_653,U_652),U_659),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
& in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_661,sK117(U_654,U_653,U_652))],[f_105_4]) ).
fof(f_105_6,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ? [U_662,U_660] :
( ~ in(ordered_pair(U_662,U_660),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,U_660),U_653)
& in(ordered_pair(U_662,U_649),U_654) ) )
| ( ! [U_648] :
( ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654) )
& in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
& in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_659,sK118(U_654,U_653,U_652))],[f_105_5]) ).
fof(f_105_7,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ? [U_660] :
( ~ in(ordered_pair(sK119(U_654,U_653,U_652),U_660),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,U_660),U_653)
& in(ordered_pair(sK119(U_654,U_653,U_652),U_649),U_654) ) )
| ( ! [U_648] :
( ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654) )
& in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
& in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_662,sK119(U_654,U_653,U_652))],[f_105_6]) ).
fof(f_105_8,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ( ~ in(ordered_pair(sK119(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_652)
& ? [U_649] :
( in(ordered_pair(U_649,sK120(U_654,U_653,U_652)),U_653)
& in(ordered_pair(sK119(U_654,U_653,U_652),U_649),U_654) ) )
| ( ! [U_648] :
( ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654) )
& in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
& in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_660,sK120(U_654,U_653,U_652))],[f_105_7]) ).
fof(f_105_9,plain,
! [U_654] :
( ! [U_653] :
( ! [U_652] :
( ( ( U_652 = relation_composition(U_654,U_653)
| ( ~ in(ordered_pair(sK119(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_652)
& in(ordered_pair(sK121(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_653)
& in(ordered_pair(sK119(U_654,U_653,U_652),sK121(U_654,U_653,U_652)),U_654) )
| ( ! [U_648] :
( ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654) )
& in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652) ) )
& ( ( ! [U_658,U_656] :
( in(ordered_pair(U_658,U_656),U_652)
| ! [U_645] :
( ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654) ) )
& ! [U_657,U_655] :
( ( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
& in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654) )
| ~ in(ordered_pair(U_657,U_655),U_652) ) )
| U_652 != relation_composition(U_654,U_653) ) )
| ~ relation(U_652) )
| ~ relation(U_653) )
| ~ relation(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_649,sK121(U_654,U_653,U_652))],[f_105_8]) ).
cnf(f_105_10,plain,
( in(ordered_pair(U_657,sK116(U_654,U_653,U_652,U_657,U_655)),U_654)
| ~ in(ordered_pair(U_657,U_655),U_652)
| U_652 != relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_11,plain,
( in(ordered_pair(sK116(U_654,U_653,U_652,U_657,U_655),U_655),U_653)
| ~ in(ordered_pair(U_657,U_655),U_652)
| U_652 != relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_12,plain,
( in(ordered_pair(U_658,U_656),U_652)
| ~ in(ordered_pair(U_645,U_656),U_653)
| ~ in(ordered_pair(U_658,U_645),U_654)
| U_652 != relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_13,plain,
( in(ordered_pair(sK119(U_654,U_653,U_652),sK121(U_654,U_653,U_652)),U_654)
| in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652)
| U_652 = relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_14,plain,
( in(ordered_pair(sK121(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_653)
| in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652)
| U_652 = relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_15,plain,
( ~ in(ordered_pair(sK119(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_652)
| in(ordered_pair(sK117(U_654,U_653,U_652),sK118(U_654,U_653,U_652)),U_652)
| U_652 = relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_16,plain,
( in(ordered_pair(sK119(U_654,U_653,U_652),sK121(U_654,U_653,U_652)),U_654)
| ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654)
| U_652 = relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_17,plain,
( in(ordered_pair(sK121(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654)
| U_652 = relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
cnf(f_105_18,plain,
( ~ in(ordered_pair(sK119(U_654,U_653,U_652),sK120(U_654,U_653,U_652)),U_652)
| ~ in(ordered_pair(U_648,sK118(U_654,U_653,U_652)),U_653)
| ~ in(ordered_pair(sK117(U_654,U_653,U_652),U_648),U_654)
| U_652 = relation_composition(U_654,U_653)
| ~ relation(U_652)
| ~ relation(U_653)
| ~ relation(U_654) ),
inference(clausify,[status(thm)],[f_105_9]) ).
fof(f_106_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_106_2,plain,
! [U_670] :
( ! [U_669] :
( ( is_transitive_in(U_670,U_669)
| ? [U_668,U_667,U_666] :
( ~ in(ordered_pair(U_668,U_666),U_670)
& in(ordered_pair(U_667,U_666),U_670)
& in(ordered_pair(U_668,U_667),U_670)
& in(U_666,U_669)
& in(U_667,U_669)
& in(U_668,U_669) ) )
& ( ! [U_665,U_664,U_663] :
( in(ordered_pair(U_665,U_663),U_670)
| ~ in(ordered_pair(U_664,U_663),U_670)
| ~ in(ordered_pair(U_665,U_664),U_670)
| ~ in(U_663,U_669)
| ~ in(U_664,U_669)
| ~ in(U_665,U_669) )
| ~ is_transitive_in(U_670,U_669) ) )
| ~ relation(U_670) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_670] :
( ( ! [U_672] :
( is_transitive_in(U_670,U_672)
| ? [U_668,U_667,U_666] :
( ~ in(ordered_pair(U_668,U_666),U_670)
& in(ordered_pair(U_667,U_666),U_670)
& in(ordered_pair(U_668,U_667),U_670)
& in(U_666,U_672)
& in(U_667,U_672)
& in(U_668,U_672) ) )
& ! [U_671] :
( ! [U_665,U_664,U_663] :
( in(ordered_pair(U_665,U_663),U_670)
| ~ in(ordered_pair(U_664,U_663),U_670)
| ~ in(ordered_pair(U_665,U_664),U_670)
| ~ in(U_663,U_671)
| ~ in(U_664,U_671)
| ~ in(U_665,U_671) )
| ~ is_transitive_in(U_670,U_671) ) )
| ~ relation(U_670) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
! [U_670] :
( ( ! [U_672] :
( is_transitive_in(U_670,U_672)
| ? [U_667,U_666] :
( ~ in(ordered_pair(sK122(U_670,U_672),U_666),U_670)
& in(ordered_pair(U_667,U_666),U_670)
& in(ordered_pair(sK122(U_670,U_672),U_667),U_670)
& in(U_666,U_672)
& in(U_667,U_672)
& in(sK122(U_670,U_672),U_672) ) )
& ! [U_671] :
( ! [U_665,U_664,U_663] :
( in(ordered_pair(U_665,U_663),U_670)
| ~ in(ordered_pair(U_664,U_663),U_670)
| ~ in(ordered_pair(U_665,U_664),U_670)
| ~ in(U_663,U_671)
| ~ in(U_664,U_671)
| ~ in(U_665,U_671) )
| ~ is_transitive_in(U_670,U_671) ) )
| ~ relation(U_670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_668,sK122(U_670,U_672))],[f_106_3]) ).
fof(f_106_5,plain,
! [U_670] :
( ( ! [U_672] :
( is_transitive_in(U_670,U_672)
| ? [U_666] :
( ~ in(ordered_pair(sK122(U_670,U_672),U_666),U_670)
& in(ordered_pair(sK123(U_670,U_672),U_666),U_670)
& in(ordered_pair(sK122(U_670,U_672),sK123(U_670,U_672)),U_670)
& in(U_666,U_672)
& in(sK123(U_670,U_672),U_672)
& in(sK122(U_670,U_672),U_672) ) )
& ! [U_671] :
( ! [U_665,U_664,U_663] :
( in(ordered_pair(U_665,U_663),U_670)
| ~ in(ordered_pair(U_664,U_663),U_670)
| ~ in(ordered_pair(U_665,U_664),U_670)
| ~ in(U_663,U_671)
| ~ in(U_664,U_671)
| ~ in(U_665,U_671) )
| ~ is_transitive_in(U_670,U_671) ) )
| ~ relation(U_670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_667,sK123(U_670,U_672))],[f_106_4]) ).
fof(f_106_6,plain,
! [U_670] :
( ( ! [U_672] :
( is_transitive_in(U_670,U_672)
| ( ~ in(ordered_pair(sK122(U_670,U_672),sK124(U_670,U_672)),U_670)
& in(ordered_pair(sK123(U_670,U_672),sK124(U_670,U_672)),U_670)
& in(ordered_pair(sK122(U_670,U_672),sK123(U_670,U_672)),U_670)
& in(sK124(U_670,U_672),U_672)
& in(sK123(U_670,U_672),U_672)
& in(sK122(U_670,U_672),U_672) ) )
& ! [U_671] :
( ! [U_665,U_664,U_663] :
( in(ordered_pair(U_665,U_663),U_670)
| ~ in(ordered_pair(U_664,U_663),U_670)
| ~ in(ordered_pair(U_665,U_664),U_670)
| ~ in(U_663,U_671)
| ~ in(U_664,U_671)
| ~ in(U_665,U_671) )
| ~ is_transitive_in(U_670,U_671) ) )
| ~ relation(U_670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_666,sK124(U_670,U_672))],[f_106_5]) ).
cnf(f_106_7,plain,
( in(ordered_pair(U_665,U_663),U_670)
| ~ in(ordered_pair(U_664,U_663),U_670)
| ~ in(ordered_pair(U_665,U_664),U_670)
| ~ in(U_663,U_671)
| ~ in(U_664,U_671)
| ~ in(U_665,U_671)
| ~ is_transitive_in(U_670,U_671)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
cnf(f_106_8,plain,
( in(sK122(U_670,U_672),U_672)
| is_transitive_in(U_670,U_672)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
cnf(f_106_9,plain,
( in(sK123(U_670,U_672),U_672)
| is_transitive_in(U_670,U_672)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
cnf(f_106_10,plain,
( in(sK124(U_670,U_672),U_672)
| is_transitive_in(U_670,U_672)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
cnf(f_106_11,plain,
( in(ordered_pair(sK122(U_670,U_672),sK123(U_670,U_672)),U_670)
| is_transitive_in(U_670,U_672)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
cnf(f_106_12,plain,
( in(ordered_pair(sK123(U_670,U_672),sK124(U_670,U_672)),U_670)
| is_transitive_in(U_670,U_672)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
cnf(f_106_13,plain,
( ~ in(ordered_pair(sK122(U_670,U_672),sK124(U_670,U_672)),U_670)
| is_transitive_in(U_670,U_672)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_106_6]) ).
fof(f_107_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_107_2,plain,
! [U_677,U_676] :
( ! [U_675] :
( ( ( U_675 = complements_of_subsets(U_677,U_676)
| ? [U_674] :
( ( ( ~ in(U_674,U_675)
& in(subset_complement(U_677,U_674),U_676) )
| ( ~ in(subset_complement(U_677,U_674),U_676)
& in(U_674,U_675) ) )
& element(U_674,powerset(U_677)) ) )
& ( ! [U_673] :
( ( ( in(U_673,U_675)
| ~ in(subset_complement(U_677,U_673),U_676) )
& ( in(subset_complement(U_677,U_673),U_676)
| ~ in(U_673,U_675) ) )
| ~ element(U_673,powerset(U_677)) )
| U_675 != complements_of_subsets(U_677,U_676) ) )
| ~ element(U_675,powerset(powerset(U_677))) )
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_677,U_676] :
( ! [U_675] :
( ( ( U_675 = complements_of_subsets(U_677,U_676)
| ( ( ( ~ in(sK125(U_677,U_676,U_675),U_675)
& in(subset_complement(U_677,sK125(U_677,U_676,U_675)),U_676) )
| ( ~ in(subset_complement(U_677,sK125(U_677,U_676,U_675)),U_676)
& in(sK125(U_677,U_676,U_675),U_675) ) )
& element(sK125(U_677,U_676,U_675),powerset(U_677)) ) )
& ( ! [U_673] :
( ( ( in(U_673,U_675)
| ~ in(subset_complement(U_677,U_673),U_676) )
& ( in(subset_complement(U_677,U_673),U_676)
| ~ in(U_673,U_675) ) )
| ~ element(U_673,powerset(U_677)) )
| U_675 != complements_of_subsets(U_677,U_676) ) )
| ~ element(U_675,powerset(powerset(U_677))) )
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_674,sK125(U_677,U_676,U_675))],[f_107_2]) ).
cnf(f_107_4,plain,
( in(subset_complement(U_677,U_673),U_676)
| ~ in(U_673,U_675)
| ~ element(U_673,powerset(U_677))
| U_675 != complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_5,plain,
( in(U_673,U_675)
| ~ in(subset_complement(U_677,U_673),U_676)
| ~ element(U_673,powerset(U_677))
| U_675 != complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_6,plain,
( element(sK125(U_677,U_676,U_675),powerset(U_677))
| U_675 = complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_7,plain,
( in(subset_complement(U_677,sK125(U_677,U_676,U_675)),U_676)
| in(sK125(U_677,U_676,U_675),U_675)
| U_675 = complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_8,plain,
( ~ in(sK125(U_677,U_676,U_675),U_675)
| in(sK125(U_677,U_676,U_675),U_675)
| U_675 = complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_9,plain,
( in(subset_complement(U_677,sK125(U_677,U_676,U_675)),U_676)
| ~ in(subset_complement(U_677,sK125(U_677,U_676,U_675)),U_676)
| U_675 = complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_10,plain,
( ~ in(sK125(U_677,U_676,U_675),U_675)
| ~ in(subset_complement(U_677,sK125(U_677,U_676,U_675)),U_676)
| U_675 = complements_of_subsets(U_677,U_676)
| ~ element(U_675,powerset(powerset(U_677)))
| ~ element(U_676,powerset(powerset(U_677))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_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_108_2,plain,
! [U_679,U_678] :
( ( proper_subset(U_679,U_678)
| U_679 = U_678
| ~ subset(U_679,U_678) )
& ( ( U_679 != U_678
& subset(U_679,U_678) )
| ~ proper_subset(U_679,U_678) ) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
( ! [U_683,U_681] :
( proper_subset(U_683,U_681)
| U_683 = U_681
| ~ subset(U_683,U_681) )
& ! [U_682,U_680] :
( ( U_682 != U_680
& subset(U_682,U_680) )
| ~ proper_subset(U_682,U_680) ) ),
inference(miniscope,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( subset(U_682,U_680)
| ~ proper_subset(U_682,U_680) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( U_682 != U_680
| ~ proper_subset(U_682,U_680) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_6,plain,
( proper_subset(U_683,U_681)
| U_683 = U_681
| ~ subset(U_683,U_681) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_684] :
( function_inverse(U_684) = relation_inverse(U_684)
| ~ one_to_one(U_684)
| ~ function(U_684)
| ~ relation(U_684) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( function_inverse(U_684) = relation_inverse(U_684)
| ~ one_to_one(U_684)
| ~ function(U_684)
| ~ relation(U_684) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_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_110_2,plain,
! [U_685] :
( ( ( reflexive(U_685)
| ~ is_reflexive_in(U_685,relation_field(U_685)) )
& ( is_reflexive_in(U_685,relation_field(U_685))
| ~ reflexive(U_685) ) )
| ~ relation(U_685) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( is_reflexive_in(U_685,relation_field(U_685))
| ~ reflexive(U_685)
| ~ relation(U_685) ),
inference(clausify,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( reflexive(U_685)
| ~ is_reflexive_in(U_685,relation_field(U_685))
| ~ relation(U_685) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_111_2,plain,
$true,
inference(clausify,[status(thm)],[f_111_1]) ).
fof(f_112_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_binop_1]) ).
cnf(f_112_2,plain,
$true,
inference(clausify,[status(thm)],[f_112_1]) ).
fof(f_113_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
cnf(f_113_2,plain,
$true,
inference(clausify,[status(thm)],[f_113_1]) ).
fof(f_114_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_114_2,plain,
$true,
inference(clausify,[status(thm)],[f_114_1]) ).
fof(f_115_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_115_2,plain,
! [U_688,U_687,U_686] :
( element(join(U_688,U_687,U_686),the_carrier(U_688))
| ~ element(U_686,the_carrier(U_688))
| ~ element(U_687,the_carrier(U_688))
| ~ join_semilatt_str(U_688)
| empty_carrier(U_688) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( element(join(U_688,U_687,U_686),the_carrier(U_688))
| ~ element(U_686,the_carrier(U_688))
| ~ element(U_687,the_carrier(U_688))
| ~ join_semilatt_str(U_688)
| empty_carrier(U_688) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_mcart_1]) ).
cnf(f_116_2,plain,
$true,
inference(clausify,[status(thm)],[f_116_1]) ).
fof(f_117_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
cnf(f_117_2,plain,
$true,
inference(clausify,[status(thm)],[f_117_1]) ).
fof(f_118_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_118_2,plain,
$true,
inference(clausify,[status(thm)],[f_118_1]) ).
fof(f_119_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_119_2,plain,
$true,
inference(clausify,[status(thm)],[f_119_1]) ).
fof(f_120_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_120_2,plain,
$true,
inference(clausify,[status(thm)],[f_120_1]) ).
fof(f_121_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
cnf(f_121_2,plain,
$true,
inference(clausify,[status(thm)],[f_121_1]) ).
fof(f_122_1,plain,
! [A] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_122_2,plain,
! [U_689] : relation(inclusion_relation(U_689)),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
relation(inclusion_relation(U_689)),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_123_2,plain,
$true,
inference(clausify,[status(thm)],[f_123_1]) ).
fof(f_124_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_124_2,plain,
$true,
inference(clausify,[status(thm)],[f_124_1]) ).
fof(f_125_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_125_2,plain,
! [U_695,U_694,U_693,U_692,U_691,U_690] :
( element(apply_binary_as_element(U_695,U_694,U_693,U_692,U_691,U_690),U_693)
| ~ element(U_690,U_694)
| ~ element(U_691,U_695)
| ~ relation_of2(U_692,cartesian_product2(U_695,U_694),U_693)
| ~ quasi_total(U_692,cartesian_product2(U_695,U_694),U_693)
| ~ function(U_692)
| empty(U_694)
| empty(U_695) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( element(apply_binary_as_element(U_695,U_694,U_693,U_692,U_691,U_690),U_693)
| ~ element(U_690,U_694)
| ~ element(U_691,U_695)
| ~ relation_of2(U_692,cartesian_product2(U_695,U_694),U_693)
| ~ quasi_total(U_692,cartesian_product2(U_695,U_694),U_693)
| ~ function(U_692)
| empty(U_694)
| empty(U_695) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_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_126_2,plain,
! [U_696] :
( ( function(function_inverse(U_696))
& relation(function_inverse(U_696)) )
| ~ function(U_696)
| ~ relation(U_696) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( relation(function_inverse(U_696))
| ~ function(U_696)
| ~ relation(U_696) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_4,plain,
( function(function_inverse(U_696))
| ~ function(U_696)
| ~ relation(U_696) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_699,U_698,U_697] :
( element(meet(U_699,U_698,U_697),the_carrier(U_699))
| ~ element(U_697,the_carrier(U_699))
| ~ element(U_698,the_carrier(U_699))
| ~ meet_semilatt_str(U_699)
| empty_carrier(U_699) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( element(meet(U_699,U_698,U_697),the_carrier(U_699))
| ~ element(U_697,the_carrier(U_699))
| ~ element(U_698,the_carrier(U_699))
| ~ meet_semilatt_str(U_699)
| empty_carrier(U_699) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_mcart_1]) ).
cnf(f_128_2,plain,
$true,
inference(clausify,[status(thm)],[f_128_1]) ).
fof(f_129_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_129_2,plain,
! [U_700] :
( element(cast_as_carrier_subset(U_700),powerset(the_carrier(U_700)))
| ~ one_sorted_str(U_700) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( element(cast_as_carrier_subset(U_700),powerset(the_carrier(U_700)))
| ~ one_sorted_str(U_700) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_130_2,plain,
$true,
inference(clausify,[status(thm)],[f_130_1]) ).
fof(f_131_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_131_2,plain,
! [U_701] : element(cast_to_subset(U_701),powerset(U_701)),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
element(cast_to_subset(U_701),powerset(U_701)),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_132_2,plain,
$true,
inference(clausify,[status(thm)],[f_132_1]) ).
fof(f_133_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_133_2,plain,
! [U_703,U_702] :
( relation(relation_restriction(U_703,U_702))
| ~ relation(U_703) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_703] :
( ! [U_702] : relation(relation_restriction(U_703,U_702))
| ~ relation(U_703) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
cnf(f_133_4,plain,
( relation(relation_restriction(U_703,U_702))
| ~ relation(U_703) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_134_2,plain,
$true,
inference(clausify,[status(thm)],[f_134_1]) ).
fof(f_135_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_135_2,plain,
$true,
inference(clausify,[status(thm)],[f_135_1]) ).
fof(f_136_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_136_2,plain,
! [U_706,U_705,U_704] :
( element(join_commut(U_706,U_705,U_704),the_carrier(U_706))
| ~ element(U_704,the_carrier(U_706))
| ~ element(U_705,the_carrier(U_706))
| ~ join_semilatt_str(U_706)
| ~ join_commutative(U_706)
| empty_carrier(U_706) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( element(join_commut(U_706,U_705,U_704),the_carrier(U_706))
| ~ element(U_704,the_carrier(U_706))
| ~ element(U_705,the_carrier(U_706))
| ~ join_semilatt_str(U_706)
| ~ join_commutative(U_706)
| empty_carrier(U_706) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_137_2,plain,
$true,
inference(clausify,[status(thm)],[f_137_1]) ).
fof(f_138_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_138_2,plain,
! [U_708,U_707] :
( element(subset_complement(U_708,U_707),powerset(U_708))
| ~ element(U_707,powerset(U_708)) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( element(subset_complement(U_708,U_707),powerset(U_708))
| ~ element(U_707,powerset(U_708)) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_139_2,plain,
$true,
inference(clausify,[status(thm)],[f_139_1]) ).
fof(f_140_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_140_2,plain,
$true,
inference(clausify,[status(thm)],[f_140_1]) ).
fof(f_141_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_141_2,plain,
! [U_711,U_710,U_709] :
( element(meet_commut(U_711,U_710,U_709),the_carrier(U_711))
| ~ element(U_709,the_carrier(U_711))
| ~ element(U_710,the_carrier(U_711))
| ~ meet_semilatt_str(U_711)
| ~ meet_commutative(U_711)
| empty_carrier(U_711) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( element(meet_commut(U_711,U_710,U_709),the_carrier(U_711))
| ~ element(U_709,the_carrier(U_711))
| ~ element(U_710,the_carrier(U_711))
| ~ meet_semilatt_str(U_711)
| ~ meet_commutative(U_711)
| empty_carrier(U_711) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_142_2,plain,
! [U_712] :
( relation(relation_inverse(U_712))
| ~ relation(U_712) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( relation(relation_inverse(U_712))
| ~ relation(U_712) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_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_143_2,plain,
! [U_715,U_714,U_713] :
( element(relation_dom_as_subset(U_715,U_714,U_713),powerset(U_715))
| ~ relation_of2(U_713,U_715,U_714) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( element(relation_dom_as_subset(U_715,U_714,U_713),powerset(U_715))
| ~ relation_of2(U_713,U_715,U_714) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_144_2,plain,
$true,
inference(clausify,[status(thm)],[f_144_1]) ).
fof(f_145_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_145_2,plain,
$true,
inference(clausify,[status(thm)],[f_145_1]) ).
fof(f_146_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k5_ordinal2]) ).
cnf(f_146_2,plain,
$true,
inference(clausify,[status(thm)],[f_146_1]) ).
fof(f_147_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_147_2,plain,
! [U_717,U_716] :
( relation(relation_composition(U_717,U_716))
| ~ relation(U_716)
| ~ relation(U_717) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( relation(relation_composition(U_717,U_716))
| ~ relation(U_716)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_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_148_2,plain,
! [U_720,U_719,U_718] :
( element(relation_rng_as_subset(U_720,U_719,U_718),powerset(U_719))
| ~ relation_of2(U_718,U_720,U_719) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( element(relation_rng_as_subset(U_720,U_719,U_718),powerset(U_719))
| ~ relation_of2(U_718,U_720,U_719) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_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_149_2,plain,
! [U_722,U_721] :
( element(union_of_subsets(U_722,U_721),powerset(U_722))
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( element(union_of_subsets(U_722,U_721),powerset(U_722))
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_150_2,plain,
! [U_723] : relation(identity_relation(U_723)),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
relation(identity_relation(U_723)),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_725,U_724] :
( element(meet_of_subsets(U_725,U_724),powerset(U_725))
| ~ element(U_724,powerset(powerset(U_725))) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( element(meet_of_subsets(U_725,U_724),powerset(U_725))
| ~ element(U_724,powerset(powerset(U_725))) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_728,U_727,U_726] :
( element(subset_difference(U_728,U_727,U_726),powerset(U_728))
| ~ element(U_726,powerset(U_728))
| ~ element(U_727,powerset(U_728)) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( element(subset_difference(U_728,U_727,U_726),powerset(U_728))
| ~ element(U_726,powerset(U_728))
| ~ element(U_727,powerset(U_728)) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_153_2,plain,
! [U_730,U_729] :
( relation(relation_dom_restriction(U_730,U_729))
| ~ relation(U_730) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_730] :
( ! [U_729] : relation(relation_dom_restriction(U_730,U_729))
| ~ relation(U_730) ),
inference(miniscope,[status(thm)],[f_153_2]) ).
cnf(f_153_4,plain,
( relation(relation_dom_restriction(U_730,U_729))
| ~ relation(U_730) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_732,U_731] :
( element(complements_of_subsets(U_732,U_731),powerset(powerset(U_732)))
| ~ element(U_731,powerset(powerset(U_732))) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( element(complements_of_subsets(U_732,U_731),powerset(powerset(U_732)))
| ~ element(U_731,powerset(powerset(U_732))) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_155_2,plain,
! [U_734,U_733] :
( relation(relation_rng_restriction(U_734,U_733))
| ~ relation(U_733) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( relation(relation_rng_restriction(U_734,U_733))
| ~ relation(U_733) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_156_2,plain,
$true,
inference(clausify,[status(thm)],[f_156_1]) ).
fof(f_157_1,plain,
! [A] :
( one_sorted_str(A)
| ~ meet_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_157_2,plain,
! [U_735] :
( one_sorted_str(U_735)
| ~ meet_semilatt_str(U_735) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( one_sorted_str(U_735)
| ~ meet_semilatt_str(U_735) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_158_2,plain,
$true,
inference(clausify,[status(thm)],[f_158_1]) ).
fof(f_159_1,plain,
! [A] :
( one_sorted_str(A)
| ~ join_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_159_2,plain,
! [U_736] :
( one_sorted_str(U_736)
| ~ join_semilatt_str(U_736) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( one_sorted_str(U_736)
| ~ join_semilatt_str(U_736) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_160_2,plain,
! [U_737] :
( ( join_semilatt_str(U_737)
& meet_semilatt_str(U_737) )
| ~ latt_str(U_737) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( meet_semilatt_str(U_737)
| ~ latt_str(U_737) ),
inference(clausify,[status(thm)],[f_160_2]) ).
cnf(f_160_4,plain,
( join_semilatt_str(U_737)
| ~ latt_str(U_737) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_161_2,plain,
$true,
inference(clausify,[status(thm)],[f_161_1]) ).
fof(f_162_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_162_2,plain,
$true,
inference(clausify,[status(thm)],[f_162_1]) ).
fof(f_163_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_163_2,plain,
! [U_740,U_739,U_738] :
( element(U_738,powerset(cartesian_product2(U_740,U_739)))
| ~ relation_of2_as_subset(U_738,U_740,U_739) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( element(U_738,powerset(cartesian_product2(U_740,U_739)))
| ~ relation_of2_as_subset(U_738,U_740,U_739) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_741] :
( ( relation_of2_as_subset(the_L_meet(U_741),cartesian_product2(the_carrier(U_741),the_carrier(U_741)),the_carrier(U_741))
& quasi_total(the_L_meet(U_741),cartesian_product2(the_carrier(U_741),the_carrier(U_741)),the_carrier(U_741))
& function(the_L_meet(U_741)) )
| ~ meet_semilatt_str(U_741) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( function(the_L_meet(U_741))
| ~ meet_semilatt_str(U_741) ),
inference(clausify,[status(thm)],[f_164_2]) ).
cnf(f_164_4,plain,
( quasi_total(the_L_meet(U_741),cartesian_product2(the_carrier(U_741),the_carrier(U_741)),the_carrier(U_741))
| ~ meet_semilatt_str(U_741) ),
inference(clausify,[status(thm)],[f_164_2]) ).
cnf(f_164_5,plain,
( relation_of2_as_subset(the_L_meet(U_741),cartesian_product2(the_carrier(U_741),the_carrier(U_741)),the_carrier(U_741))
| ~ meet_semilatt_str(U_741) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_165_2,plain,
$true,
inference(clausify,[status(thm)],[f_165_1]) ).
fof(f_166_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_166_2,plain,
! [U_742] :
( ( relation_of2_as_subset(the_L_join(U_742),cartesian_product2(the_carrier(U_742),the_carrier(U_742)),the_carrier(U_742))
& quasi_total(the_L_join(U_742),cartesian_product2(the_carrier(U_742),the_carrier(U_742)),the_carrier(U_742))
& function(the_L_join(U_742)) )
| ~ join_semilatt_str(U_742) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( function(the_L_join(U_742))
| ~ join_semilatt_str(U_742) ),
inference(clausify,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
( quasi_total(the_L_join(U_742),cartesian_product2(the_carrier(U_742),the_carrier(U_742)),the_carrier(U_742))
| ~ join_semilatt_str(U_742) ),
inference(clausify,[status(thm)],[f_166_2]) ).
cnf(f_166_5,plain,
( relation_of2_as_subset(the_L_join(U_742),cartesian_product2(the_carrier(U_742),the_carrier(U_742)),the_carrier(U_742))
| ~ join_semilatt_str(U_742) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
? [A] : meet_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_167_2,plain,
? [U_743] : meet_semilatt_str(U_743),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
meet_semilatt_str(sK126),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_743,sK126)],[f_167_2]) ).
cnf(f_167_4,plain,
meet_semilatt_str(sK126),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_168_2,plain,
? [U_744] : one_sorted_str(U_744),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
one_sorted_str(sK127),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_744,sK127)],[f_168_2]) ).
cnf(f_168_4,plain,
one_sorted_str(sK127),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
? [A] : join_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_169_2,plain,
? [U_745] : join_semilatt_str(U_745),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
join_semilatt_str(sK128),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_745,sK128)],[f_169_2]) ).
cnf(f_169_4,plain,
join_semilatt_str(sK128),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
? [A] : latt_str(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_170_2,plain,
? [U_746] : latt_str(U_746),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
latt_str(sK129),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_746,sK129)],[f_170_2]) ).
cnf(f_170_4,plain,
latt_str(sK129),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_171_2,plain,
! [U_749,U_748] :
? [U_747] : relation_of2(U_747,U_749,U_748),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_749,U_748] : relation_of2(sK130(U_749,U_748),U_749,U_748),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_747,sK130(U_749,U_748))],[f_171_2]) ).
cnf(f_171_4,plain,
relation_of2(sK130(U_749,U_748),U_749,U_748),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_172_2,plain,
! [U_751] :
? [U_750] : element(U_750,U_751),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_751] : element(sK131(U_751),U_751),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_750,sK131(U_751))],[f_172_2]) ).
cnf(f_172_4,plain,
element(sK131(U_751),U_751),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_173_2,plain,
! [U_754,U_753] :
? [U_752] : relation_of2_as_subset(U_752,U_754,U_753),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_754,U_753] : relation_of2_as_subset(sK132(U_754,U_753),U_754,U_753),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_752,sK132(U_754,U_753))],[f_173_2]) ).
cnf(f_173_4,plain,
relation_of2_as_subset(sK132(U_754,U_753),U_754,U_753),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(B) ),
inference(fof_nnf,[status(thm)],[fc10_finset_1]) ).
fof(f_174_2,plain,
! [U_756,U_755] :
( finite(set_intersection2(U_756,U_755))
| ~ finite(U_755) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( finite(set_intersection2(U_756,U_755))
| ~ finite(U_755) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_758,U_757] :
( ( relation(relation_composition(U_757,U_758))
& empty(relation_composition(U_757,U_758)) )
| ~ relation(U_757)
| ~ empty(U_758) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( empty(relation_composition(U_757,U_758))
| ~ relation(U_757)
| ~ empty(U_758) ),
inference(clausify,[status(thm)],[f_175_2]) ).
cnf(f_175_4,plain,
( relation(relation_composition(U_757,U_758))
| ~ relation(U_757)
| ~ empty(U_758) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc11_finset_1]) ).
fof(f_176_2,plain,
! [U_760,U_759] :
( finite(set_intersection2(U_760,U_759))
| ~ finite(U_760) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_760] :
( ! [U_759] : finite(set_intersection2(U_760,U_759))
| ~ finite(U_760) ),
inference(miniscope,[status(thm)],[f_176_2]) ).
cnf(f_176_4,plain,
( finite(set_intersection2(U_760,U_759))
| ~ finite(U_760) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_177_2,plain,
! [U_761] :
( ( relation(relation_inverse(U_761))
& empty(relation_inverse(U_761)) )
| ~ empty(U_761) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( empty(relation_inverse(U_761))
| ~ empty(U_761) ),
inference(clausify,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( relation(relation_inverse(U_761))
| ~ empty(U_761) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc12_finset_1]) ).
fof(f_178_2,plain,
! [U_763,U_762] :
( finite(set_difference(U_763,U_762))
| ~ finite(U_763) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_763] :
( ! [U_762] : finite(set_difference(U_763,U_762))
| ~ finite(U_763) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( finite(set_difference(U_763,U_762))
| ~ finite(U_763) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_179_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_179_1]) ).
cnf(f_179_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_179_1]) ).
fof(f_180_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_180_2,plain,
! [U_765,U_764] :
( finite(relation_image(U_765,U_764))
| ~ finite(U_764)
| ~ function(U_765)
| ~ relation(U_765) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( finite(relation_image(U_765,U_764))
| ~ finite(U_764)
| ~ function(U_765)
| ~ relation(U_765) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_767,U_766] :
( ( relation_empty_yielding(relation_dom_restriction(U_767,U_766))
& relation(relation_dom_restriction(U_767,U_766)) )
| ~ relation_empty_yielding(U_767)
| ~ relation(U_767) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_767] :
( ( ! [U_769] : relation_empty_yielding(relation_dom_restriction(U_767,U_769))
& ! [U_768] : relation(relation_dom_restriction(U_767,U_768)) )
| ~ relation_empty_yielding(U_767)
| ~ relation(U_767) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
cnf(f_181_4,plain,
( relation(relation_dom_restriction(U_767,U_768))
| ~ relation_empty_yielding(U_767)
| ~ relation(U_767) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_767,U_769))
| ~ relation_empty_yielding(U_767)
| ~ relation(U_767) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finset_1]) ).
fof(f_182_2,plain,
! [U_770] :
( finite(singleton(U_770))
& ~ empty(singleton(U_770)) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_772] : finite(singleton(U_772))
& ! [U_771] : ~ empty(singleton(U_771)) ),
inference(miniscope,[status(thm)],[f_182_2]) ).
cnf(f_182_4,plain,
~ empty(singleton(U_771)),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
finite(singleton(U_772)),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_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_183_2,plain,
! [U_773] :
( preboolean(powerset(U_773))
& diff_closed(powerset(U_773))
& cup_closed(powerset(U_773))
& ~ empty(powerset(U_773)) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_777] : preboolean(powerset(U_777))
& ! [U_776] : diff_closed(powerset(U_776))
& ! [U_775] : cup_closed(powerset(U_775))
& ! [U_774] : ~ empty(powerset(U_774)) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
~ empty(powerset(U_774)),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
cup_closed(powerset(U_775)),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_6,plain,
diff_closed(powerset(U_776)),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_7,plain,
preboolean(powerset(U_777)),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_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_184_2,plain,
! [U_779,U_778] :
( ( function(relation_composition(U_779,U_778))
& relation(relation_composition(U_779,U_778)) )
| ~ function(U_778)
| ~ relation(U_778)
| ~ function(U_779)
| ~ relation(U_779) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( relation(relation_composition(U_779,U_778))
| ~ function(U_778)
| ~ relation(U_778)
| ~ function(U_779)
| ~ relation(U_779) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( function(relation_composition(U_779,U_778))
| ~ function(U_778)
| ~ relation(U_778)
| ~ function(U_779)
| ~ relation(U_779) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_185_2,plain,
! [U_780] : ~ empty(succ(U_780)),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
~ empty(succ(U_780)),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(fof_nnf,[status(thm)],[fc1_ordinal2]) ).
cnf(f_186_2,plain,
epsilon_transitive(omega),
inference(clausify,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
epsilon_connected(omega),
inference(clausify,[status(thm)],[f_186_1]) ).
cnf(f_186_4,plain,
ordinal(omega),
inference(clausify,[status(thm)],[f_186_1]) ).
cnf(f_186_5,plain,
~ empty(omega),
inference(clausify,[status(thm)],[f_186_1]) ).
fof(f_187_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_187_2,plain,
! [U_782,U_781] :
( relation(set_intersection2(U_782,U_781))
| ~ relation(U_781)
| ~ relation(U_782) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( relation(set_intersection2(U_782,U_781))
| ~ relation(U_781)
| ~ relation(U_782) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_188_2,plain,
! [U_783] :
( ~ empty(the_carrier(U_783))
| ~ one_sorted_str(U_783)
| empty_carrier(U_783) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( ~ empty(the_carrier(U_783))
| ~ one_sorted_str(U_783)
| empty_carrier(U_783) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_189_2,plain,
! [U_784] : ~ empty(powerset(U_784)),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
~ empty(powerset(U_784)),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_190_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_190_1]) ).
fof(f_191_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_191_2,plain,
! [U_786,U_785] : ~ empty(ordered_pair(U_786,U_785)),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
~ empty(ordered_pair(U_786,U_785)),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_787] :
( ( natural(succ(U_787))
& ordinal(succ(U_787))
& epsilon_connected(succ(U_787))
& epsilon_transitive(succ(U_787))
& ~ empty(succ(U_787)) )
| ~ natural(U_787)
| ~ ordinal(U_787) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( ~ empty(succ(U_787))
| ~ natural(U_787)
| ~ ordinal(U_787) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( epsilon_transitive(succ(U_787))
| ~ natural(U_787)
| ~ ordinal(U_787) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_5,plain,
( epsilon_connected(succ(U_787))
| ~ natural(U_787)
| ~ ordinal(U_787) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_6,plain,
( ordinal(succ(U_787))
| ~ natural(U_787)
| ~ ordinal(U_787) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_7,plain,
( natural(succ(U_787))
| ~ natural(U_787)
| ~ ordinal(U_787) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_193_2,plain,
! [U_788] :
( function(identity_relation(U_788))
& relation(identity_relation(U_788)) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( ! [U_790] : function(identity_relation(U_790))
& ! [U_789] : relation(identity_relation(U_789)) ),
inference(miniscope,[status(thm)],[f_193_2]) ).
cnf(f_193_4,plain,
relation(identity_relation(U_789)),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_5,plain,
function(identity_relation(U_790)),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
cnf(f_194_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
cnf(f_194_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_194_1]) ).
fof(f_195_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_195_2,plain,
! [U_792,U_791] :
( relation(set_union2(U_792,U_791))
| ~ relation(U_791)
| ~ relation(U_792) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( relation(set_union2(U_792,U_791))
| ~ relation(U_791)
| ~ relation(U_792) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_196_2,plain,
! [U_793] : ~ empty(singleton(U_793)),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
~ empty(singleton(U_793)),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_197_2,plain,
! [U_795,U_794] :
( ~ empty(set_union2(U_795,U_794))
| empty(U_795) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_795] :
( ! [U_794] : ~ empty(set_union2(U_795,U_794))
| empty(U_795) ),
inference(miniscope,[status(thm)],[f_197_2]) ).
cnf(f_197_4,plain,
( ~ empty(set_union2(U_795,U_794))
| empty(U_795) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_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_198_2,plain,
! [U_796] :
( ( function(relation_inverse(U_796))
& relation(relation_inverse(U_796)) )
| ~ one_to_one(U_796)
| ~ function(U_796)
| ~ relation(U_796) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( relation(relation_inverse(U_796))
| ~ one_to_one(U_796)
| ~ function(U_796)
| ~ relation(U_796) ),
inference(clausify,[status(thm)],[f_198_2]) ).
cnf(f_198_4,plain,
( function(relation_inverse(U_796))
| ~ one_to_one(U_796)
| ~ function(U_796)
| ~ relation(U_796) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_797] :
( ( ordinal(succ(U_797))
& epsilon_connected(succ(U_797))
& epsilon_transitive(succ(U_797))
& ~ empty(succ(U_797)) )
| ~ ordinal(U_797) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( ~ empty(succ(U_797))
| ~ ordinal(U_797) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( epsilon_transitive(succ(U_797))
| ~ ordinal(U_797) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_199_5,plain,
( epsilon_connected(succ(U_797))
| ~ ordinal(U_797) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_199_6,plain,
( ordinal(succ(U_797))
| ~ ordinal(U_797) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_200_2,plain,
! [U_799,U_798] :
( relation(set_difference(U_799,U_798))
| ~ relation(U_798)
| ~ relation(U_799) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( relation(set_difference(U_799,U_798))
| ~ relation(U_798)
| ~ relation(U_799) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_201_2,plain,
! [U_801,U_800] : ~ empty(unordered_pair(U_801,U_800)),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
~ empty(unordered_pair(U_801,U_800)),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_202_2,plain,
! [U_803,U_802] :
( ~ empty(set_union2(U_802,U_803))
| empty(U_803) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_803] :
( ! [U_802] : ~ empty(set_union2(U_802,U_803))
| empty(U_803) ),
inference(miniscope,[status(thm)],[f_202_2]) ).
cnf(f_202_4,plain,
( ~ empty(set_union2(U_802,U_803))
| empty(U_803) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_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_203_2,plain,
! [U_805,U_804] :
( ( function(relation_dom_restriction(U_805,U_804))
& relation(relation_dom_restriction(U_805,U_804)) )
| ~ function(U_805)
| ~ relation(U_805) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_805] :
( ( ! [U_807] : function(relation_dom_restriction(U_805,U_807))
& ! [U_806] : relation(relation_dom_restriction(U_805,U_806)) )
| ~ function(U_805)
| ~ relation(U_805) ),
inference(miniscope,[status(thm)],[f_203_2]) ).
cnf(f_203_4,plain,
( relation(relation_dom_restriction(U_805,U_806))
| ~ function(U_805)
| ~ relation(U_805) ),
inference(clausify,[status(thm)],[f_203_3]) ).
cnf(f_203_5,plain,
( function(relation_dom_restriction(U_805,U_807))
| ~ function(U_805)
| ~ relation(U_805) ),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_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_204_2,plain,
! [U_808] :
( ( ordinal(union(U_808))
& epsilon_connected(union(U_808))
& epsilon_transitive(union(U_808)) )
| ~ ordinal(U_808) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( epsilon_transitive(union(U_808))
| ~ ordinal(U_808) ),
inference(clausify,[status(thm)],[f_204_2]) ).
cnf(f_204_4,plain,
( epsilon_connected(union(U_808))
| ~ ordinal(U_808) ),
inference(clausify,[status(thm)],[f_204_2]) ).
cnf(f_204_5,plain,
( ordinal(union(U_808))
| ~ ordinal(U_808) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_205_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_205_1]) ).
fof(f_206_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_206_2,plain,
! [U_810,U_809] :
( ~ empty(cartesian_product2(U_810,U_809))
| empty(U_809)
| empty(U_810) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( ~ empty(cartesian_product2(U_810,U_809))
| empty(U_809)
| empty(U_810) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_812,U_811] :
( ( function(relation_rng_restriction(U_812,U_811))
& relation(relation_rng_restriction(U_812,U_811)) )
| ~ function(U_811)
| ~ relation(U_811) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( relation(relation_rng_restriction(U_812,U_811))
| ~ function(U_811)
| ~ relation(U_811) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( function(relation_rng_restriction(U_812,U_811))
| ~ function(U_811)
| ~ relation(U_811) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_208_2,plain,
! [U_813] :
( ~ empty(relation_dom(U_813))
| ~ relation(U_813)
| empty(U_813) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( ~ empty(relation_dom(U_813))
| ~ relation(U_813)
| empty(U_813) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_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]) ).
cnf(f_209_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
v1_membered(empty_set),
inference(clausify,[status(thm)],[f_209_1]) ).
cnf(f_209_4,plain,
v2_membered(empty_set),
inference(clausify,[status(thm)],[f_209_1]) ).
cnf(f_209_5,plain,
v3_membered(empty_set),
inference(clausify,[status(thm)],[f_209_1]) ).
cnf(f_209_6,plain,
v4_membered(empty_set),
inference(clausify,[status(thm)],[f_209_1]) ).
cnf(f_209_7,plain,
v5_membered(empty_set),
inference(clausify,[status(thm)],[f_209_1]) ).
fof(f_210_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_210_2,plain,
! [U_814] :
( ~ empty(relation_rng(U_814))
| ~ relation(U_814)
| empty(U_814) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( ~ empty(relation_rng(U_814))
| ~ relation(U_814)
| empty(U_814) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_211_2,plain,
! [U_815] :
( ( relation(relation_dom(U_815))
& empty(relation_dom(U_815)) )
| ~ empty(U_815) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( empty(relation_dom(U_815))
| ~ empty(U_815) ),
inference(clausify,[status(thm)],[f_211_2]) ).
cnf(f_211_4,plain,
( relation(relation_dom(U_815))
| ~ empty(U_815) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_212_2,plain,
! [U_816] :
( ( relation(relation_rng(U_816))
& empty(relation_rng(U_816)) )
| ~ empty(U_816) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( empty(relation_rng(U_816))
| ~ empty(U_816) ),
inference(clausify,[status(thm)],[f_212_2]) ).
cnf(f_212_4,plain,
( relation(relation_rng(U_816))
| ~ empty(U_816) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc9_finset_1]) ).
fof(f_213_2,plain,
! [U_818,U_817] :
( finite(set_union2(U_818,U_817))
| ~ finite(U_817)
| ~ finite(U_818) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( finite(set_union2(U_818,U_817))
| ~ finite(U_817)
| ~ finite(U_818) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_820,U_819] :
( ( relation(relation_composition(U_820,U_819))
& empty(relation_composition(U_820,U_819)) )
| ~ relation(U_819)
| ~ empty(U_820) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( empty(relation_composition(U_820,U_819))
| ~ relation(U_819)
| ~ empty(U_820) ),
inference(clausify,[status(thm)],[f_214_2]) ).
cnf(f_214_4,plain,
( relation(relation_composition(U_820,U_819))
| ~ relation(U_819)
| ~ empty(U_820) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_215_2,plain,
! [U_822,U_821] : set_union2(U_822,U_822) = U_822,
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_822] : set_union2(U_822,U_822) = U_822,
inference(miniscope,[status(thm)],[f_215_2]) ).
cnf(f_215_4,plain,
set_union2(U_822,U_822) = U_822,
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_216_2,plain,
! [U_824,U_823] : set_intersection2(U_824,U_824) = U_824,
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_824] : set_intersection2(U_824,U_824) = U_824,
inference(miniscope,[status(thm)],[f_216_2]) ).
cnf(f_216_4,plain,
set_intersection2(U_824,U_824) = U_824,
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_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_217_2,plain,
! [U_826,U_825] :
( subset_complement(U_826,subset_complement(U_826,U_825)) = U_825
| ~ element(U_825,powerset(U_826)) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( subset_complement(U_826,subset_complement(U_826,U_825)) = U_825
| ~ element(U_825,powerset(U_826)) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_218_2,plain,
! [U_827] :
( relation_inverse(relation_inverse(U_827)) = U_827
| ~ relation(U_827) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( relation_inverse(relation_inverse(U_827)) = U_827
| ~ relation(U_827) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_829,U_828] :
( complements_of_subsets(U_829,complements_of_subsets(U_829,U_828)) = U_828
| ~ element(U_828,powerset(powerset(U_829))) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( complements_of_subsets(U_829,complements_of_subsets(U_829,U_828)) = U_828
| ~ element(U_828,powerset(powerset(U_829))) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_220_2,plain,
! [U_831,U_830] : ~ proper_subset(U_831,U_831),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_831] : ~ proper_subset(U_831,U_831),
inference(miniscope,[status(thm)],[f_220_2]) ).
cnf(f_220_4,plain,
~ proper_subset(U_831,U_831),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_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_221_2,plain,
! [U_834] :
( ( ( reflexive(U_834)
| ? [U_833] :
( ~ in(ordered_pair(U_833,U_833),U_834)
& in(U_833,relation_field(U_834)) ) )
& ( ! [U_832] :
( in(ordered_pair(U_832,U_832),U_834)
| ~ in(U_832,relation_field(U_834)) )
| ~ reflexive(U_834) ) )
| ~ relation(U_834) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_834] :
( ( ( reflexive(U_834)
| ( ~ in(ordered_pair(sK133(U_834),sK133(U_834)),U_834)
& in(sK133(U_834),relation_field(U_834)) ) )
& ( ! [U_832] :
( in(ordered_pair(U_832,U_832),U_834)
| ~ in(U_832,relation_field(U_834)) )
| ~ reflexive(U_834) ) )
| ~ relation(U_834) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_833,sK133(U_834))],[f_221_2]) ).
cnf(f_221_4,plain,
( in(ordered_pair(U_832,U_832),U_834)
| ~ in(U_832,relation_field(U_834))
| ~ reflexive(U_834)
| ~ relation(U_834) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_5,plain,
( in(sK133(U_834),relation_field(U_834))
| reflexive(U_834)
| ~ relation(U_834) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_6,plain,
( ~ in(ordered_pair(sK133(U_834),sK133(U_834)),U_834)
| reflexive(U_834)
| ~ relation(U_834) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_222_2,plain,
! [U_835] : singleton(U_835) != empty_set,
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
singleton(U_835) != empty_set,
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_223_2,plain,
! [U_837,U_836] :
( set_union2(singleton(U_837),U_836) = U_836
| ~ in(U_837,U_836) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( set_union2(singleton(U_837),U_836) = U_836
| ~ in(U_837,U_836) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_224_2,plain,
! [U_839,U_838] :
( ~ in(U_839,U_838)
| ~ disjoint(singleton(U_839),U_838) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( ~ in(U_839,U_838)
| ~ disjoint(singleton(U_839),U_838) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_225_2,plain,
! [U_841,U_840] :
( disjoint(singleton(U_841),U_840)
| in(U_841,U_840) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( disjoint(singleton(U_841),U_840)
| in(U_841,U_840) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_843,U_842] :
( subset(relation_dom(relation_rng_restriction(U_843,U_842)),relation_dom(U_842))
| ~ relation(U_842) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( subset(relation_dom(relation_rng_restriction(U_843,U_842)),relation_dom(U_842))
| ~ relation(U_842) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_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_227_2,plain,
! [U_850] :
( ( ( transitive(U_850)
| ? [U_849,U_848,U_847] :
( ~ in(ordered_pair(U_849,U_847),U_850)
& in(ordered_pair(U_848,U_847),U_850)
& in(ordered_pair(U_849,U_848),U_850) ) )
& ( ! [U_846,U_845,U_844] :
( in(ordered_pair(U_846,U_844),U_850)
| ~ in(ordered_pair(U_845,U_844),U_850)
| ~ in(ordered_pair(U_846,U_845),U_850) )
| ~ transitive(U_850) ) )
| ~ relation(U_850) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_850] :
( ( ( transitive(U_850)
| ? [U_848,U_847] :
( ~ in(ordered_pair(sK134(U_850),U_847),U_850)
& in(ordered_pair(U_848,U_847),U_850)
& in(ordered_pair(sK134(U_850),U_848),U_850) ) )
& ( ! [U_846,U_845,U_844] :
( in(ordered_pair(U_846,U_844),U_850)
| ~ in(ordered_pair(U_845,U_844),U_850)
| ~ in(ordered_pair(U_846,U_845),U_850) )
| ~ transitive(U_850) ) )
| ~ relation(U_850) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_849,sK134(U_850))],[f_227_2]) ).
fof(f_227_4,plain,
! [U_850] :
( ( ( transitive(U_850)
| ? [U_847] :
( ~ in(ordered_pair(sK134(U_850),U_847),U_850)
& in(ordered_pair(sK135(U_850),U_847),U_850)
& in(ordered_pair(sK134(U_850),sK135(U_850)),U_850) ) )
& ( ! [U_846,U_845,U_844] :
( in(ordered_pair(U_846,U_844),U_850)
| ~ in(ordered_pair(U_845,U_844),U_850)
| ~ in(ordered_pair(U_846,U_845),U_850) )
| ~ transitive(U_850) ) )
| ~ relation(U_850) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_848,sK135(U_850))],[f_227_3]) ).
fof(f_227_5,plain,
! [U_850] :
( ( ( transitive(U_850)
| ( ~ in(ordered_pair(sK134(U_850),sK136(U_850)),U_850)
& in(ordered_pair(sK135(U_850),sK136(U_850)),U_850)
& in(ordered_pair(sK134(U_850),sK135(U_850)),U_850) ) )
& ( ! [U_846,U_845,U_844] :
( in(ordered_pair(U_846,U_844),U_850)
| ~ in(ordered_pair(U_845,U_844),U_850)
| ~ in(ordered_pair(U_846,U_845),U_850) )
| ~ transitive(U_850) ) )
| ~ relation(U_850) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_847,sK136(U_850))],[f_227_4]) ).
cnf(f_227_6,plain,
( in(ordered_pair(U_846,U_844),U_850)
| ~ in(ordered_pair(U_845,U_844),U_850)
| ~ in(ordered_pair(U_846,U_845),U_850)
| ~ transitive(U_850)
| ~ relation(U_850) ),
inference(clausify,[status(thm)],[f_227_5]) ).
cnf(f_227_7,plain,
( in(ordered_pair(sK134(U_850),sK135(U_850)),U_850)
| transitive(U_850)
| ~ relation(U_850) ),
inference(clausify,[status(thm)],[f_227_5]) ).
cnf(f_227_8,plain,
( in(ordered_pair(sK135(U_850),sK136(U_850)),U_850)
| transitive(U_850)
| ~ relation(U_850) ),
inference(clausify,[status(thm)],[f_227_5]) ).
cnf(f_227_9,plain,
( ~ in(ordered_pair(sK134(U_850),sK136(U_850)),U_850)
| transitive(U_850)
| ~ relation(U_850) ),
inference(clausify,[status(thm)],[f_227_5]) ).
fof(f_228_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_228_2,plain,
! [U_852,U_851] :
( ( subset(singleton(U_852),U_851)
| ~ in(U_852,U_851) )
& ( in(U_852,U_851)
| ~ subset(singleton(U_852),U_851) ) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
( ! [U_856,U_854] :
( subset(singleton(U_856),U_854)
| ~ in(U_856,U_854) )
& ! [U_855,U_853] :
( in(U_855,U_853)
| ~ subset(singleton(U_855),U_853) ) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
cnf(f_228_4,plain,
( in(U_855,U_853)
| ~ subset(singleton(U_855),U_853) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_5,plain,
( subset(singleton(U_856),U_854)
| ~ in(U_856,U_854) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_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_229_2,plain,
! [U_859,U_858] :
( ? [U_857] :
( well_orders(U_857,U_859)
& relation(U_857) )
| ~ equipotent(U_859,relation_field(U_858))
| ~ well_ordering(U_858)
| ~ relation(U_858) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_859,U_858] :
( ( well_orders(sK137(U_859,U_858),U_859)
& relation(sK137(U_859,U_858)) )
| ~ equipotent(U_859,relation_field(U_858))
| ~ well_ordering(U_858)
| ~ relation(U_858) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_857,sK137(U_859,U_858))],[f_229_2]) ).
cnf(f_229_4,plain,
( relation(sK137(U_859,U_858))
| ~ equipotent(U_859,relation_field(U_858))
| ~ well_ordering(U_858)
| ~ relation(U_858) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_5,plain,
( well_orders(sK137(U_859,U_858),U_859)
| ~ equipotent(U_859,relation_field(U_858))
| ~ well_ordering(U_858)
| ~ relation(U_858) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_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_230_2,plain,
! [U_861,U_860] :
( ( set_difference(U_861,U_860) = empty_set
| ~ subset(U_861,U_860) )
& ( subset(U_861,U_860)
| set_difference(U_861,U_860) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
( ! [U_865,U_863] :
( set_difference(U_865,U_863) = empty_set
| ~ subset(U_865,U_863) )
& ! [U_864,U_862] :
( subset(U_864,U_862)
| set_difference(U_864,U_862) != empty_set ) ),
inference(miniscope,[status(thm)],[f_230_2]) ).
cnf(f_230_4,plain,
( subset(U_864,U_862)
| set_difference(U_864,U_862) != empty_set ),
inference(clausify,[status(thm)],[f_230_3]) ).
cnf(f_230_5,plain,
( set_difference(U_865,U_863) = empty_set
| ~ subset(U_865,U_863) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_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_231_2,plain,
! [U_868,U_867] :
( ! [U_866] :
( in(U_866,U_868)
| ~ in(U_866,U_867) )
| ~ element(U_867,powerset(U_868)) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( in(U_866,U_868)
| ~ in(U_866,U_867)
| ~ element(U_867,powerset(U_868)) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_873] :
( ( ( antisymmetric(U_873)
| ? [U_872,U_871] :
( U_872 != U_871
& in(ordered_pair(U_871,U_872),U_873)
& in(ordered_pair(U_872,U_871),U_873) ) )
& ( ! [U_870,U_869] :
( U_870 = U_869
| ~ in(ordered_pair(U_869,U_870),U_873)
| ~ in(ordered_pair(U_870,U_869),U_873) )
| ~ antisymmetric(U_873) ) )
| ~ relation(U_873) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_873] :
( ( ( antisymmetric(U_873)
| ? [U_871] :
( sK138(U_873) != U_871
& in(ordered_pair(U_871,sK138(U_873)),U_873)
& in(ordered_pair(sK138(U_873),U_871),U_873) ) )
& ( ! [U_870,U_869] :
( U_870 = U_869
| ~ in(ordered_pair(U_869,U_870),U_873)
| ~ in(ordered_pair(U_870,U_869),U_873) )
| ~ antisymmetric(U_873) ) )
| ~ relation(U_873) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_872,sK138(U_873))],[f_232_2]) ).
fof(f_232_4,plain,
! [U_873] :
( ( ( antisymmetric(U_873)
| ( sK138(U_873) != sK139(U_873)
& in(ordered_pair(sK139(U_873),sK138(U_873)),U_873)
& in(ordered_pair(sK138(U_873),sK139(U_873)),U_873) ) )
& ( ! [U_870,U_869] :
( U_870 = U_869
| ~ in(ordered_pair(U_869,U_870),U_873)
| ~ in(ordered_pair(U_870,U_869),U_873) )
| ~ antisymmetric(U_873) ) )
| ~ relation(U_873) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_871,sK139(U_873))],[f_232_3]) ).
cnf(f_232_5,plain,
( U_870 = U_869
| ~ in(ordered_pair(U_869,U_870),U_873)
| ~ in(ordered_pair(U_870,U_869),U_873)
| ~ antisymmetric(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_232_4]) ).
cnf(f_232_6,plain,
( in(ordered_pair(sK138(U_873),sK139(U_873)),U_873)
| antisymmetric(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_232_4]) ).
cnf(f_232_7,plain,
( in(ordered_pair(sK139(U_873),sK138(U_873)),U_873)
| antisymmetric(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_232_4]) ).
cnf(f_232_8,plain,
( sK138(U_873) != sK139(U_873)
| antisymmetric(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_232_4]) ).
fof(f_233_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_233_2,plain,
! [U_876,U_875,U_874] :
( subset(U_876,set_difference(U_875,singleton(U_874)))
| in(U_874,U_876)
| ~ subset(U_876,U_875) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_876,U_875] :
( ! [U_874] :
( subset(U_876,set_difference(U_875,singleton(U_874)))
| in(U_874,U_876) )
| ~ subset(U_876,U_875) ),
inference(miniscope,[status(thm)],[f_233_2]) ).
cnf(f_233_4,plain,
( subset(U_876,set_difference(U_875,singleton(U_874)))
| in(U_874,U_876)
| ~ subset(U_876,U_875) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_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_234_2,plain,
! [U_881] :
( ( ( connected(U_881)
| ? [U_880,U_879] :
( ~ in(ordered_pair(U_879,U_880),U_881)
& ~ in(ordered_pair(U_880,U_879),U_881)
& U_880 != U_879
& in(U_879,relation_field(U_881))
& in(U_880,relation_field(U_881)) ) )
& ( ! [U_878,U_877] :
( in(ordered_pair(U_877,U_878),U_881)
| in(ordered_pair(U_878,U_877),U_881)
| U_878 = U_877
| ~ in(U_877,relation_field(U_881))
| ~ in(U_878,relation_field(U_881)) )
| ~ connected(U_881) ) )
| ~ relation(U_881) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_881] :
( ( ( connected(U_881)
| ? [U_880] :
( ? [U_879] :
( ~ in(ordered_pair(U_879,U_880),U_881)
& ~ in(ordered_pair(U_880,U_879),U_881)
& U_880 != U_879
& in(U_879,relation_field(U_881)) )
& in(U_880,relation_field(U_881)) ) )
& ( ! [U_878] :
( ! [U_877] :
( in(ordered_pair(U_877,U_878),U_881)
| in(ordered_pair(U_878,U_877),U_881)
| U_878 = U_877
| ~ in(U_877,relation_field(U_881)) )
| ~ in(U_878,relation_field(U_881)) )
| ~ connected(U_881) ) )
| ~ relation(U_881) ),
inference(miniscope,[status(thm)],[f_234_2]) ).
fof(f_234_4,plain,
! [U_881] :
( ( ( connected(U_881)
| ( ? [U_879] :
( ~ in(ordered_pair(U_879,sK140(U_881)),U_881)
& ~ in(ordered_pair(sK140(U_881),U_879),U_881)
& sK140(U_881) != U_879
& in(U_879,relation_field(U_881)) )
& in(sK140(U_881),relation_field(U_881)) ) )
& ( ! [U_878] :
( ! [U_877] :
( in(ordered_pair(U_877,U_878),U_881)
| in(ordered_pair(U_878,U_877),U_881)
| U_878 = U_877
| ~ in(U_877,relation_field(U_881)) )
| ~ in(U_878,relation_field(U_881)) )
| ~ connected(U_881) ) )
| ~ relation(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_880,sK140(U_881))],[f_234_3]) ).
fof(f_234_5,plain,
! [U_881] :
( ( ( connected(U_881)
| ( ~ in(ordered_pair(sK141(U_881),sK140(U_881)),U_881)
& ~ in(ordered_pair(sK140(U_881),sK141(U_881)),U_881)
& sK140(U_881) != sK141(U_881)
& in(sK141(U_881),relation_field(U_881))
& in(sK140(U_881),relation_field(U_881)) ) )
& ( ! [U_878] :
( ! [U_877] :
( in(ordered_pair(U_877,U_878),U_881)
| in(ordered_pair(U_878,U_877),U_881)
| U_878 = U_877
| ~ in(U_877,relation_field(U_881)) )
| ~ in(U_878,relation_field(U_881)) )
| ~ connected(U_881) ) )
| ~ relation(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_879,sK141(U_881))],[f_234_4]) ).
cnf(f_234_6,plain,
( in(ordered_pair(U_877,U_878),U_881)
| in(ordered_pair(U_878,U_877),U_881)
| U_878 = U_877
| ~ in(U_877,relation_field(U_881))
| ~ in(U_878,relation_field(U_881))
| ~ connected(U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_234_5]) ).
cnf(f_234_7,plain,
( in(sK140(U_881),relation_field(U_881))
| connected(U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_234_5]) ).
cnf(f_234_8,plain,
( in(sK141(U_881),relation_field(U_881))
| connected(U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_234_5]) ).
cnf(f_234_9,plain,
( sK140(U_881) != sK141(U_881)
| connected(U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_234_5]) ).
cnf(f_234_10,plain,
( ~ in(ordered_pair(sK140(U_881),sK141(U_881)),U_881)
| connected(U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_234_5]) ).
cnf(f_234_11,plain,
( ~ in(ordered_pair(sK141(U_881),sK140(U_881)),U_881)
| connected(U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_234_5]) ).
fof(f_235_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_235_2,plain,
! [U_883,U_882] :
( ( subset(U_883,singleton(U_882))
| ( U_883 != singleton(U_882)
& U_883 != empty_set ) )
& ( U_883 = singleton(U_882)
| U_883 = empty_set
| ~ subset(U_883,singleton(U_882)) ) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
( ! [U_887,U_885] :
( subset(U_887,singleton(U_885))
| ( U_887 != singleton(U_885)
& U_887 != empty_set ) )
& ! [U_886,U_884] :
( U_886 = singleton(U_884)
| U_886 = empty_set
| ~ subset(U_886,singleton(U_884)) ) ),
inference(miniscope,[status(thm)],[f_235_2]) ).
cnf(f_235_4,plain,
( U_886 = singleton(U_884)
| U_886 = empty_set
| ~ subset(U_886,singleton(U_884)) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_5,plain,
( U_887 != empty_set
| subset(U_887,singleton(U_885)) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_6,plain,
( U_887 != singleton(U_885)
| subset(U_887,singleton(U_885)) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_236_2,plain,
! [U_889,U_888] :
( subset(U_889,union(U_888))
| ~ in(U_889,U_888) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( subset(U_889,union(U_888))
| ~ in(U_889,U_888) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_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_237_2,plain,
! [U_893,U_892,U_891,U_890] :
( ( in(ordered_pair(U_893,U_892),cartesian_product2(U_891,U_890))
| ~ in(U_892,U_890)
| ~ in(U_893,U_891) )
& ( ( in(U_892,U_890)
& in(U_893,U_891) )
| ~ in(ordered_pair(U_893,U_892),cartesian_product2(U_891,U_890)) ) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
( ! [U_901,U_899,U_897,U_895] :
( in(ordered_pair(U_901,U_899),cartesian_product2(U_897,U_895))
| ~ in(U_899,U_895)
| ~ in(U_901,U_897) )
& ! [U_900,U_898,U_896,U_894] :
( ( in(U_898,U_894)
& in(U_900,U_896) )
| ~ in(ordered_pair(U_900,U_898),cartesian_product2(U_896,U_894)) ) ),
inference(miniscope,[status(thm)],[f_237_2]) ).
cnf(f_237_4,plain,
( in(U_900,U_896)
| ~ in(ordered_pair(U_900,U_898),cartesian_product2(U_896,U_894)) ),
inference(clausify,[status(thm)],[f_237_3]) ).
cnf(f_237_5,plain,
( in(U_898,U_894)
| ~ in(ordered_pair(U_900,U_898),cartesian_product2(U_896,U_894)) ),
inference(clausify,[status(thm)],[f_237_3]) ).
cnf(f_237_6,plain,
( in(ordered_pair(U_901,U_899),cartesian_product2(U_897,U_895))
| ~ in(U_899,U_895)
| ~ in(U_901,U_897) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_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_238_2,plain,
! [U_904,U_903] :
( element(U_904,powerset(U_903))
| ? [U_902] :
( ~ in(U_902,U_903)
& in(U_902,U_904) ) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_904,U_903] :
( element(U_904,powerset(U_903))
| ( ~ in(sK142(U_904,U_903),U_903)
& in(sK142(U_904,U_903),U_904) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_902,sK142(U_904,U_903))],[f_238_2]) ).
cnf(f_238_4,plain,
( in(sK142(U_904,U_903),U_904)
| element(U_904,powerset(U_903)) ),
inference(clausify,[status(thm)],[f_238_3]) ).
cnf(f_238_5,plain,
( ~ in(sK142(U_904,U_903),U_903)
| element(U_904,powerset(U_903)) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_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_239_2,plain,
! [U_907,U_906,U_905] :
( ( ( in(U_906,relation_dom(relation_dom_restriction(U_905,U_907)))
| ~ in(U_906,U_907)
| ~ in(U_906,relation_dom(U_905)) )
& ( ( in(U_906,U_907)
& in(U_906,relation_dom(U_905)) )
| ~ in(U_906,relation_dom(relation_dom_restriction(U_905,U_907))) ) )
| ~ function(U_905)
| ~ relation(U_905) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( in(U_906,relation_dom(U_905))
| ~ in(U_906,relation_dom(relation_dom_restriction(U_905,U_907)))
| ~ function(U_905)
| ~ relation(U_905) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
( in(U_906,U_907)
| ~ in(U_906,relation_dom(relation_dom_restriction(U_905,U_907)))
| ~ function(U_905)
| ~ relation(U_905) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_5,plain,
( in(U_906,relation_dom(relation_dom_restriction(U_905,U_907)))
| ~ in(U_906,U_907)
| ~ in(U_906,relation_dom(U_905))
| ~ function(U_905)
| ~ relation(U_905) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
? [U_908] :
( natural(U_908)
& ordinal(U_908)
& epsilon_connected(U_908)
& epsilon_transitive(U_908)
& ~ empty(U_908) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
( natural(sK143)
& ordinal(sK143)
& epsilon_connected(sK143)
& epsilon_transitive(sK143)
& ~ empty(sK143) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_908,sK143)],[f_240_2]) ).
cnf(f_240_4,plain,
~ empty(sK143),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
epsilon_transitive(sK143),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_6,plain,
epsilon_connected(sK143),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_7,plain,
ordinal(sK143),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_8,plain,
natural(sK143),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_241_2,plain,
? [U_909] :
( finite(U_909)
& ~ empty(U_909) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
( finite(sK144)
& ~ empty(sK144) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_909,sK144)],[f_241_2]) ).
cnf(f_241_4,plain,
~ empty(sK144),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_5,plain,
finite(sK144),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_242_2,plain,
? [U_910] :
( function(U_910)
& relation(U_910) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
( function(sK145)
& relation(sK145) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_910,sK145)],[f_242_2]) ).
cnf(f_242_4,plain,
relation(sK145),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_5,plain,
function(sK145),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_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_243_2,plain,
! [U_913,U_912] :
? [U_911] :
( quasi_total(U_911,U_913,U_912)
& function(U_911)
& relation(U_911)
& relation_of2(U_911,U_913,U_912) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_913,U_912] :
( quasi_total(sK146(U_913,U_912),U_913,U_912)
& function(sK146(U_913,U_912))
& relation(sK146(U_913,U_912))
& relation_of2(sK146(U_913,U_912),U_913,U_912) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_911,sK146(U_913,U_912))],[f_243_2]) ).
cnf(f_243_4,plain,
relation_of2(sK146(U_913,U_912),U_913,U_912),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
relation(sK146(U_913,U_912)),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
function(sK146(U_913,U_912)),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_7,plain,
quasi_total(sK146(U_913,U_912),U_913,U_912),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
? [U_914] :
( v5_membered(U_914)
& v4_membered(U_914)
& v3_membered(U_914)
& v2_membered(U_914)
& v1_membered(U_914)
& ~ empty(U_914) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( v5_membered(sK147)
& v4_membered(sK147)
& v3_membered(sK147)
& v2_membered(sK147)
& v1_membered(sK147)
& ~ empty(sK147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_914,sK147)],[f_244_2]) ).
cnf(f_244_4,plain,
~ empty(sK147),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
v1_membered(sK147),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_6,plain,
v2_membered(sK147),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_7,plain,
v3_membered(sK147),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_8,plain,
v4_membered(sK147),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_9,plain,
v5_membered(sK147),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_245_2,plain,
? [U_915] :
( ordinal(U_915)
& epsilon_connected(U_915)
& epsilon_transitive(U_915) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
( ordinal(sK148)
& epsilon_connected(sK148)
& epsilon_transitive(sK148) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_915,sK148)],[f_245_2]) ).
cnf(f_245_4,plain,
epsilon_transitive(sK148),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_5,plain,
epsilon_connected(sK148),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_6,plain,
ordinal(sK148),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal2]) ).
fof(f_246_2,plain,
? [U_916] :
( being_limit_ordinal(U_916)
& ordinal(U_916)
& epsilon_connected(U_916)
& epsilon_transitive(U_916) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
( being_limit_ordinal(sK149)
& ordinal(sK149)
& epsilon_connected(sK149)
& epsilon_transitive(sK149) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_916,sK149)],[f_246_2]) ).
cnf(f_246_4,plain,
epsilon_transitive(sK149),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_5,plain,
epsilon_connected(sK149),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_6,plain,
ordinal(sK149),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_7,plain,
being_limit_ordinal(sK149),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(f_247_2,plain,
? [U_917] :
( empty(U_917)
& one_to_one(U_917)
& function(U_917)
& relation(U_917) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
( empty(sK150)
& one_to_one(sK150)
& function(sK150)
& relation(sK150) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_917,sK150)],[f_247_2]) ).
cnf(f_247_4,plain,
relation(sK150),
inference(clausify,[status(thm)],[f_247_3]) ).
cnf(f_247_5,plain,
function(sK150),
inference(clausify,[status(thm)],[f_247_3]) ).
cnf(f_247_6,plain,
one_to_one(sK150),
inference(clausify,[status(thm)],[f_247_3]) ).
cnf(f_247_7,plain,
empty(sK150),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_248_2,plain,
? [U_918] :
( relation(U_918)
& empty(U_918) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
( relation(sK151)
& empty(sK151) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_918,sK151)],[f_248_2]) ).
cnf(f_248_4,plain,
empty(sK151),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_5,plain,
relation(sK151),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_249_2,plain,
! [U_920] :
( ? [U_919] :
( ~ empty(U_919)
& element(U_919,powerset(U_920)) )
| empty(U_920) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_920] :
( ( ~ empty(sK152(U_920))
& element(sK152(U_920),powerset(U_920)) )
| empty(U_920) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_919,sK152(U_920))],[f_249_2]) ).
cnf(f_249_4,plain,
( element(sK152(U_920),powerset(U_920))
| empty(U_920) ),
inference(clausify,[status(thm)],[f_249_3]) ).
cnf(f_249_5,plain,
( ~ empty(sK152(U_920))
| empty(U_920) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_250_2,plain,
? [U_921] : empty(U_921),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
empty(sK153),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_921,sK153)],[f_250_2]) ).
cnf(f_250_4,plain,
empty(sK153),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_923] :
? [U_922] :
( finite(U_922)
& natural(U_922)
& ordinal(U_922)
& epsilon_connected(U_922)
& epsilon_transitive(U_922)
& one_to_one(U_922)
& function(U_922)
& relation(U_922)
& empty(U_922)
& element(U_922,powerset(U_923)) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_923] :
( finite(sK154(U_923))
& natural(sK154(U_923))
& ordinal(sK154(U_923))
& epsilon_connected(sK154(U_923))
& epsilon_transitive(sK154(U_923))
& one_to_one(sK154(U_923))
& function(sK154(U_923))
& relation(sK154(U_923))
& empty(sK154(U_923))
& element(sK154(U_923),powerset(U_923)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_922,sK154(U_923))],[f_251_2]) ).
cnf(f_251_4,plain,
element(sK154(U_923),powerset(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
empty(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_6,plain,
relation(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_7,plain,
function(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_8,plain,
one_to_one(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_9,plain,
epsilon_transitive(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_10,plain,
epsilon_connected(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_11,plain,
ordinal(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_12,plain,
natural(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_13,plain,
finite(sK154(U_923)),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_252_2,plain,
? [U_924] :
( function(U_924)
& empty(U_924)
& relation(U_924) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
( function(sK155)
& empty(sK155)
& relation(sK155) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_924,sK155)],[f_252_2]) ).
cnf(f_252_4,plain,
relation(sK155),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_5,plain,
empty(sK155),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_6,plain,
function(sK155),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
? [U_925] :
( ordinal(U_925)
& epsilon_connected(U_925)
& epsilon_transitive(U_925)
& empty(U_925)
& one_to_one(U_925)
& function(U_925)
& relation(U_925) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ordinal(sK156)
& epsilon_connected(sK156)
& epsilon_transitive(sK156)
& empty(sK156)
& one_to_one(sK156)
& function(sK156)
& relation(sK156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_925,sK156)],[f_253_2]) ).
cnf(f_253_4,plain,
relation(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
function(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
one_to_one(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_7,plain,
empty(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_8,plain,
epsilon_transitive(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_9,plain,
epsilon_connected(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_10,plain,
ordinal(sK156),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_254_2,plain,
! [U_928,U_927] :
? [U_926] :
( function(U_926)
& relation(U_926)
& relation_of2(U_926,U_928,U_927) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_928,U_927] :
( function(sK157(U_928,U_927))
& relation(sK157(U_928,U_927))
& relation_of2(sK157(U_928,U_927),U_928,U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_926,sK157(U_928,U_927))],[f_254_2]) ).
cnf(f_254_4,plain,
relation_of2(sK157(U_928,U_927),U_928,U_927),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_5,plain,
relation(sK157(U_928,U_927)),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_6,plain,
function(sK157(U_928,U_927)),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_255_2,plain,
? [U_929] :
( relation(U_929)
& ~ empty(U_929) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
( relation(sK158)
& ~ empty(sK158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_929,sK158)],[f_255_2]) ).
cnf(f_255_4,plain,
~ empty(sK158),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_5,plain,
relation(sK158),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_256_2,plain,
! [U_931] :
? [U_930] :
( empty(U_930)
& element(U_930,powerset(U_931)) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_931] :
( empty(sK159(U_931))
& element(sK159(U_931),powerset(U_931)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_930,sK159(U_931))],[f_256_2]) ).
cnf(f_256_4,plain,
element(sK159(U_931),powerset(U_931)),
inference(clausify,[status(thm)],[f_256_3]) ).
cnf(f_256_5,plain,
empty(sK159(U_931)),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_257_2,plain,
? [U_932] : ~ empty(U_932),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
~ empty(sK160),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_932,sK160)],[f_257_2]) ).
cnf(f_257_4,plain,
~ empty(sK160),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_258_2,plain,
! [U_934] :
( ? [U_933] :
( finite(U_933)
& ~ empty(U_933)
& element(U_933,powerset(U_934)) )
| empty(U_934) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_934] :
( ( finite(sK161(U_934))
& ~ empty(sK161(U_934))
& element(sK161(U_934),powerset(U_934)) )
| empty(U_934) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_933,sK161(U_934))],[f_258_2]) ).
cnf(f_258_4,plain,
( element(sK161(U_934),powerset(U_934))
| empty(U_934) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_5,plain,
( ~ empty(sK161(U_934))
| empty(U_934) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_6,plain,
( finite(sK161(U_934))
| empty(U_934) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_259_2,plain,
? [U_935] :
( one_to_one(U_935)
& function(U_935)
& relation(U_935) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( one_to_one(sK162)
& function(sK162)
& relation(sK162) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_935,sK162)],[f_259_2]) ).
cnf(f_259_4,plain,
relation(sK162),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_5,plain,
function(sK162),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_6,plain,
one_to_one(sK162),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_260_2,plain,
? [U_936] :
( ordinal(U_936)
& epsilon_connected(U_936)
& epsilon_transitive(U_936)
& ~ empty(U_936) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ordinal(sK163)
& epsilon_connected(sK163)
& epsilon_transitive(sK163)
& ~ empty(sK163) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_936,sK163)],[f_260_2]) ).
cnf(f_260_4,plain,
~ empty(sK163),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
epsilon_transitive(sK163),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_6,plain,
epsilon_connected(sK163),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_7,plain,
ordinal(sK163),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_261_2,plain,
? [U_937] :
( relation_empty_yielding(U_937)
& relation(U_937) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( relation_empty_yielding(sK164)
& relation(sK164) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_937,sK164)],[f_261_2]) ).
cnf(f_261_4,plain,
relation(sK164),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_5,plain,
relation_empty_yielding(sK164),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_262_2,plain,
? [U_938] :
( ~ empty_carrier(U_938)
& one_sorted_str(U_938) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
( ~ empty_carrier(sK165)
& one_sorted_str(sK165) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_938,sK165)],[f_262_2]) ).
cnf(f_262_4,plain,
one_sorted_str(sK165),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_5,plain,
~ empty_carrier(sK165),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_263_2,plain,
? [U_939] :
( function(U_939)
& relation_empty_yielding(U_939)
& relation(U_939) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
( function(sK166)
& relation_empty_yielding(sK166)
& relation(sK166) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_939,sK166)],[f_263_2]) ).
cnf(f_263_4,plain,
relation(sK166),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_5,plain,
relation_empty_yielding(sK166),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_6,plain,
function(sK166),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_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_264_2,plain,
! [U_941] :
( ? [U_940] :
( ~ empty(U_940)
& element(U_940,powerset(the_carrier(U_941))) )
| ~ one_sorted_str(U_941)
| empty_carrier(U_941) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_941] :
( ( ~ empty(sK167(U_941))
& element(sK167(U_941),powerset(the_carrier(U_941))) )
| ~ one_sorted_str(U_941)
| empty_carrier(U_941) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_940,sK167(U_941))],[f_264_2]) ).
cnf(f_264_4,plain,
( element(sK167(U_941),powerset(the_carrier(U_941)))
| ~ one_sorted_str(U_941)
| empty_carrier(U_941) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_5,plain,
( ~ empty(sK167(U_941))
| ~ one_sorted_str(U_941)
| empty_carrier(U_941) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_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_265_2,plain,
! [U_947,U_946,U_945,U_944,U_943,U_942] :
( apply_binary_as_element(U_947,U_946,U_945,U_944,U_943,U_942) = apply_binary(U_944,U_943,U_942)
| ~ element(U_942,U_946)
| ~ element(U_943,U_947)
| ~ relation_of2(U_944,cartesian_product2(U_947,U_946),U_945)
| ~ quasi_total(U_944,cartesian_product2(U_947,U_946),U_945)
| ~ function(U_944)
| empty(U_946)
| empty(U_947) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( apply_binary_as_element(U_947,U_946,U_945,U_944,U_943,U_942) = apply_binary(U_944,U_943,U_942)
| ~ element(U_942,U_946)
| ~ element(U_943,U_947)
| ~ relation_of2(U_944,cartesian_product2(U_947,U_946),U_945)
| ~ quasi_total(U_944,cartesian_product2(U_947,U_946),U_945)
| ~ function(U_944)
| empty(U_946)
| empty(U_947) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_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_266_2,plain,
! [U_950,U_949,U_948] :
( join_commut(U_950,U_949,U_948) = join(U_950,U_949,U_948)
| ~ element(U_948,the_carrier(U_950))
| ~ element(U_949,the_carrier(U_950))
| ~ join_semilatt_str(U_950)
| ~ join_commutative(U_950)
| empty_carrier(U_950) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( join_commut(U_950,U_949,U_948) = join(U_950,U_949,U_948)
| ~ element(U_948,the_carrier(U_950))
| ~ element(U_949,the_carrier(U_950))
| ~ join_semilatt_str(U_950)
| ~ join_commutative(U_950)
| empty_carrier(U_950) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_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_267_2,plain,
! [U_953,U_952,U_951] :
( meet_commut(U_953,U_952,U_951) = meet(U_953,U_952,U_951)
| ~ element(U_951,the_carrier(U_953))
| ~ element(U_952,the_carrier(U_953))
| ~ meet_semilatt_str(U_953)
| ~ meet_commutative(U_953)
| empty_carrier(U_953) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
( meet_commut(U_953,U_952,U_951) = meet(U_953,U_952,U_951)
| ~ element(U_951,the_carrier(U_953))
| ~ element(U_952,the_carrier(U_953))
| ~ meet_semilatt_str(U_953)
| ~ meet_commutative(U_953)
| empty_carrier(U_953) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_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_268_2,plain,
! [U_956,U_955,U_954] :
( relation_dom_as_subset(U_956,U_955,U_954) = relation_dom(U_954)
| ~ relation_of2(U_954,U_956,U_955) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( relation_dom_as_subset(U_956,U_955,U_954) = relation_dom(U_954)
| ~ relation_of2(U_954,U_956,U_955) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_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_269_2,plain,
! [U_959,U_958,U_957] :
( relation_rng_as_subset(U_959,U_958,U_957) = relation_rng(U_957)
| ~ relation_of2(U_957,U_959,U_958) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( relation_rng_as_subset(U_959,U_958,U_957) = relation_rng(U_957)
| ~ relation_of2(U_957,U_959,U_958) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_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_270_2,plain,
! [U_961,U_960] :
( union_of_subsets(U_961,U_960) = union(U_960)
| ~ element(U_960,powerset(powerset(U_961))) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( union_of_subsets(U_961,U_960) = union(U_960)
| ~ element(U_960,powerset(powerset(U_961))) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_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_271_2,plain,
! [U_963,U_962] :
( meet_of_subsets(U_963,U_962) = set_meet(U_962)
| ~ element(U_962,powerset(powerset(U_963))) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( meet_of_subsets(U_963,U_962) = set_meet(U_962)
| ~ element(U_962,powerset(powerset(U_963))) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_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_272_2,plain,
! [U_966,U_965,U_964] :
( subset_difference(U_966,U_965,U_964) = set_difference(U_965,U_964)
| ~ element(U_964,powerset(U_966))
| ~ element(U_965,powerset(U_966)) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( subset_difference(U_966,U_965,U_964) = set_difference(U_965,U_964)
| ~ element(U_964,powerset(U_966))
| ~ element(U_965,powerset(U_966)) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_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_273_2,plain,
! [U_969,U_968,U_967] :
( ( relation_of2_as_subset(U_967,U_969,U_968)
| ~ relation_of2(U_967,U_969,U_968) )
& ( relation_of2(U_967,U_969,U_968)
| ~ relation_of2_as_subset(U_967,U_969,U_968) ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_975,U_973,U_971] :
( relation_of2_as_subset(U_971,U_975,U_973)
| ~ relation_of2(U_971,U_975,U_973) )
& ! [U_974,U_972,U_970] :
( relation_of2(U_970,U_974,U_972)
| ~ relation_of2_as_subset(U_970,U_974,U_972) ) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
cnf(f_273_4,plain,
( relation_of2(U_970,U_974,U_972)
| ~ relation_of2_as_subset(U_970,U_974,U_972) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_5,plain,
( relation_of2_as_subset(U_971,U_975,U_973)
| ~ relation_of2(U_971,U_975,U_973) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_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_274_2,plain,
! [U_977,U_976] :
( ( ( ordinal_subset(U_977,U_976)
| ~ subset(U_977,U_976) )
& ( subset(U_977,U_976)
| ~ ordinal_subset(U_977,U_976) ) )
| ~ ordinal(U_976)
| ~ ordinal(U_977) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( subset(U_977,U_976)
| ~ ordinal_subset(U_977,U_976)
| ~ ordinal(U_976)
| ~ ordinal(U_977) ),
inference(clausify,[status(thm)],[f_274_2]) ).
cnf(f_274_4,plain,
( ordinal_subset(U_977,U_976)
| ~ subset(U_977,U_976)
| ~ ordinal(U_976)
| ~ ordinal(U_977) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_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_275_2,plain,
! [U_979,U_978] :
( ( equipotent(U_979,U_978)
| ~ are_equipotent(U_979,U_978) )
& ( are_equipotent(U_979,U_978)
| ~ equipotent(U_979,U_978) ) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_983,U_981] :
( equipotent(U_983,U_981)
| ~ are_equipotent(U_983,U_981) )
& ! [U_982,U_980] :
( are_equipotent(U_982,U_980)
| ~ equipotent(U_982,U_980) ) ),
inference(miniscope,[status(thm)],[f_275_2]) ).
cnf(f_275_4,plain,
( are_equipotent(U_982,U_980)
| ~ equipotent(U_982,U_980) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( equipotent(U_983,U_981)
| ~ are_equipotent(U_983,U_981) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_276_2,plain,
! [U_985,U_984] :
( ordinal_subset(U_985,U_985)
| ~ ordinal(U_984)
| ~ ordinal(U_985) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_985] :
( ! [U_984] : ~ ordinal(U_984)
| ~ ordinal(U_985)
| ordinal_subset(U_985,U_985) ),
inference(miniscope,[status(thm)],[f_276_2]) ).
cnf(f_276_4,plain,
( ~ ordinal(U_984)
| ~ ordinal(U_985)
| ordinal_subset(U_985,U_985) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_277_2,plain,
! [U_987,U_986] : subset(U_987,U_987),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_987] : subset(U_987,U_987),
inference(miniscope,[status(thm)],[f_277_2]) ).
cnf(f_277_4,plain,
subset(U_987,U_987),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [A,B] : equipotent(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r2_wellord2]) ).
fof(f_278_2,plain,
! [U_989,U_988] : equipotent(U_989,U_989),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_989] : equipotent(U_989,U_989),
inference(miniscope,[status(thm)],[f_278_2]) ).
cnf(f_278_4,plain,
equipotent(U_989,U_989),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_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_279_2,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1002,U_1001] :
( ( in(ordered_pair(U_1002,U_1001),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1001,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1001,U_1000)
| U_1002 != U_1000 )
| ~ in(U_1002,U_1005)
| ~ in(U_1002,U_1005) )
& ( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1001,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1001,U_998)
& U_1002 = U_998 )
& in(U_1002,U_1005)
& in(U_1002,U_1005) )
| ~ in(ordered_pair(U_1002,U_1001),U_1003) ) )
& function(U_1003)
& relation(U_1003) )
| ? [U_996,U_995,U_994] :
( U_995 != U_994
& ? [U_993] :
( ! [U_992] :
( in(ordered_pair(U_994,U_992),U_1004)
| ~ in(U_992,U_993) )
& in(U_994,U_993)
& U_996 = U_993 )
& in(U_996,U_1005)
& ? [U_991] :
( ! [U_990] :
( in(ordered_pair(U_995,U_990),U_1004)
| ~ in(U_990,U_991) )
& in(U_995,U_991)
& U_996 = U_991 )
& in(U_996,U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),U_1003) )
& function(U_1003)
& relation(U_1003) )
| ? [U_996,U_995,U_994] :
( U_995 != U_994
& ? [U_993] :
( ! [U_992] :
( in(ordered_pair(U_994,U_992),U_1004)
| ~ in(U_992,U_993) )
& in(U_994,U_993)
& U_996 = U_993 )
& in(U_996,U_1005)
& ? [U_991] :
( ! [U_990] :
( in(ordered_pair(U_995,U_990),U_1004)
| ~ in(U_990,U_991) )
& in(U_995,U_991)
& U_996 = U_991 )
& in(U_996,U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(miniscope,[status(thm)],[f_279_2]) ).
fof(f_279_4,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),U_1003) )
& function(U_1003)
& relation(U_1003) )
| ? [U_995,U_994] :
( U_995 != U_994
& ? [U_993] :
( ! [U_992] :
( in(ordered_pair(U_994,U_992),U_1004)
| ~ in(U_992,U_993) )
& in(U_994,U_993)
& sK168(U_1005,U_1004) = U_993 )
& in(sK168(U_1005,U_1004),U_1005)
& ? [U_991] :
( ! [U_990] :
( in(ordered_pair(U_995,U_990),U_1004)
| ~ in(U_990,U_991) )
& in(U_995,U_991)
& sK168(U_1005,U_1004) = U_991 )
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_996,sK168(U_1005,U_1004))],[f_279_3]) ).
fof(f_279_5,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),U_1003) )
& function(U_1003)
& relation(U_1003) )
| ? [U_994] :
( sK169(U_1005,U_1004) != U_994
& ? [U_993] :
( ! [U_992] :
( in(ordered_pair(U_994,U_992),U_1004)
| ~ in(U_992,U_993) )
& in(U_994,U_993)
& sK168(U_1005,U_1004) = U_993 )
& in(sK168(U_1005,U_1004),U_1005)
& ? [U_991] :
( ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,U_991) )
& in(sK169(U_1005,U_1004),U_991)
& sK168(U_1005,U_1004) = U_991 )
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_995,sK169(U_1005,U_1004))],[f_279_4]) ).
fof(f_279_6,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),U_1003) )
& function(U_1003)
& relation(U_1003) )
| ( sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
& ? [U_993] :
( ! [U_992] :
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,U_993) )
& in(sK170(U_1005,U_1004),U_993)
& sK168(U_1005,U_1004) = U_993 )
& in(sK168(U_1005,U_1004),U_1005)
& ? [U_991] :
( ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,U_991) )
& in(sK169(U_1005,U_1004),U_991)
& sK168(U_1005,U_1004) = U_991 )
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_994,sK170(U_1005,U_1004))],[f_279_5]) ).
fof(f_279_7,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),U_1003) )
& function(U_1003)
& relation(U_1003) )
| ( sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
& ? [U_993] :
( ! [U_992] :
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,U_993) )
& in(sK170(U_1005,U_1004),U_993)
& sK168(U_1005,U_1004) = U_993 )
& in(sK168(U_1005,U_1004),U_1005)
& ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004)) )
& in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_991,sK171(U_1005,U_1004))],[f_279_6]) ).
fof(f_279_8,plain,
! [U_1005,U_1004] :
( ? [U_1003] :
( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),U_1003)
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),U_1003) )
& function(U_1003)
& relation(U_1003) )
| ( sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
& ! [U_992] :
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004)) )
& in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005)
& ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004)) )
& in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_993,sK172(U_1005,U_1004))],[f_279_7]) ).
fof(f_279_9,plain,
! [U_1005,U_1004] :
( ( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ? [U_998] :
( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,U_998) )
& in(U_1006,U_998)
& U_1008 = U_998 )
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004)) )
& function(sK173(U_1005,U_1004))
& relation(sK173(U_1005,U_1004)) )
| ( sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
& ! [U_992] :
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004)) )
& in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005)
& ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004)) )
& in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_1003,sK173(U_1005,U_1004))],[f_279_8]) ).
fof(f_279_10,plain,
! [U_1005,U_1004] :
( ( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| ! [U_1000] :
( ? [U_999] :
( ~ in(ordered_pair(U_1007,U_999),U_1004)
& in(U_999,U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006)) )
& in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
& U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004)) )
& function(sK173(U_1005,U_1004))
& relation(sK173(U_1005,U_1004)) )
| ( sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
& ! [U_992] :
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004)) )
& in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005)
& ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004)) )
& in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_998,sK174(U_1005,U_1004,U_1008,U_1006))],[f_279_9]) ).
fof(f_279_11,plain,
! [U_1005,U_1004] :
( ( ! [U_1009,U_1007] :
( in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| ! [U_1000] :
( ( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
& in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000) )
| ~ in(U_1007,U_1000)
| U_1009 != U_1000 )
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005) )
& ! [U_1008,U_1006] :
( ( ! [U_997] :
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006)) )
& in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
& U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
& in(U_1008,U_1005)
& in(U_1008,U_1005) )
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004)) )
& function(sK173(U_1005,U_1004))
& relation(sK173(U_1005,U_1004)) )
| ( sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
& ! [U_992] :
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004)) )
& in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005)
& ! [U_990] :
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004)) )
& in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
& sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
& in(sK168(U_1005,U_1004),U_1005) )
| ~ relation(U_1004)
| empty(U_1005) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_999,sK175(U_1005,U_1004,U_1009,U_1007,U_1000))],[f_279_10]) ).
cnf(f_279_12,plain,
( in(sK168(U_1005,U_1004),U_1005)
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_13,plain,
( sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_14,plain,
( in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_15,plain,
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_16,plain,
( in(sK168(U_1005,U_1004),U_1005)
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_17,plain,
( sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_18,plain,
( in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_19,plain,
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| relation(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_20,plain,
( in(sK168(U_1005,U_1004),U_1005)
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_21,plain,
( sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_22,plain,
( in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_23,plain,
( in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_24,plain,
( in(sK168(U_1005,U_1004),U_1005)
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_25,plain,
( sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_26,plain,
( in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_27,plain,
( in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| function(sK173(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_28,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_29,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_30,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_31,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_32,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_33,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_34,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_35,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_36,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_37,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_38,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_39,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_40,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_41,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_42,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_43,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_44,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_45,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_46,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_47,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_48,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_49,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_50,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_51,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_52,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_53,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_54,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_55,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_56,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_57,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_58,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_59,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_60,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_61,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_62,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_63,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_64,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_65,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_66,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_67,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_68,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_69,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_70,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_71,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_72,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_73,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_74,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_75,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_76,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_77,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_78,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_79,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_80,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_81,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_82,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_83,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_84,plain,
( relation(sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_85,plain,
( function(sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_86,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_87,plain,
( in(U_1008,U_1005)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_88,plain,
( U_1008 = sK174(U_1005,U_1004,U_1008,U_1006)
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_89,plain,
( in(U_1006,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_90,plain,
( in(ordered_pair(U_1006,U_997),U_1004)
| ~ in(U_997,sK174(U_1005,U_1004,U_1008,U_1006))
| ~ in(ordered_pair(U_1008,U_1006),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_91,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
cnf(f_279_92,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(clausify,[status(thm)],[f_279_11]) ).
fof(f_280_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_280_2,plain,
! [U_1016] :
( ? [U_1015] :
( ! [U_1014,U_1013] :
( ( in(ordered_pair(U_1014,U_1013),U_1015)
| U_1013 != singleton(U_1014)
| ~ in(U_1014,U_1016)
| ~ in(U_1014,U_1016) )
& ( ( U_1013 = singleton(U_1014)
& in(U_1014,U_1016)
& in(U_1014,U_1016) )
| ~ in(ordered_pair(U_1014,U_1013),U_1015) ) )
& function(U_1015)
& relation(U_1015) )
| ? [U_1012,U_1011,U_1010] :
( U_1011 != U_1010
& U_1010 = singleton(U_1012)
& in(U_1012,U_1016)
& U_1011 = singleton(U_1012)
& in(U_1012,U_1016) ) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1016] :
( ? [U_1015] :
( ! [U_1020,U_1018] :
( in(ordered_pair(U_1020,U_1018),U_1015)
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016) )
& ! [U_1019,U_1017] :
( ( U_1017 = singleton(U_1019)
& in(U_1019,U_1016)
& in(U_1019,U_1016) )
| ~ in(ordered_pair(U_1019,U_1017),U_1015) )
& function(U_1015)
& relation(U_1015) )
| ? [U_1012,U_1011,U_1010] :
( U_1011 != U_1010
& U_1010 = singleton(U_1012)
& in(U_1012,U_1016)
& U_1011 = singleton(U_1012)
& in(U_1012,U_1016) ) ),
inference(miniscope,[status(thm)],[f_280_2]) ).
fof(f_280_4,plain,
! [U_1016] :
( ? [U_1015] :
( ! [U_1020,U_1018] :
( in(ordered_pair(U_1020,U_1018),U_1015)
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016) )
& ! [U_1019,U_1017] :
( ( U_1017 = singleton(U_1019)
& in(U_1019,U_1016)
& in(U_1019,U_1016) )
| ~ in(ordered_pair(U_1019,U_1017),U_1015) )
& function(U_1015)
& relation(U_1015) )
| ? [U_1011,U_1010] :
( U_1011 != U_1010
& U_1010 = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016)
& U_1011 = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_1012,sK176(U_1016))],[f_280_3]) ).
fof(f_280_5,plain,
! [U_1016] :
( ? [U_1015] :
( ! [U_1020,U_1018] :
( in(ordered_pair(U_1020,U_1018),U_1015)
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016) )
& ! [U_1019,U_1017] :
( ( U_1017 = singleton(U_1019)
& in(U_1019,U_1016)
& in(U_1019,U_1016) )
| ~ in(ordered_pair(U_1019,U_1017),U_1015) )
& function(U_1015)
& relation(U_1015) )
| ? [U_1010] :
( sK177(U_1016) != U_1010
& U_1010 = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016)
& sK177(U_1016) = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_1011,sK177(U_1016))],[f_280_4]) ).
fof(f_280_6,plain,
! [U_1016] :
( ? [U_1015] :
( ! [U_1020,U_1018] :
( in(ordered_pair(U_1020,U_1018),U_1015)
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016) )
& ! [U_1019,U_1017] :
( ( U_1017 = singleton(U_1019)
& in(U_1019,U_1016)
& in(U_1019,U_1016) )
| ~ in(ordered_pair(U_1019,U_1017),U_1015) )
& function(U_1015)
& relation(U_1015) )
| ( sK177(U_1016) != sK178(U_1016)
& sK178(U_1016) = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016)
& sK177(U_1016) = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_1010,sK178(U_1016))],[f_280_5]) ).
fof(f_280_7,plain,
! [U_1016] :
( ( ! [U_1020,U_1018] :
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016) )
& ! [U_1019,U_1017] :
( ( U_1017 = singleton(U_1019)
& in(U_1019,U_1016)
& in(U_1019,U_1016) )
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016)) )
& function(sK179(U_1016))
& relation(sK179(U_1016)) )
| ( sK177(U_1016) != sK178(U_1016)
& sK178(U_1016) = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016)
& sK177(U_1016) = singleton(sK176(U_1016))
& in(sK176(U_1016),U_1016) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_1015,sK179(U_1016))],[f_280_6]) ).
cnf(f_280_8,plain,
( in(sK176(U_1016),U_1016)
| relation(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_9,plain,
( sK177(U_1016) = singleton(sK176(U_1016))
| relation(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_10,plain,
( in(sK176(U_1016),U_1016)
| relation(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_11,plain,
( sK178(U_1016) = singleton(sK176(U_1016))
| relation(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_12,plain,
( in(sK176(U_1016),U_1016)
| function(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_13,plain,
( sK177(U_1016) = singleton(sK176(U_1016))
| function(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_14,plain,
( in(sK176(U_1016),U_1016)
| function(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_15,plain,
( sK178(U_1016) = singleton(sK176(U_1016))
| function(sK179(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_16,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_17,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_18,plain,
( U_1017 = singleton(U_1019)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_19,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016)
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_20,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK177(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_21,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK177(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_22,plain,
( U_1017 = singleton(U_1019)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK177(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_23,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016)
| sK177(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_24,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_25,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_26,plain,
( U_1017 = singleton(U_1019)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_27,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016)
| in(sK176(U_1016),U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_28,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK178(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_29,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK178(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_30,plain,
( U_1017 = singleton(U_1019)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK178(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_31,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016)
| sK178(U_1016) = singleton(sK176(U_1016)) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_32,plain,
( relation(sK179(U_1016))
| sK177(U_1016) != sK178(U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_33,plain,
( function(sK179(U_1016))
| sK177(U_1016) != sK178(U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_34,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK177(U_1016) != sK178(U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_35,plain,
( in(U_1019,U_1016)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK177(U_1016) != sK178(U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_36,plain,
( U_1017 = singleton(U_1019)
| ~ in(ordered_pair(U_1019,U_1017),sK179(U_1016))
| sK177(U_1016) != sK178(U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
cnf(f_280_37,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| ~ in(U_1020,U_1016)
| sK177(U_1016) != sK178(U_1016) ),
inference(clausify,[status(thm)],[f_280_7]) ).
fof(f_281_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_281_2,plain,
! [U_1024] :
( ? [U_1023] :
( ! [U_1022] :
( ordinal_subset(U_1023,U_1022)
| ~ in(U_1022,U_1024)
| ~ ordinal(U_1022) )
& in(U_1023,U_1024)
& ordinal(U_1023) )
| ! [U_1021] :
( ~ in(U_1021,U_1024)
| ~ ordinal(U_1021) ) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_1024] :
( ( ! [U_1022] :
( ordinal_subset(sK180(U_1024),U_1022)
| ~ in(U_1022,U_1024)
| ~ ordinal(U_1022) )
& in(sK180(U_1024),U_1024)
& ordinal(sK180(U_1024)) )
| ! [U_1021] :
( ~ in(U_1021,U_1024)
| ~ ordinal(U_1021) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_1023,sK180(U_1024))],[f_281_2]) ).
cnf(f_281_4,plain,
( ordinal(sK180(U_1024))
| ~ in(U_1021,U_1024)
| ~ ordinal(U_1021) ),
inference(clausify,[status(thm)],[f_281_3]) ).
cnf(f_281_5,plain,
( in(sK180(U_1024),U_1024)
| ~ in(U_1021,U_1024)
| ~ ordinal(U_1021) ),
inference(clausify,[status(thm)],[f_281_3]) ).
cnf(f_281_6,plain,
( ordinal_subset(sK180(U_1024),U_1022)
| ~ in(U_1022,U_1024)
| ~ ordinal(U_1022)
| ~ in(U_1021,U_1024)
| ~ ordinal(U_1021) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_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_282_2,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ? [U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( ? [U_1031] :
( U_1031 != U_1032
& subset(U_1032,U_1031)
& in(U_1031,U_1033) )
| ~ in(U_1032,U_1033) )
& U_1033 != empty_set
& element(U_1033,powerset(powerset(succ(U_1034)))) )
& in(succ(U_1034),omega)
& ( ! [U_1030] :
( ? [U_1029] :
( ! [U_1028] :
( U_1028 = U_1029
| ~ subset(U_1029,U_1028)
| ~ in(U_1028,U_1030) )
& in(U_1029,U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(U_1034))) )
| ~ in(U_1034,omega) )
& ordinal(U_1034) )
| ( ? [U_1027] :
( ! [U_1026] :
( ? [U_1025] :
( U_1025 != U_1026
& subset(U_1026,U_1025)
& in(U_1025,U_1027) )
| ~ in(U_1026,U_1027) )
& U_1027 != empty_set
& element(U_1027,powerset(powerset(empty_set))) )
& in(empty_set,omega) ) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ? [U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( ? [U_1031] :
( U_1031 != U_1032
& subset(U_1032,U_1031)
& in(U_1031,U_1033) )
| ~ in(U_1032,U_1033) )
& U_1033 != empty_set
& element(U_1033,powerset(powerset(succ(U_1034)))) )
& in(succ(U_1034),omega)
& ( ! [U_1030] :
( ? [U_1029] :
( ! [U_1028] :
( U_1028 = U_1029
| ~ subset(U_1029,U_1028)
| ~ in(U_1028,U_1030) )
& in(U_1029,U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(U_1034))) )
| ~ in(U_1034,omega) )
& ordinal(U_1034) )
| ( ! [U_1026] :
( ? [U_1025] :
( U_1025 != U_1026
& subset(U_1026,U_1025)
& in(U_1025,sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_1027,sK181)],[f_282_2]) ).
fof(f_282_4,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ? [U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( ? [U_1031] :
( U_1031 != U_1032
& subset(U_1032,U_1031)
& in(U_1031,U_1033) )
| ~ in(U_1032,U_1033) )
& U_1033 != empty_set
& element(U_1033,powerset(powerset(succ(U_1034)))) )
& in(succ(U_1034),omega)
& ( ! [U_1030] :
( ? [U_1029] :
( ! [U_1028] :
( U_1028 = U_1029
| ~ subset(U_1029,U_1028)
| ~ in(U_1028,U_1030) )
& in(U_1029,U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(U_1034))) )
| ~ in(U_1034,omega) )
& ordinal(U_1034) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_1025,sK182(U_1026))],[f_282_3]) ).
fof(f_282_5,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ( ? [U_1033] :
( ! [U_1032] :
( ? [U_1031] :
( U_1031 != U_1032
& subset(U_1032,U_1031)
& in(U_1031,U_1033) )
| ~ in(U_1032,U_1033) )
& U_1033 != empty_set
& element(U_1033,powerset(powerset(succ(sK183)))) )
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ? [U_1029] :
( ! [U_1028] :
( U_1028 = U_1029
| ~ subset(U_1029,U_1028)
| ~ in(U_1028,U_1030) )
& in(U_1029,U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_1034,sK183)],[f_282_4]) ).
fof(f_282_6,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ( ? [U_1033] :
( ! [U_1032] :
( ? [U_1031] :
( U_1031 != U_1032
& subset(U_1032,U_1031)
& in(U_1031,U_1033) )
| ~ in(U_1032,U_1033) )
& U_1033 != empty_set
& element(U_1033,powerset(powerset(succ(sK183)))) )
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_1029,sK184(U_1030))],[f_282_5]) ).
fof(f_282_7,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ( ! [U_1032] :
( ? [U_1031] :
( U_1031 != U_1032
& subset(U_1032,U_1031)
& in(U_1031,sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_1033,sK185)],[f_282_6]) ).
fof(f_282_8,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ? [U_1042] :
( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(U_1042))) )
& in(U_1042,omega)
& U_1042 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,U_1042)
| ~ ordinal(U_1038) )
& being_limit_ordinal(U_1042)
& ordinal(U_1042) )
| ( ! [U_1032] :
( ( sK186(U_1032) != U_1032
& subset(U_1032,sK186(U_1032))
& in(sK186(U_1032),sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_1031,sK186(U_1032))],[f_282_7]) ).
fof(f_282_9,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(sK187))) )
& in(sK187,omega)
& sK187 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ! [U_1035] :
( U_1035 = U_1036
| ~ subset(U_1036,U_1035)
| ~ in(U_1035,U_1037) )
& in(U_1036,U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038) )
& being_limit_ordinal(sK187)
& ordinal(sK187) )
| ( ! [U_1032] :
( ( sK186(U_1032) != U_1032
& subset(U_1032,sK186(U_1032))
& in(sK186(U_1032),sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_1042,sK187)],[f_282_8]) ).
fof(f_282_10,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ( ? [U_1041] :
( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,U_1041) )
| ~ in(U_1040,U_1041) )
& U_1041 != empty_set
& element(U_1041,powerset(powerset(sK187))) )
& in(sK187,omega)
& sK187 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ( ! [U_1035] :
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037) )
& in(sK188(U_1038,U_1037),U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038) )
& being_limit_ordinal(sK187)
& ordinal(sK187) )
| ( ! [U_1032] :
( ( sK186(U_1032) != U_1032
& subset(U_1032,sK186(U_1032))
& in(sK186(U_1032),sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_1036,sK188(U_1038,U_1037))],[f_282_9]) ).
fof(f_282_11,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ( ! [U_1040] :
( ? [U_1039] :
( U_1039 != U_1040
& subset(U_1040,U_1039)
& in(U_1039,sK189) )
| ~ in(U_1040,sK189) )
& sK189 != empty_set
& element(sK189,powerset(powerset(sK187)))
& in(sK187,omega)
& sK187 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ( ! [U_1035] :
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037) )
& in(sK188(U_1038,U_1037),U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038) )
& being_limit_ordinal(sK187)
& ordinal(sK187) )
| ( ! [U_1032] :
( ( sK186(U_1032) != U_1032
& subset(U_1032,sK186(U_1032))
& in(sK186(U_1032),sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_1041,sK189)],[f_282_10]) ).
fof(f_282_12,plain,
( ! [U_1046] :
( ! [U_1045] :
( ? [U_1044] :
( ! [U_1043] :
( U_1043 = U_1044
| ~ subset(U_1044,U_1043)
| ~ in(U_1043,U_1045) )
& in(U_1044,U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ( ! [U_1040] :
( ( sK190(U_1040) != U_1040
& subset(U_1040,sK190(U_1040))
& in(sK190(U_1040),sK189) )
| ~ in(U_1040,sK189) )
& sK189 != empty_set
& element(sK189,powerset(powerset(sK187)))
& in(sK187,omega)
& sK187 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ( ! [U_1035] :
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037) )
& in(sK188(U_1038,U_1037),U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038) )
& being_limit_ordinal(sK187)
& ordinal(sK187) )
| ( ! [U_1032] :
( ( sK186(U_1032) != U_1032
& subset(U_1032,sK186(U_1032))
& in(sK186(U_1032),sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_1039,sK190(U_1040))],[f_282_11]) ).
fof(f_282_13,plain,
( ! [U_1046] :
( ! [U_1045] :
( ( ! [U_1043] :
( U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045) )
& in(sK191(U_1046,U_1045),U_1045) )
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) )
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) )
| ( ! [U_1040] :
( ( sK190(U_1040) != U_1040
& subset(U_1040,sK190(U_1040))
& in(sK190(U_1040),sK189) )
| ~ in(U_1040,sK189) )
& sK189 != empty_set
& element(sK189,powerset(powerset(sK187)))
& in(sK187,omega)
& sK187 != empty_set
& ! [U_1038] :
( ! [U_1037] :
( ( ! [U_1035] :
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037) )
& in(sK188(U_1038,U_1037),U_1037) )
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) )
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038) )
& being_limit_ordinal(sK187)
& ordinal(sK187) )
| ( ! [U_1032] :
( ( sK186(U_1032) != U_1032
& subset(U_1032,sK186(U_1032))
& in(sK186(U_1032),sK185) )
| ~ in(U_1032,sK185) )
& sK185 != empty_set
& element(sK185,powerset(powerset(succ(sK183))))
& in(succ(sK183),omega)
& ( ! [U_1030] :
( ( ! [U_1028] :
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030) )
& in(sK184(U_1030),U_1030) )
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183))) )
| ~ in(sK183,omega) )
& ordinal(sK183) )
| ( ! [U_1026] :
( ( sK182(U_1026) != U_1026
& subset(U_1026,sK182(U_1026))
& in(sK182(U_1026),sK181) )
| ~ in(U_1026,sK181) )
& sK181 != empty_set
& element(sK181,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_1044,sK191(U_1046,U_1045))],[f_282_12]) ).
cnf(f_282_14,plain,
( ordinal(sK183)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_15,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_16,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_17,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_18,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_19,plain,
( sK185 != empty_set
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_20,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_21,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_22,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_23,plain,
( ordinal(sK183)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_24,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_25,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_26,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_27,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_28,plain,
( sK185 != empty_set
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_29,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_30,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_31,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_32,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_33,plain,
( sK181 != empty_set
| ordinal(sK183)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_34,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_35,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_36,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_37,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_38,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_39,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_40,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_41,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_42,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_43,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_44,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_45,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_46,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_47,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_48,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_49,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_50,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_51,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_52,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_53,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_54,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_55,plain,
( sK185 != empty_set
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_56,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_57,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_58,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_59,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_60,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_61,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_62,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_63,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_64,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_65,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_66,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_67,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_68,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_69,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_70,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_71,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_72,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_73,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_74,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_75,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_76,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_77,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_78,plain,
( sK181 != empty_set
| ordinal(sK183)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_79,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_80,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_81,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_82,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_83,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_84,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_85,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_86,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_87,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_88,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_89,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_90,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_91,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_92,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_93,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_94,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_95,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_96,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_97,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_98,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_99,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_100,plain,
( sK185 != empty_set
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_101,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_102,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_103,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_104,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_105,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_106,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_107,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_108,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_109,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_110,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_111,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_112,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_113,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_114,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_115,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_116,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_117,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_118,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_119,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_120,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_121,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_122,plain,
( ordinal(sK183)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_123,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_124,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_125,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_126,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_127,plain,
( sK185 != empty_set
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_128,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_129,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_130,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_131,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| ordinal(sK183)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_132,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| ordinal(sK183)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_133,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_134,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_135,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_136,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_137,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_138,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_139,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_140,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_141,plain,
( sK185 != empty_set
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_142,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_143,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_144,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_145,plain,
( sK185 != empty_set
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_146,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_147,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_148,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_149,plain,
( ordinal(sK183)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_150,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_151,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_152,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_153,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_154,plain,
( sK185 != empty_set
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_155,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_156,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_157,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_158,plain,
( ordinal(sK183)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_159,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_160,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_161,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_162,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_163,plain,
( sK185 != empty_set
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_164,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_165,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_166,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_167,plain,
( ordinal(sK183)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_168,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_169,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_170,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_171,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_172,plain,
( sK185 != empty_set
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_173,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_174,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_175,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_176,plain,
( ordinal(sK183)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_177,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_178,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_179,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_180,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_181,plain,
( sK185 != empty_set
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_182,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_183,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_184,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_185,plain,
( in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| ordinal(sK183)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_186,plain,
( subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| ordinal(sK183)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_187,plain,
( sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| ordinal(sK183)
| in(empty_set,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_188,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_189,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_190,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_191,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_192,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_193,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_194,plain,
( sK185 != empty_set
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_195,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_196,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_197,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_198,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_199,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_200,plain,
( sK185 != empty_set
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_201,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_202,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_203,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_204,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_205,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_206,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_207,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_208,plain,
( sK185 != empty_set
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_209,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_210,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_211,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_212,plain,
( ordinal(sK183)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_213,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_214,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_215,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_216,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_217,plain,
( sK185 != empty_set
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_218,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_219,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_220,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_221,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| ordinal(sK183)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_222,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| ordinal(sK183)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_223,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_224,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_225,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_226,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_227,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_228,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_229,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_230,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_231,plain,
( sK185 != empty_set
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_232,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_233,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_234,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_235,plain,
( sK185 != empty_set
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_236,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_237,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_238,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_239,plain,
( ordinal(sK183)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_240,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_241,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_242,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_243,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_244,plain,
( sK185 != empty_set
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_245,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_246,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_247,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_248,plain,
( ordinal(sK183)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_249,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_250,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_251,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_252,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_253,plain,
( sK185 != empty_set
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_254,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_255,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_256,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_257,plain,
( ordinal(sK183)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_258,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_259,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_260,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_261,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_262,plain,
( sK185 != empty_set
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_263,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_264,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_265,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_266,plain,
( ordinal(sK183)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_267,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_268,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_269,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_270,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_271,plain,
( sK185 != empty_set
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_272,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_273,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_274,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_275,plain,
( in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| ordinal(sK183)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_276,plain,
( subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| ordinal(sK183)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_277,plain,
( sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| ordinal(sK183)
| in(empty_set,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_278,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_279,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_280,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_281,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_282,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_283,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_284,plain,
( sK185 != empty_set
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_285,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_286,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_287,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_288,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_289,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_290,plain,
( sK185 != empty_set
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_291,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_292,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_293,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_294,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_295,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_296,plain,
( in(succ(sK183),omega)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_297,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_298,plain,
( sK185 != empty_set
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_299,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_300,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_301,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(empty_set,omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_302,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_303,plain,
( sK181 != empty_set
| ordinal(sK183)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_304,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_305,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_306,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_307,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_308,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_309,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_310,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_311,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_312,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_313,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_314,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_315,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_316,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_317,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_318,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_319,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_320,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_321,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_322,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_323,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_324,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_325,plain,
( sK185 != empty_set
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_326,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_327,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_328,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_329,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_330,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_331,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_332,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_333,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_334,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_335,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_336,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_337,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_338,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_339,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_340,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_341,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_342,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_343,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_344,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_345,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_346,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_347,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_348,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_349,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| sK181 != empty_set
| ordinal(sK183)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_350,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| sK181 != empty_set
| ordinal(sK183)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_351,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_352,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_353,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_354,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_355,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_356,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_357,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_358,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_359,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_360,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_361,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_362,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_363,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_364,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_365,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_366,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_367,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_368,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_369,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_370,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_371,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_372,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_373,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_374,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_375,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_376,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_377,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_378,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_379,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_380,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_381,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_382,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_383,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_384,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_385,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_386,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_387,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_388,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_389,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_390,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_391,plain,
( sK185 != empty_set
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_392,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_393,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_394,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_395,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_396,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_397,plain,
( sK185 != empty_set
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_398,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_399,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_400,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_401,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_402,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_403,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_404,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_405,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_406,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_407,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_408,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_409,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_410,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_411,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_412,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_413,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_414,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_415,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_416,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_417,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_418,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_419,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_420,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_421,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_422,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_423,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_424,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_425,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_426,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_427,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_428,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_429,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_430,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_431,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_432,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_433,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_434,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_435,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_436,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_437,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_438,plain,
( sK181 != empty_set
| ordinal(sK183)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_439,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_440,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_441,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_442,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_443,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_444,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_445,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_446,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_447,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_448,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_449,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_450,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_451,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_452,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_453,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_454,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_455,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_456,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_457,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_458,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_459,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_460,plain,
( sK185 != empty_set
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_461,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_462,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_463,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_464,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_465,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_466,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_467,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_468,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_469,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_470,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_471,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_472,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_473,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_474,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_475,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_476,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_477,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_478,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_479,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_480,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_481,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_482,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_483,plain,
( sK181 != empty_set
| ordinal(sK183)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_484,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_485,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_486,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_487,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_488,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_489,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_490,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_491,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_492,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_493,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_494,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_495,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_496,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_497,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_498,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_499,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_500,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_501,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_502,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_503,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_504,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_505,plain,
( sK185 != empty_set
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_506,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_507,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_508,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_509,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_510,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_511,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_512,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_513,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_514,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_515,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_516,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_517,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_518,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_519,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_520,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_521,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_522,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_523,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_524,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_525,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_526,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_527,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_528,plain,
( sK181 != empty_set
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_529,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_530,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_531,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_532,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_533,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_534,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_535,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_536,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_537,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_538,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_539,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_540,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_541,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_542,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_543,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_544,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_545,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_546,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_547,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_548,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_549,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_550,plain,
( sK185 != empty_set
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_551,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_552,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_553,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_554,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_555,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_556,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_557,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_558,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_559,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_560,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_561,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_562,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_563,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_564,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_565,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_566,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_567,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_568,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_569,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_570,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_571,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_572,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_573,plain,
( sK181 != empty_set
| ordinal(sK183)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_574,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_575,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_576,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_577,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_578,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_579,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_580,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_581,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_582,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_583,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_584,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_585,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_586,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_587,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_588,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_589,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_590,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_591,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_592,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_593,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_594,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_595,plain,
( sK185 != empty_set
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_596,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_597,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_598,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_599,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_600,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_601,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_602,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_603,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_604,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_605,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_606,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_607,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_608,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_609,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_610,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_611,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_612,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_613,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_614,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_615,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_616,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_617,plain,
( in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_618,plain,
( subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_619,plain,
( sK181 != empty_set
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_620,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_621,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_622,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_623,plain,
( sK181 != empty_set
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_624,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_625,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_626,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_627,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_628,plain,
( sK181 != empty_set
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_629,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_630,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_631,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_632,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_633,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_634,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_635,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_636,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_637,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_638,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_639,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_640,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_641,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_642,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_643,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_644,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_645,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_646,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_647,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_648,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_649,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_650,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_651,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_652,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_653,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_654,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_655,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_656,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_657,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_658,plain,
( sK185 != empty_set
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_659,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_660,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_661,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_662,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_663,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_664,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_665,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_666,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_667,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_668,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_669,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_670,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_671,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_672,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_673,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_674,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_675,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_676,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_677,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_678,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_679,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_680,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_681,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_682,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_683,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_684,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_685,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_686,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_687,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_688,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_689,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_690,plain,
( sK185 != empty_set
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_691,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_692,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_693,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_694,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_695,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_696,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_697,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_698,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_699,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_700,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_701,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_702,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_703,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_704,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_705,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_706,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_707,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_708,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_709,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_710,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_711,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_712,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_713,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_714,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_715,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_716,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_717,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_718,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_719,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_720,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_721,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_722,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_723,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_724,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_725,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_726,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_727,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_728,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_729,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_730,plain,
( sK185 != empty_set
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_731,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_732,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_733,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_734,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_735,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_736,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_737,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_738,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_739,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_740,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_741,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_742,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_743,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_744,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_745,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_746,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_747,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_748,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_749,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_750,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_751,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| in(sK191(U_1046,U_1045),U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_752,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_753,plain,
( sK181 != empty_set
| ordinal(sK183)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_754,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_755,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_756,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_757,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_758,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_759,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_760,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_761,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_762,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_763,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_764,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_765,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_766,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_767,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_768,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_769,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_770,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_771,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_772,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_773,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_774,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_775,plain,
( sK185 != empty_set
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_776,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_777,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_778,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_779,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_780,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_781,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_782,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_783,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_784,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_785,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_786,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_787,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_788,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_789,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_790,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_791,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_792,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_793,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_794,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_795,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_796,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| being_limit_ordinal(sK187)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_797,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_798,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_799,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| sK181 != empty_set
| ordinal(sK183)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_800,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| sK181 != empty_set
| ordinal(sK183)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_801,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_802,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_803,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_804,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_805,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_806,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_807,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_808,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_809,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_810,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_811,plain,
( in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_812,plain,
( U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_813,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_814,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_815,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_816,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_817,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_818,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_819,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_820,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_821,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_822,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_823,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_824,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_825,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_826,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_827,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_828,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_829,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_830,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_831,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_832,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_833,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_834,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_835,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_836,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_837,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_838,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_839,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_840,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_841,plain,
( sK185 != empty_set
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_842,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_843,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_844,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_845,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_846,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_847,plain,
( sK185 != empty_set
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_848,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_849,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_850,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_851,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_852,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_853,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_854,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_855,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_856,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_857,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_858,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_859,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_860,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_861,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_862,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_863,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_864,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_865,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_866,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_867,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_868,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK188(U_1038,U_1037),U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_869,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_870,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_871,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_872,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_873,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_874,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_875,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_876,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_877,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_878,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_879,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_880,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_881,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_882,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_883,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_884,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_885,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_886,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| U_1035 = sK188(U_1038,U_1037)
| ~ subset(sK188(U_1038,U_1037),U_1035)
| ~ in(U_1035,U_1037)
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038)))
| ~ in(U_1038,omega)
| ~ in(U_1038,sK187)
| ~ ordinal(U_1038)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_887,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_888,plain,
( sK181 != empty_set
| ordinal(sK183)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_889,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_890,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_891,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_892,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_893,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_894,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_895,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_896,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_897,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_898,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_899,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_900,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_901,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_902,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_903,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_904,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_905,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_906,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_907,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_908,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_909,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_910,plain,
( sK185 != empty_set
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_911,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_912,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_913,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_914,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_915,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_916,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_917,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_918,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_919,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_920,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_921,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_922,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_923,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_924,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_925,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_926,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_927,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_928,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_929,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_930,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_931,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK187 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_932,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_933,plain,
( sK181 != empty_set
| ordinal(sK183)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_934,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_935,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_936,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_937,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_938,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_939,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_940,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_941,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_942,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_943,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_944,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_945,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_946,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_947,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_948,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_949,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_950,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_951,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_952,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_953,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_954,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_955,plain,
( sK185 != empty_set
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_956,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_957,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_958,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_959,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_960,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_961,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_962,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_963,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_964,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_965,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_966,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_967,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_968,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_969,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_970,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_971,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_972,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_973,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_974,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_975,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_976,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK187,omega)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_977,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_978,plain,
( sK181 != empty_set
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_979,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_980,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_981,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_982,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_983,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_984,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_985,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_986,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_987,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_988,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_989,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_990,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_991,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_992,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_993,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_994,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_995,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_996,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_997,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_998,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_999,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1000,plain,
( sK185 != empty_set
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1001,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1002,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1003,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1004,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1005,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1006,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1007,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1008,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1009,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1010,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1011,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1012,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1013,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1014,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1015,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1016,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1017,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1018,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1019,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1020,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1021,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK189,powerset(powerset(sK187)))
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1022,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1023,plain,
( sK181 != empty_set
| ordinal(sK183)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1024,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1025,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1026,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1027,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1028,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1029,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1030,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1031,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1032,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1033,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1034,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1035,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1036,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1037,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1038,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1039,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1040,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1041,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1042,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1043,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1044,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1045,plain,
( sK185 != empty_set
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1046,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1047,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1048,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1049,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1050,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1051,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1052,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1053,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1054,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1055,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1056,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1057,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1058,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1059,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1060,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1061,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1062,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1063,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1064,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1065,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1066,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK189 != empty_set
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1067,plain,
( in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1068,plain,
( subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1069,plain,
( sK181 != empty_set
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1070,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1071,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1072,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1073,plain,
( sK181 != empty_set
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1074,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1075,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1076,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1077,plain,
( element(sK181,powerset(powerset(empty_set)))
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1078,plain,
( sK181 != empty_set
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1079,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1080,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1081,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| ordinal(sK183)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1082,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1083,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1084,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1085,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1086,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1087,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1088,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1089,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1090,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1091,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1092,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1093,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1094,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1095,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1096,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1097,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1098,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1099,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1100,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1101,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1102,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1103,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1104,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1105,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1106,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1107,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1108,plain,
( sK185 != empty_set
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1109,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1110,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1111,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1112,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1113,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1114,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1115,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1116,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1117,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1118,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1119,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1120,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1121,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1122,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1123,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1124,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1125,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1126,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1127,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1128,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1129,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(sK190(U_1040),sK189)
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1130,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1131,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1132,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1133,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1134,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1135,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1136,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1137,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1138,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1139,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1140,plain,
( sK185 != empty_set
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1141,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1142,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1143,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1144,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1145,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1146,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1147,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1148,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1149,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1150,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1151,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1152,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1153,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1154,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1155,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1156,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1157,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1158,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1159,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1160,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1161,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| subset(U_1040,sK190(U_1040))
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1162,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1163,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1164,plain,
( in(succ(sK183),omega)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1165,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1166,plain,
( sK185 != empty_set
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1167,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1168,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1169,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| element(sK181,powerset(powerset(empty_set)))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1170,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1171,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1172,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1173,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1174,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1175,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1176,plain,
( in(sK184(U_1030),U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1177,plain,
( U_1028 = sK184(U_1030)
| ~ subset(sK184(U_1030),U_1028)
| ~ in(U_1028,U_1030)
| U_1030 = empty_set
| ~ element(U_1030,powerset(powerset(sK183)))
| ~ in(sK183,omega)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1178,plain,
( in(succ(sK183),omega)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1179,plain,
( element(sK185,powerset(powerset(succ(sK183))))
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1180,plain,
( sK185 != empty_set
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1181,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1182,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1183,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK181 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1184,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1185,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1186,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| in(succ(sK183),omega)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1187,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1188,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1189,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| element(sK185,powerset(powerset(succ(sK183))))
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1190,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1191,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1192,plain,
( sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK185 != empty_set
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1193,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1194,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1195,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1196,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1197,plain,
( in(sK182(U_1026),sK181)
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1198,plain,
( subset(U_1026,sK182(U_1026))
| ~ in(U_1026,sK181)
| sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1199,plain,
( in(sK186(U_1032),sK185)
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1200,plain,
( subset(U_1032,sK186(U_1032))
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
cnf(f_282_1201,plain,
( sK186(U_1032) != U_1032
| ~ in(U_1032,sK185)
| sK182(U_1026) != U_1026
| ~ in(U_1026,sK181)
| sK190(U_1040) != U_1040
| ~ in(U_1040,sK189)
| U_1043 = sK191(U_1046,U_1045)
| ~ subset(sK191(U_1046,U_1045),U_1043)
| ~ in(U_1043,U_1045)
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046)))
| ~ in(U_1046,omega)
| ~ ordinal(U_1046) ),
inference(clausify,[status(thm)],[f_282_13]) ).
fof(f_283_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_283_2,plain,
! [U_1052,U_1051,U_1050] :
( ? [U_1049] :
( ! [U_1048,U_1047] :
( ( in(ordered_pair(U_1048,U_1047),U_1049)
| ~ in(ordered_pair(apply(U_1050,U_1048),apply(U_1050,U_1047)),U_1051)
| ~ in(U_1047,U_1052)
| ~ in(U_1048,U_1052) )
& ( ( in(ordered_pair(apply(U_1050,U_1048),apply(U_1050,U_1047)),U_1051)
& in(U_1047,U_1052)
& in(U_1048,U_1052) )
| ~ in(ordered_pair(U_1048,U_1047),U_1049) ) )
& relation(U_1049) )
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1052,U_1051,U_1050] :
( ? [U_1049] :
( ! [U_1056,U_1054] :
( in(ordered_pair(U_1056,U_1054),U_1049)
| ~ in(ordered_pair(apply(U_1050,U_1056),apply(U_1050,U_1054)),U_1051)
| ~ in(U_1054,U_1052)
| ~ in(U_1056,U_1052) )
& ! [U_1055,U_1053] :
( ( in(ordered_pair(apply(U_1050,U_1055),apply(U_1050,U_1053)),U_1051)
& in(U_1053,U_1052)
& in(U_1055,U_1052) )
| ~ in(ordered_pair(U_1055,U_1053),U_1049) )
& relation(U_1049) )
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(miniscope,[status(thm)],[f_283_2]) ).
fof(f_283_4,plain,
! [U_1052,U_1051,U_1050] :
( ( ! [U_1056,U_1054] :
( in(ordered_pair(U_1056,U_1054),sK192(U_1052,U_1051,U_1050))
| ~ in(ordered_pair(apply(U_1050,U_1056),apply(U_1050,U_1054)),U_1051)
| ~ in(U_1054,U_1052)
| ~ in(U_1056,U_1052) )
& ! [U_1055,U_1053] :
( ( in(ordered_pair(apply(U_1050,U_1055),apply(U_1050,U_1053)),U_1051)
& in(U_1053,U_1052)
& in(U_1055,U_1052) )
| ~ in(ordered_pair(U_1055,U_1053),sK192(U_1052,U_1051,U_1050)) )
& relation(sK192(U_1052,U_1051,U_1050)) )
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_1049,sK192(U_1052,U_1051,U_1050))],[f_283_3]) ).
cnf(f_283_5,plain,
( relation(sK192(U_1052,U_1051,U_1050))
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(clausify,[status(thm)],[f_283_4]) ).
cnf(f_283_6,plain,
( in(U_1055,U_1052)
| ~ in(ordered_pair(U_1055,U_1053),sK192(U_1052,U_1051,U_1050))
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(clausify,[status(thm)],[f_283_4]) ).
cnf(f_283_7,plain,
( in(U_1053,U_1052)
| ~ in(ordered_pair(U_1055,U_1053),sK192(U_1052,U_1051,U_1050))
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(clausify,[status(thm)],[f_283_4]) ).
cnf(f_283_8,plain,
( in(ordered_pair(apply(U_1050,U_1055),apply(U_1050,U_1053)),U_1051)
| ~ in(ordered_pair(U_1055,U_1053),sK192(U_1052,U_1051,U_1050))
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(clausify,[status(thm)],[f_283_4]) ).
cnf(f_283_9,plain,
( in(ordered_pair(U_1056,U_1054),sK192(U_1052,U_1051,U_1050))
| ~ in(ordered_pair(apply(U_1050,U_1056),apply(U_1050,U_1054)),U_1051)
| ~ in(U_1054,U_1052)
| ~ in(U_1056,U_1052)
| ~ function(U_1050)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(clausify,[status(thm)],[f_283_4]) ).
fof(f_284_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_284_2,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
! [U_1070] :
( ( in(U_1070,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1070,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1070,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1070,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1070,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1070,U_1071) ) )
| ? [U_1063,U_1062,U_1061] :
( U_1062 != U_1061
& ? [U_1060] :
( ! [U_1059] :
( in(ordered_pair(U_1061,U_1059),U_1072)
| ~ in(U_1059,U_1060) )
& in(U_1061,U_1060)
& U_1063 = U_1060 )
& in(U_1063,U_1073)
& ? [U_1058] :
( ! [U_1057] :
( in(ordered_pair(U_1062,U_1057),U_1072)
| ~ in(U_1057,U_1058) )
& in(U_1062,U_1058)
& U_1063 = U_1058 )
& in(U_1063,U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
( ! [U_1075] :
( in(U_1075,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,U_1071) ) )
| ? [U_1063,U_1062,U_1061] :
( U_1062 != U_1061
& ? [U_1060] :
( ! [U_1059] :
( in(ordered_pair(U_1061,U_1059),U_1072)
| ~ in(U_1059,U_1060) )
& in(U_1061,U_1060)
& U_1063 = U_1060 )
& in(U_1063,U_1073)
& ? [U_1058] :
( ! [U_1057] :
( in(ordered_pair(U_1062,U_1057),U_1072)
| ~ in(U_1057,U_1058) )
& in(U_1062,U_1058)
& U_1063 = U_1058 )
& in(U_1063,U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(miniscope,[status(thm)],[f_284_2]) ).
fof(f_284_4,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
( ! [U_1075] :
( in(U_1075,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,U_1071) ) )
| ? [U_1062,U_1061] :
( U_1062 != U_1061
& ? [U_1060] :
( ! [U_1059] :
( in(ordered_pair(U_1061,U_1059),U_1072)
| ~ in(U_1059,U_1060) )
& in(U_1061,U_1060)
& sK193(U_1073,U_1072) = U_1060 )
& in(sK193(U_1073,U_1072),U_1073)
& ? [U_1058] :
( ! [U_1057] :
( in(ordered_pair(U_1062,U_1057),U_1072)
| ~ in(U_1057,U_1058) )
& in(U_1062,U_1058)
& sK193(U_1073,U_1072) = U_1058 )
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_1063,sK193(U_1073,U_1072))],[f_284_3]) ).
fof(f_284_5,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
( ! [U_1075] :
( in(U_1075,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,U_1071) ) )
| ? [U_1061] :
( sK194(U_1073,U_1072) != U_1061
& ? [U_1060] :
( ! [U_1059] :
( in(ordered_pair(U_1061,U_1059),U_1072)
| ~ in(U_1059,U_1060) )
& in(U_1061,U_1060)
& sK193(U_1073,U_1072) = U_1060 )
& in(sK193(U_1073,U_1072),U_1073)
& ? [U_1058] :
( ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,U_1058) )
& in(sK194(U_1073,U_1072),U_1058)
& sK193(U_1073,U_1072) = U_1058 )
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_1062,sK194(U_1073,U_1072))],[f_284_4]) ).
fof(f_284_6,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
( ! [U_1075] :
( in(U_1075,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,U_1071) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ? [U_1060] :
( ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,U_1060) )
& in(sK195(U_1073,U_1072),U_1060)
& sK193(U_1073,U_1072) = U_1060 )
& in(sK193(U_1073,U_1072),U_1073)
& ? [U_1058] :
( ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,U_1058) )
& in(sK194(U_1073,U_1072),U_1058)
& sK193(U_1073,U_1072) = U_1058 )
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_1061,sK195(U_1073,U_1072))],[f_284_5]) ).
fof(f_284_7,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
( ! [U_1075] :
( in(U_1075,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,U_1071) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ? [U_1060] :
( ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,U_1060) )
& in(sK195(U_1073,U_1072),U_1060)
& sK193(U_1073,U_1072) = U_1060 )
& in(sK193(U_1073,U_1072),U_1073)
& ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072)) )
& in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_1058,sK196(U_1073,U_1072))],[f_284_6]) ).
fof(f_284_8,plain,
! [U_1073,U_1072] :
( ? [U_1071] :
( ! [U_1075] :
( in(U_1075,U_1071)
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,U_1071) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072)) )
& in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073)
& ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072)) )
& in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_1060,sK197(U_1073,U_1072))],[f_284_7]) ).
fof(f_284_9,plain,
! [U_1073,U_1072] :
( ( ! [U_1075] :
( in(U_1075,sK198(U_1073,U_1072))
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ? [U_1066] :
( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& U_1066 = U_1065 )
& in(U_1066,U_1073)
& in(U_1066,U_1073) )
| ~ in(U_1074,sK198(U_1073,U_1072)) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072)) )
& in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073)
& ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072)) )
& in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_1071,sK198(U_1073,U_1072))],[f_284_8]) ).
fof(f_284_10,plain,
! [U_1073,U_1072] :
( ( ! [U_1075] :
( in(U_1075,sK198(U_1073,U_1072))
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ( ? [U_1065] :
( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,U_1065) )
& in(U_1074,U_1065)
& sK199(U_1073,U_1072,U_1074) = U_1065 )
& in(sK199(U_1073,U_1072,U_1074),U_1073)
& in(sK199(U_1073,U_1072,U_1074),U_1073) )
| ~ in(U_1074,sK198(U_1073,U_1072)) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072)) )
& in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073)
& ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072)) )
& in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_1066,sK199(U_1073,U_1072,U_1074))],[f_284_9]) ).
fof(f_284_11,plain,
! [U_1073,U_1072] :
( ( ! [U_1075] :
( in(U_1075,sK198(U_1073,U_1072))
| ! [U_1069] :
( ! [U_1068] :
( ? [U_1067] :
( ~ in(ordered_pair(U_1075,U_1067),U_1072)
& in(U_1067,U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074)) )
& in(U_1074,sK200(U_1073,U_1072,U_1074))
& sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
& in(sK199(U_1073,U_1072,U_1074),U_1073)
& in(sK199(U_1073,U_1072,U_1074),U_1073) )
| ~ in(U_1074,sK198(U_1073,U_1072)) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072)) )
& in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073)
& ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072)) )
& in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_1065,sK200(U_1073,U_1072,U_1074))],[f_284_10]) ).
fof(f_284_12,plain,
! [U_1073,U_1072] :
( ( ! [U_1075] :
( in(U_1075,sK198(U_1073,U_1072))
| ! [U_1069] :
( ! [U_1068] :
( ( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
& in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068) )
| ~ in(U_1075,U_1068)
| U_1069 != U_1068 )
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073) ) )
& ! [U_1074] :
( ( ! [U_1064] :
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074)) )
& in(U_1074,sK200(U_1073,U_1072,U_1074))
& sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
& in(sK199(U_1073,U_1072,U_1074),U_1073)
& in(sK199(U_1073,U_1072,U_1074),U_1073) )
| ~ in(U_1074,sK198(U_1073,U_1072)) ) )
| ( sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
& ! [U_1059] :
( in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072)) )
& in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073)
& ! [U_1057] :
( in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072)) )
& in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
& sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
& in(sK193(U_1073,U_1072),U_1073) )
| ~ relation(U_1072)
| empty(U_1073) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_1067,sK201(U_1073,U_1072,U_1075,U_1069,U_1068))],[f_284_11]) ).
cnf(f_284_13,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_14,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_15,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_16,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_17,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_18,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_19,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_20,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_21,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_22,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_23,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_24,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_25,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_26,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_27,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_28,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_29,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_30,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_31,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_32,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_33,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_34,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_35,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_36,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_37,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_38,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_39,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_40,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_41,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_42,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_43,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_44,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_45,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_46,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_47,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_48,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_49,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_50,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_51,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_52,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_53,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_54,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_55,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_56,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_57,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_58,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_59,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_60,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_61,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_62,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_63,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_64,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_65,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_66,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_67,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_68,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_69,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_70,plain,
( in(sK199(U_1073,U_1072,U_1074),U_1073)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_71,plain,
( sK199(U_1073,U_1072,U_1074) = sK200(U_1073,U_1072,U_1074)
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_72,plain,
( in(U_1074,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_73,plain,
( in(ordered_pair(U_1074,U_1064),U_1072)
| ~ in(U_1064,sK200(U_1073,U_1072,U_1074))
| ~ in(U_1074,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_74,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
cnf(f_284_75,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(clausify,[status(thm)],[f_284_12]) ).
fof(f_285_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_285_2,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ? [U_1098] :
! [U_1097] :
( ( in(U_1097,U_1098)
| ! [U_1096] :
( ! [U_1095,U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ~ in(U_1095,U_1101)
| ordered_pair(U_1095,U_1094) != U_1097 )
| U_1096 != U_1097
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) ) )
& ( ? [U_1091] :
( ? [U_1090,U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& in(U_1090,U_1101)
& ordered_pair(U_1090,U_1089) = U_1097 )
& U_1091 = U_1097
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
| ~ in(U_1097,U_1098) ) )
| ? [U_1086,U_1085,U_1084] :
( U_1085 != U_1084
& ? [U_1083,U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& in(U_1083,U_1101)
& ordered_pair(U_1083,U_1082) = U_1084 )
& U_1086 = U_1084
& ? [U_1079,U_1078] :
( ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(U_1078,U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(U_1078,U_1077)
& U_1079 = U_1077 )
& in(U_1079,U_1101)
& ordered_pair(U_1079,U_1078) = U_1085 )
& U_1086 = U_1085 ) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ? [U_1086,U_1085,U_1084] :
( U_1085 != U_1084
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = U_1084 )
& in(U_1083,U_1101) )
& U_1086 = U_1084
& ? [U_1079] :
( ? [U_1078] :
( ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(U_1078,U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(U_1078,U_1077)
& U_1079 = U_1077 )
& ordered_pair(U_1079,U_1078) = U_1085 )
& in(U_1079,U_1101) )
& U_1086 = U_1085 )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
fof(f_285_4,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ? [U_1085,U_1084] :
( U_1085 != U_1084
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = U_1084 )
& in(U_1083,U_1101) )
& sK202(U_1101,U_1100) = U_1084
& ? [U_1079] :
( ? [U_1078] :
( ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(U_1078,U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(U_1078,U_1077)
& U_1079 = U_1077 )
& ordered_pair(U_1079,U_1078) = U_1085 )
& in(U_1079,U_1101) )
& sK202(U_1101,U_1100) = U_1085 )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_1086,sK202(U_1101,U_1100))],[f_285_3]) ).
fof(f_285_5,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ? [U_1084] :
( sK203(U_1101,U_1100) != U_1084
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = U_1084 )
& in(U_1083,U_1101) )
& sK202(U_1101,U_1100) = U_1084
& ? [U_1079] :
( ? [U_1078] :
( ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(U_1078,U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(U_1078,U_1077)
& U_1079 = U_1077 )
& ordered_pair(U_1079,U_1078) = sK203(U_1101,U_1100) )
& in(U_1079,U_1101) )
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_1085,sK203(U_1101,U_1100))],[f_285_4]) ).
fof(f_285_6,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = sK204(U_1101,U_1100) )
& in(U_1083,U_1101) )
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ? [U_1079] :
( ? [U_1078] :
( ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(U_1078,U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(U_1078,U_1077)
& U_1079 = U_1077 )
& ordered_pair(U_1079,U_1078) = sK203(U_1101,U_1100) )
& in(U_1079,U_1101) )
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_1084,sK204(U_1101,U_1100))],[f_285_5]) ).
fof(f_285_7,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = sK204(U_1101,U_1100) )
& in(U_1083,U_1101) )
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ? [U_1078] :
( ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(U_1078,U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(U_1078,U_1077)
& sK205(U_1101,U_1100) = U_1077 )
& ordered_pair(sK205(U_1101,U_1100),U_1078) = sK203(U_1101,U_1100) )
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_1079,sK205(U_1101,U_1100))],[f_285_6]) ).
fof(f_285_8,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = sK204(U_1101,U_1100) )
& in(U_1083,U_1101) )
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ? [U_1077] :
( ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,U_1077) )
& in(sK206(U_1101,U_1100),U_1077)
& sK205(U_1101,U_1100) = U_1077 )
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_1078,sK206(U_1101,U_1100))],[f_285_7]) ).
fof(f_285_9,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ? [U_1083] :
( ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& U_1083 = U_1081 )
& ordered_pair(U_1083,U_1082) = sK204(U_1101,U_1100) )
& in(U_1083,U_1101) )
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_1077,sK207(U_1101,U_1100))],[f_285_8]) ).
fof(f_285_10,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ? [U_1082] :
( ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(U_1082,U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(U_1082,U_1081)
& sK208(U_1101,U_1100) = U_1081 )
& ordered_pair(sK208(U_1101,U_1100),U_1082) = sK204(U_1101,U_1100) )
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_1083,sK208(U_1101,U_1100))],[f_285_9]) ).
fof(f_285_11,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ? [U_1081] :
( ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,U_1081) )
& in(sK209(U_1101,U_1100),U_1081)
& sK208(U_1101,U_1100) = U_1081 )
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_1082,sK209(U_1101,U_1100))],[f_285_10]) ).
fof(f_285_12,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
? [U_1098] :
( ! [U_1103] :
( in(U_1103,U_1098)
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,U_1098) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_1081,sK210(U_1101,U_1100))],[f_285_11]) ).
fof(f_285_13,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ! [U_1103] :
( in(U_1103,sK211(U_1101,U_1100,U_1099))
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1090] :
( ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& U_1090 = U_1088 )
& ordered_pair(U_1090,U_1089) = U_1102 )
& in(U_1090,U_1101) ) )
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099)) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_1098,sK211(U_1101,U_1100,U_1099))],[f_285_12]) ).
fof(f_285_14,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ! [U_1103] :
( in(U_1103,sK211(U_1101,U_1100,U_1099))
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1089] :
( ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(U_1089,U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(U_1089,U_1088)
& sK212(U_1101,U_1100,U_1099,U_1102) = U_1088 )
& ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),U_1089) = U_1102 )
& in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101) )
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099)) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_1090,sK212(U_1101,U_1100,U_1099,U_1102))],[f_285_13]) ).
fof(f_285_15,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ! [U_1103] :
( in(U_1103,sK211(U_1101,U_1100,U_1099))
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ? [U_1088] :
( ! [U_1087] :
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,U_1088) )
& in(sK213(U_1101,U_1100,U_1099,U_1102),U_1088)
& sK212(U_1101,U_1100,U_1099,U_1102) = U_1088 )
& ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
& in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101) )
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099)) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_1089,sK213(U_1101,U_1100,U_1099,U_1102))],[f_285_14]) ).
fof(f_285_16,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ! [U_1103] :
( in(U_1103,sK211(U_1101,U_1100,U_1099))
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( ? [U_1091] :
( U_1091 = U_1102
& in(U_1091,cartesian_product2(U_1101,U_1099)) )
& ! [U_1087] :
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102)) )
& in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
& sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
& ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
& in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101) )
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099)) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_1088,sK214(U_1101,U_1100,U_1099,U_1102))],[f_285_15]) ).
fof(f_285_17,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ! [U_1103] :
( in(U_1103,sK211(U_1101,U_1100,U_1099))
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ? [U_1092] :
( ~ in(ordered_pair(U_1094,U_1092),U_1100)
& in(U_1092,U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
& in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
& ! [U_1087] :
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102)) )
& in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
& sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
& ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
& in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101) )
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099)) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_1091,sK215(U_1101,U_1100,U_1099,U_1102))],[f_285_16]) ).
fof(f_285_18,plain,
! [U_1101,U_1100] :
( ! [U_1099] :
( ! [U_1103] :
( in(U_1103,sK211(U_1101,U_1100,U_1099))
| ! [U_1096] :
( U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099)) )
| ! [U_1095] :
( ! [U_1094] :
( ! [U_1093] :
( ( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
& in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093) )
| ~ in(U_1094,U_1093)
| U_1095 != U_1093 )
| ordered_pair(U_1095,U_1094) != U_1103 )
| ~ in(U_1095,U_1101) ) )
& ! [U_1102] :
( ( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
& in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
& ! [U_1087] :
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102)) )
& in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
& sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
& ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
& in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101) )
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099)) ) )
| ( sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
& ! [U_1080] :
( in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100)) )
& in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
& sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
& ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
& in(sK208(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
& ! [U_1076] :
( in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100)) )
& in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
& sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
& ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
& in(sK205(U_1101,U_1100),U_1101)
& sK202(U_1101,U_1100) = sK203(U_1101,U_1100) )
| ~ relation(U_1100)
| empty(U_1101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_1092,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093))],[f_285_17]) ).
cnf(f_285_19,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_20,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_21,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_22,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_23,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_24,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_25,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_26,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_27,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_28,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_29,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_30,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_31,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_32,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_33,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_34,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_35,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_36,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_37,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_38,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_39,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_40,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_41,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_42,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_43,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_44,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_45,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_46,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_47,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_48,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_49,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_50,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_51,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_52,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_53,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_54,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_55,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_56,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_57,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_58,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_59,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_60,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_61,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_62,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_63,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_64,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_65,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_66,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_67,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_68,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_69,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_70,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_71,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_72,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_73,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_74,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_75,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_76,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_77,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_78,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_79,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_80,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_81,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_82,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_83,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_84,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_85,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_86,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_87,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_88,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_89,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_90,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_91,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_92,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_93,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_94,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_95,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_96,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_97,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_98,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_99,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_100,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_101,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_102,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_103,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_104,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_105,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_106,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK205(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_107,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_108,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK205(U_1101,U_1100),sK206(U_1101,U_1100)) = sK203(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_109,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_110,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK205(U_1101,U_1100) = sK207(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_111,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_112,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK206(U_1101,U_1100),sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_113,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_114,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK206(U_1101,U_1100),U_1076),U_1100)
| ~ in(U_1076,sK207(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_115,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_116,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK202(U_1101,U_1100) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_117,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_118,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK208(U_1101,U_1100),U_1101)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_119,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_120,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| ordered_pair(sK208(U_1101,U_1100),sK209(U_1101,U_1100)) = sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_121,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_122,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK208(U_1101,U_1100) = sK210(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_123,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_124,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(sK209(U_1101,U_1100),sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_125,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_126,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| in(ordered_pair(sK209(U_1101,U_1100),U_1080),U_1100)
| ~ in(U_1080,sK210(U_1101,U_1100))
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_127,plain,
( in(sK212(U_1101,U_1100,U_1099,U_1102),U_1101)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_128,plain,
( ordered_pair(sK212(U_1101,U_1100,U_1099,U_1102),sK213(U_1101,U_1100,U_1099,U_1102)) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_129,plain,
( sK212(U_1101,U_1100,U_1099,U_1102) = sK214(U_1101,U_1100,U_1099,U_1102)
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_130,plain,
( in(sK213(U_1101,U_1100,U_1099,U_1102),sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_131,plain,
( in(ordered_pair(sK213(U_1101,U_1100,U_1099,U_1102),U_1087),U_1100)
| ~ in(U_1087,sK214(U_1101,U_1100,U_1099,U_1102))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_132,plain,
( in(sK215(U_1101,U_1100,U_1099,U_1102),cartesian_product2(U_1101,U_1099))
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_133,plain,
( sK215(U_1101,U_1100,U_1099,U_1102) = U_1102
| ~ in(U_1102,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_134,plain,
( in(sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093),U_1093)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
cnf(f_285_135,plain,
( ~ in(ordered_pair(U_1094,sK216(U_1101,U_1100,U_1099,U_1103,U_1095,U_1094,U_1093)),U_1100)
| ~ in(U_1094,U_1093)
| U_1095 != U_1093
| ordered_pair(U_1095,U_1094) != U_1103
| ~ in(U_1095,U_1101)
| U_1096 != U_1103
| ~ in(U_1096,cartesian_product2(U_1101,U_1099))
| in(U_1103,sK211(U_1101,U_1100,U_1099))
| sK203(U_1101,U_1100) != sK204(U_1101,U_1100)
| ~ relation(U_1100)
| empty(U_1101) ),
inference(clausify,[status(thm)],[f_285_18]) ).
fof(f_286_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_286_2,plain,
! [U_1111] :
( ? [U_1110] :
! [U_1109] :
( ( in(U_1109,U_1110)
| ! [U_1108] :
( U_1109 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ( ? [U_1107] :
( U_1109 = singleton(U_1107)
& in(U_1107,U_1111)
& in(U_1107,U_1111) )
| ~ in(U_1109,U_1110) ) )
| ? [U_1106,U_1105,U_1104] :
( U_1105 != U_1104
& U_1104 = singleton(U_1106)
& in(U_1106,U_1111)
& U_1105 = singleton(U_1106)
& in(U_1106,U_1111) ) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1111] :
( ? [U_1110] :
( ! [U_1113] :
( in(U_1113,U_1110)
| ! [U_1108] :
( U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ! [U_1112] :
( ? [U_1107] :
( U_1112 = singleton(U_1107)
& in(U_1107,U_1111)
& in(U_1107,U_1111) )
| ~ in(U_1112,U_1110) ) )
| ? [U_1106,U_1105,U_1104] :
( U_1105 != U_1104
& U_1104 = singleton(U_1106)
& in(U_1106,U_1111)
& U_1105 = singleton(U_1106)
& in(U_1106,U_1111) ) ),
inference(miniscope,[status(thm)],[f_286_2]) ).
fof(f_286_4,plain,
! [U_1111] :
( ? [U_1110] :
( ! [U_1113] :
( in(U_1113,U_1110)
| ! [U_1108] :
( U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ! [U_1112] :
( ? [U_1107] :
( U_1112 = singleton(U_1107)
& in(U_1107,U_1111)
& in(U_1107,U_1111) )
| ~ in(U_1112,U_1110) ) )
| ? [U_1105,U_1104] :
( U_1105 != U_1104
& U_1104 = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111)
& U_1105 = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_1106,sK217(U_1111))],[f_286_3]) ).
fof(f_286_5,plain,
! [U_1111] :
( ? [U_1110] :
( ! [U_1113] :
( in(U_1113,U_1110)
| ! [U_1108] :
( U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ! [U_1112] :
( ? [U_1107] :
( U_1112 = singleton(U_1107)
& in(U_1107,U_1111)
& in(U_1107,U_1111) )
| ~ in(U_1112,U_1110) ) )
| ? [U_1104] :
( sK218(U_1111) != U_1104
& U_1104 = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111)
& sK218(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_1105,sK218(U_1111))],[f_286_4]) ).
fof(f_286_6,plain,
! [U_1111] :
( ? [U_1110] :
( ! [U_1113] :
( in(U_1113,U_1110)
| ! [U_1108] :
( U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ! [U_1112] :
( ? [U_1107] :
( U_1112 = singleton(U_1107)
& in(U_1107,U_1111)
& in(U_1107,U_1111) )
| ~ in(U_1112,U_1110) ) )
| ( sK218(U_1111) != sK219(U_1111)
& sK219(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111)
& sK218(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_1104,sK219(U_1111))],[f_286_5]) ).
fof(f_286_7,plain,
! [U_1111] :
( ( ! [U_1113] :
( in(U_1113,sK220(U_1111))
| ! [U_1108] :
( U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ! [U_1112] :
( ? [U_1107] :
( U_1112 = singleton(U_1107)
& in(U_1107,U_1111)
& in(U_1107,U_1111) )
| ~ in(U_1112,sK220(U_1111)) ) )
| ( sK218(U_1111) != sK219(U_1111)
& sK219(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111)
& sK218(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_1110,sK220(U_1111))],[f_286_6]) ).
fof(f_286_8,plain,
! [U_1111] :
( ( ! [U_1113] :
( in(U_1113,sK220(U_1111))
| ! [U_1108] :
( U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ) )
& ! [U_1112] :
( ( U_1112 = singleton(sK221(U_1111,U_1112))
& in(sK221(U_1111,U_1112),U_1111)
& in(sK221(U_1111,U_1112),U_1111) )
| ~ in(U_1112,sK220(U_1111)) ) )
| ( sK218(U_1111) != sK219(U_1111)
& sK219(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111)
& sK218(U_1111) = singleton(sK217(U_1111))
& in(sK217(U_1111),U_1111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_1107,sK221(U_1111,U_1112))],[f_286_7]) ).
cnf(f_286_9,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| in(sK217(U_1111),U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_10,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| in(sK217(U_1111),U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_11,plain,
( U_1112 = singleton(sK221(U_1111,U_1112))
| ~ in(U_1112,sK220(U_1111))
| in(sK217(U_1111),U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_12,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| sK218(U_1111) = singleton(sK217(U_1111)) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_13,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| sK218(U_1111) = singleton(sK217(U_1111)) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_14,plain,
( U_1112 = singleton(sK221(U_1111,U_1112))
| ~ in(U_1112,sK220(U_1111))
| sK218(U_1111) = singleton(sK217(U_1111)) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_15,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| in(sK217(U_1111),U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_16,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| in(sK217(U_1111),U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_17,plain,
( U_1112 = singleton(sK221(U_1111,U_1112))
| ~ in(U_1112,sK220(U_1111))
| in(sK217(U_1111),U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_18,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| sK219(U_1111) = singleton(sK217(U_1111)) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_19,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| sK219(U_1111) = singleton(sK217(U_1111)) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_20,plain,
( U_1112 = singleton(sK221(U_1111,U_1112))
| ~ in(U_1112,sK220(U_1111))
| sK219(U_1111) = singleton(sK217(U_1111)) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_21,plain,
( in(sK217(U_1111),U_1111)
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_22,plain,
( sK218(U_1111) = singleton(sK217(U_1111))
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_23,plain,
( in(sK217(U_1111),U_1111)
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_24,plain,
( sK219(U_1111) = singleton(sK217(U_1111))
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_25,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| sK218(U_1111) != sK219(U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_26,plain,
( in(sK221(U_1111,U_1112),U_1111)
| ~ in(U_1112,sK220(U_1111))
| sK218(U_1111) != sK219(U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_27,plain,
( U_1112 = singleton(sK221(U_1111,U_1112))
| ~ in(U_1112,sK220(U_1111))
| sK218(U_1111) != sK219(U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
cnf(f_286_28,plain,
( in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| ~ in(U_1108,U_1111)
| sK218(U_1111) != sK219(U_1111) ),
inference(clausify,[status(thm)],[f_286_8]) ).
fof(f_287_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_287_2,plain,
! [U_1130,U_1129] :
( ? [U_1128] :
! [U_1127] :
( ( in(U_1127,U_1128)
| ! [U_1126] :
( ! [U_1125,U_1124] :
( U_1124 != singleton(U_1125)
| ~ in(U_1125,U_1130)
| ordered_pair(U_1125,U_1124) != U_1127 )
| U_1126 != U_1127
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) ) )
& ( ? [U_1123] :
( ? [U_1122,U_1121] :
( U_1121 = singleton(U_1122)
& in(U_1122,U_1130)
& ordered_pair(U_1122,U_1121) = U_1127 )
& U_1123 = U_1127
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
| ~ in(U_1127,U_1128) ) )
| ? [U_1120,U_1119,U_1118] :
( U_1119 != U_1118
& ? [U_1117,U_1116] :
( U_1116 = singleton(U_1117)
& in(U_1117,U_1130)
& ordered_pair(U_1117,U_1116) = U_1118 )
& U_1120 = U_1118
& ? [U_1115,U_1114] :
( U_1114 = singleton(U_1115)
& in(U_1115,U_1130)
& ordered_pair(U_1115,U_1114) = U_1119 )
& U_1120 = U_1119 ) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ? [U_1120,U_1119,U_1118] :
( U_1119 != U_1118
& ? [U_1117] :
( ? [U_1116] :
( U_1116 = singleton(U_1117)
& ordered_pair(U_1117,U_1116) = U_1118 )
& in(U_1117,U_1130) )
& U_1120 = U_1118
& ? [U_1115] :
( ? [U_1114] :
( U_1114 = singleton(U_1115)
& ordered_pair(U_1115,U_1114) = U_1119 )
& in(U_1115,U_1130) )
& U_1120 = U_1119 ) ),
inference(miniscope,[status(thm)],[f_287_2]) ).
fof(f_287_4,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ? [U_1119,U_1118] :
( U_1119 != U_1118
& ? [U_1117] :
( ? [U_1116] :
( U_1116 = singleton(U_1117)
& ordered_pair(U_1117,U_1116) = U_1118 )
& in(U_1117,U_1130) )
& sK222(U_1130) = U_1118
& ? [U_1115] :
( ? [U_1114] :
( U_1114 = singleton(U_1115)
& ordered_pair(U_1115,U_1114) = U_1119 )
& in(U_1115,U_1130) )
& sK222(U_1130) = U_1119 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_1120,sK222(U_1130))],[f_287_3]) ).
fof(f_287_5,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ? [U_1118] :
( sK223(U_1130) != U_1118
& ? [U_1117] :
( ? [U_1116] :
( U_1116 = singleton(U_1117)
& ordered_pair(U_1117,U_1116) = U_1118 )
& in(U_1117,U_1130) )
& sK222(U_1130) = U_1118
& ? [U_1115] :
( ? [U_1114] :
( U_1114 = singleton(U_1115)
& ordered_pair(U_1115,U_1114) = sK223(U_1130) )
& in(U_1115,U_1130) )
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_1119,sK223(U_1130))],[f_287_4]) ).
fof(f_287_6,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ( sK223(U_1130) != sK224(U_1130)
& ? [U_1117] :
( ? [U_1116] :
( U_1116 = singleton(U_1117)
& ordered_pair(U_1117,U_1116) = sK224(U_1130) )
& in(U_1117,U_1130) )
& sK222(U_1130) = sK224(U_1130)
& ? [U_1115] :
( ? [U_1114] :
( U_1114 = singleton(U_1115)
& ordered_pair(U_1115,U_1114) = sK223(U_1130) )
& in(U_1115,U_1130) )
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_1118,sK224(U_1130))],[f_287_5]) ).
fof(f_287_7,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ( sK223(U_1130) != sK224(U_1130)
& ? [U_1117] :
( ? [U_1116] :
( U_1116 = singleton(U_1117)
& ordered_pair(U_1117,U_1116) = sK224(U_1130) )
& in(U_1117,U_1130) )
& sK222(U_1130) = sK224(U_1130)
& ? [U_1114] :
( U_1114 = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),U_1114) = sK223(U_1130) )
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_1115,sK225(U_1130))],[f_287_6]) ).
fof(f_287_8,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ( sK223(U_1130) != sK224(U_1130)
& ? [U_1117] :
( ? [U_1116] :
( U_1116 = singleton(U_1117)
& ordered_pair(U_1117,U_1116) = sK224(U_1130) )
& in(U_1117,U_1130) )
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_1114,sK226(U_1130))],[f_287_7]) ).
fof(f_287_9,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ( sK223(U_1130) != sK224(U_1130)
& ? [U_1116] :
( U_1116 = singleton(sK227(U_1130))
& ordered_pair(sK227(U_1130),U_1116) = sK224(U_1130) )
& in(sK227(U_1130),U_1130)
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_1117,sK227(U_1130))],[f_287_8]) ).
fof(f_287_10,plain,
! [U_1130] :
( ! [U_1129] :
? [U_1128] :
( ! [U_1132] :
( in(U_1132,U_1128)
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,U_1128) ) )
| ( sK223(U_1130) != sK224(U_1130)
& sK228(U_1130) = singleton(sK227(U_1130))
& ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130)
& in(sK227(U_1130),U_1130)
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_1116,sK228(U_1130))],[f_287_9]) ).
fof(f_287_11,plain,
! [U_1130] :
( ! [U_1129] :
( ! [U_1132] :
( in(U_1132,sK229(U_1130,U_1129))
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1122] :
( ? [U_1121] :
( U_1121 = singleton(U_1122)
& ordered_pair(U_1122,U_1121) = U_1131 )
& in(U_1122,U_1130) ) )
| ~ in(U_1131,sK229(U_1130,U_1129)) ) )
| ( sK223(U_1130) != sK224(U_1130)
& sK228(U_1130) = singleton(sK227(U_1130))
& ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130)
& in(sK227(U_1130),U_1130)
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_1128,sK229(U_1130,U_1129))],[f_287_10]) ).
fof(f_287_12,plain,
! [U_1130] :
( ! [U_1129] :
( ! [U_1132] :
( in(U_1132,sK229(U_1130,U_1129))
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& ? [U_1121] :
( U_1121 = singleton(sK230(U_1130,U_1129,U_1131))
& ordered_pair(sK230(U_1130,U_1129,U_1131),U_1121) = U_1131 )
& in(sK230(U_1130,U_1129,U_1131),U_1130) )
| ~ in(U_1131,sK229(U_1130,U_1129)) ) )
| ( sK223(U_1130) != sK224(U_1130)
& sK228(U_1130) = singleton(sK227(U_1130))
& ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130)
& in(sK227(U_1130),U_1130)
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_1122,sK230(U_1130,U_1129,U_1131))],[f_287_11]) ).
fof(f_287_13,plain,
! [U_1130] :
( ! [U_1129] :
( ! [U_1132] :
( in(U_1132,sK229(U_1130,U_1129))
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( ? [U_1123] :
( U_1123 = U_1131
& in(U_1123,cartesian_product2(U_1130,U_1129)) )
& sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
& ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
& in(sK230(U_1130,U_1129,U_1131),U_1130) )
| ~ in(U_1131,sK229(U_1130,U_1129)) ) )
| ( sK223(U_1130) != sK224(U_1130)
& sK228(U_1130) = singleton(sK227(U_1130))
& ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130)
& in(sK227(U_1130),U_1130)
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_1121,sK231(U_1130,U_1129,U_1131))],[f_287_12]) ).
fof(f_287_14,plain,
! [U_1130] :
( ! [U_1129] :
( ! [U_1132] :
( in(U_1132,sK229(U_1130,U_1129))
| ! [U_1126] :
( U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129)) )
| ! [U_1125] :
( ! [U_1124] :
( U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132 )
| ~ in(U_1125,U_1130) ) )
& ! [U_1131] :
( ( sK232(U_1130,U_1129,U_1131) = U_1131
& in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
& sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
& ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
& in(sK230(U_1130,U_1129,U_1131),U_1130) )
| ~ in(U_1131,sK229(U_1130,U_1129)) ) )
| ( sK223(U_1130) != sK224(U_1130)
& sK228(U_1130) = singleton(sK227(U_1130))
& ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130)
& in(sK227(U_1130),U_1130)
& sK222(U_1130) = sK224(U_1130)
& sK226(U_1130) = singleton(sK225(U_1130))
& ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
& in(sK225(U_1130),U_1130)
& sK222(U_1130) = sK223(U_1130) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_1123,sK232(U_1130,U_1129,U_1131))],[f_287_13]) ).
cnf(f_287_15,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_16,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_17,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_18,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_19,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_20,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK225(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_21,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK225(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_22,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK225(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_23,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK225(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_24,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK225(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_25,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_26,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_27,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_28,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_29,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_30,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK226(U_1130) = singleton(sK225(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_31,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK226(U_1130) = singleton(sK225(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_32,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK226(U_1130) = singleton(sK225(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_33,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK226(U_1130) = singleton(sK225(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_34,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK226(U_1130) = singleton(sK225(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_35,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_36,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_37,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_38,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_39,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK222(U_1130) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_40,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK227(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_41,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK227(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_42,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK227(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_43,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK227(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_44,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| in(sK227(U_1130),U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_45,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_46,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_47,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_48,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_49,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_50,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK228(U_1130) = singleton(sK227(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_51,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK228(U_1130) = singleton(sK227(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_52,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK228(U_1130) = singleton(sK227(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_53,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK228(U_1130) = singleton(sK227(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_54,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK228(U_1130) = singleton(sK227(U_1130)) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_55,plain,
( sK222(U_1130) = sK223(U_1130)
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_56,plain,
( in(sK225(U_1130),U_1130)
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_57,plain,
( ordered_pair(sK225(U_1130),sK226(U_1130)) = sK223(U_1130)
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_58,plain,
( sK226(U_1130) = singleton(sK225(U_1130))
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_59,plain,
( sK222(U_1130) = sK224(U_1130)
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_60,plain,
( in(sK227(U_1130),U_1130)
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_61,plain,
( ordered_pair(sK227(U_1130),sK228(U_1130)) = sK224(U_1130)
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_62,plain,
( sK228(U_1130) = singleton(sK227(U_1130))
| in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_63,plain,
( in(sK230(U_1130,U_1129,U_1131),U_1130)
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK223(U_1130) != sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_64,plain,
( ordered_pair(sK230(U_1130,U_1129,U_1131),sK231(U_1130,U_1129,U_1131)) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK223(U_1130) != sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_65,plain,
( sK231(U_1130,U_1129,U_1131) = singleton(sK230(U_1130,U_1129,U_1131))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK223(U_1130) != sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_66,plain,
( in(sK232(U_1130,U_1129,U_1131),cartesian_product2(U_1130,U_1129))
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK223(U_1130) != sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_67,plain,
( sK232(U_1130,U_1129,U_1131) = U_1131
| ~ in(U_1131,sK229(U_1130,U_1129))
| sK223(U_1130) != sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
cnf(f_287_68,plain,
( in(U_1132,sK229(U_1130,U_1129))
| U_1126 != U_1132
| ~ in(U_1126,cartesian_product2(U_1130,U_1129))
| U_1124 != singleton(U_1125)
| ordered_pair(U_1125,U_1124) != U_1132
| ~ in(U_1125,U_1130)
| sK223(U_1130) != sK224(U_1130) ),
inference(clausify,[status(thm)],[f_287_14]) ).
fof(f_288_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_288_2,plain,
! [U_1156] :
( ? [U_1155] :
! [U_1154] :
( ( in(U_1154,U_1155)
| ! [U_1153] :
( ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1154 != U_1152
| ~ ordinal(U_1152) )
| U_1153 != U_1154
| ~ in(U_1153,succ(U_1156)) ) )
& ( ? [U_1148] :
( ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1154 = U_1147
& ordinal(U_1147) )
& U_1148 = U_1154
& in(U_1148,succ(U_1156)) )
| ~ in(U_1154,U_1155) ) )
| ? [U_1143,U_1142,U_1141] :
( U_1142 != U_1141
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& U_1141 = U_1140
& ordinal(U_1140) )
& U_1143 = U_1141
& ? [U_1136] :
( ( ! [U_1135] :
( ? [U_1134] :
( ! [U_1133] :
( U_1133 = U_1134
| ~ subset(U_1134,U_1133)
| ~ in(U_1133,U_1135) )
& in(U_1134,U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(U_1136))) )
| ~ in(U_1136,omega) )
& U_1142 = U_1136
& ordinal(U_1136) )
& U_1143 = U_1142 )
| ~ ordinal(U_1156) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ? [U_1143,U_1142,U_1141] :
( U_1142 != U_1141
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& U_1141 = U_1140
& ordinal(U_1140) )
& U_1143 = U_1141
& ? [U_1136] :
( ( ! [U_1135] :
( ? [U_1134] :
( ! [U_1133] :
( U_1133 = U_1134
| ~ subset(U_1134,U_1133)
| ~ in(U_1133,U_1135) )
& in(U_1134,U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(U_1136))) )
| ~ in(U_1136,omega) )
& U_1142 = U_1136
& ordinal(U_1136) )
& U_1143 = U_1142 )
| ~ ordinal(U_1156) ),
inference(miniscope,[status(thm)],[f_288_2]) ).
fof(f_288_4,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ? [U_1142,U_1141] :
( U_1142 != U_1141
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& U_1141 = U_1140
& ordinal(U_1140) )
& sK233(U_1156) = U_1141
& ? [U_1136] :
( ( ! [U_1135] :
( ? [U_1134] :
( ! [U_1133] :
( U_1133 = U_1134
| ~ subset(U_1134,U_1133)
| ~ in(U_1133,U_1135) )
& in(U_1134,U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(U_1136))) )
| ~ in(U_1136,omega) )
& U_1142 = U_1136
& ordinal(U_1136) )
& sK233(U_1156) = U_1142 )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_1143,sK233(U_1156))],[f_288_3]) ).
fof(f_288_5,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ? [U_1141] :
( sK234(U_1156) != U_1141
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& U_1141 = U_1140
& ordinal(U_1140) )
& sK233(U_1156) = U_1141
& ? [U_1136] :
( ( ! [U_1135] :
( ? [U_1134] :
( ! [U_1133] :
( U_1133 = U_1134
| ~ subset(U_1134,U_1133)
| ~ in(U_1133,U_1135) )
& in(U_1134,U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(U_1136))) )
| ~ in(U_1136,omega) )
& sK234(U_1156) = U_1136
& ordinal(U_1136) )
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_1142,sK234(U_1156))],[f_288_4]) ).
fof(f_288_6,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& sK235(U_1156) = U_1140
& ordinal(U_1140) )
& sK233(U_1156) = sK235(U_1156)
& ? [U_1136] :
( ( ! [U_1135] :
( ? [U_1134] :
( ! [U_1133] :
( U_1133 = U_1134
| ~ subset(U_1134,U_1133)
| ~ in(U_1133,U_1135) )
& in(U_1134,U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(U_1136))) )
| ~ in(U_1136,omega) )
& sK234(U_1156) = U_1136
& ordinal(U_1136) )
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_1141,sK235(U_1156))],[f_288_5]) ).
fof(f_288_7,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& sK235(U_1156) = U_1140
& ordinal(U_1140) )
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ? [U_1134] :
( ! [U_1133] :
( U_1133 = U_1134
| ~ subset(U_1134,U_1133)
| ~ in(U_1133,U_1135) )
& in(U_1134,U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_1136,sK236(U_1156))],[f_288_6]) ).
fof(f_288_8,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ? [U_1140] :
( ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(U_1140))) )
| ~ in(U_1140,omega) )
& sK235(U_1156) = U_1140
& ordinal(U_1140) )
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_1134,sK237(U_1156,U_1135))],[f_288_7]) ).
fof(f_288_9,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ? [U_1138] :
( ! [U_1137] :
( U_1137 = U_1138
| ~ subset(U_1138,U_1137)
| ~ in(U_1137,U_1139) )
& in(U_1138,U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_1140,sK238(U_1156))],[f_288_8]) ).
fof(f_288_10,plain,
! [U_1156] :
( ? [U_1155] :
( ! [U_1158] :
( in(U_1158,U_1155)
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,U_1155) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_1138,sK239(U_1156,U_1139))],[f_288_9]) ).
fof(f_288_11,plain,
! [U_1156] :
( ( ! [U_1158] :
( in(U_1158,sK240(U_1156))
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ? [U_1147] :
( ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(U_1147))) )
| ~ in(U_1147,omega) )
& U_1157 = U_1147
& ordinal(U_1147) ) )
| ~ in(U_1157,sK240(U_1156)) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_1155,sK240(U_1156))],[f_288_10]) ).
fof(f_288_12,plain,
! [U_1156] :
( ( ! [U_1158] :
( in(U_1158,sK240(U_1156))
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ( ! [U_1146] :
( ? [U_1145] :
( ! [U_1144] :
( U_1144 = U_1145
| ~ subset(U_1145,U_1144)
| ~ in(U_1144,U_1146) )
& in(U_1145,U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157)))) )
| ~ in(sK241(U_1156,U_1157),omega) )
& U_1157 = sK241(U_1156,U_1157)
& ordinal(sK241(U_1156,U_1157)) )
| ~ in(U_1157,sK240(U_1156)) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_1147,sK241(U_1156,U_1157))],[f_288_11]) ).
fof(f_288_13,plain,
! [U_1156] :
( ( ! [U_1158] :
( in(U_1158,sK240(U_1156))
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( ? [U_1148] :
( U_1148 = U_1157
& in(U_1148,succ(U_1156)) )
& ( ! [U_1146] :
( ( ! [U_1144] :
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146) )
& in(sK242(U_1156,U_1157,U_1146),U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157)))) )
| ~ in(sK241(U_1156,U_1157),omega) )
& U_1157 = sK241(U_1156,U_1157)
& ordinal(sK241(U_1156,U_1157)) )
| ~ in(U_1157,sK240(U_1156)) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_1145,sK242(U_1156,U_1157,U_1146))],[f_288_12]) ).
fof(f_288_14,plain,
! [U_1156] :
( ( ! [U_1158] :
( in(U_1158,sK240(U_1156))
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ? [U_1151] :
( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,U_1151) )
| ~ in(U_1150,U_1151) )
& U_1151 != empty_set
& element(U_1151,powerset(powerset(U_1152))) )
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( sK243(U_1156,U_1157) = U_1157
& in(sK243(U_1156,U_1157),succ(U_1156))
& ( ! [U_1146] :
( ( ! [U_1144] :
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146) )
& in(sK242(U_1156,U_1157,U_1146),U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157)))) )
| ~ in(sK241(U_1156,U_1157),omega) )
& U_1157 = sK241(U_1156,U_1157)
& ordinal(sK241(U_1156,U_1157)) )
| ~ in(U_1157,sK240(U_1156)) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_1148,sK243(U_1156,U_1157))],[f_288_13]) ).
fof(f_288_15,plain,
! [U_1156] :
( ( ! [U_1158] :
( in(U_1158,sK240(U_1156))
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ! [U_1150] :
( ? [U_1149] :
( U_1149 != U_1150
& subset(U_1150,U_1149)
& in(U_1149,sK244(U_1156,U_1158,U_1152)) )
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152)) )
& sK244(U_1156,U_1158,U_1152) != empty_set
& element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( sK243(U_1156,U_1157) = U_1157
& in(sK243(U_1156,U_1157),succ(U_1156))
& ( ! [U_1146] :
( ( ! [U_1144] :
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146) )
& in(sK242(U_1156,U_1157,U_1146),U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157)))) )
| ~ in(sK241(U_1156,U_1157),omega) )
& U_1157 = sK241(U_1156,U_1157)
& ordinal(sK241(U_1156,U_1157)) )
| ~ in(U_1157,sK240(U_1156)) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_1151,sK244(U_1156,U_1158,U_1152))],[f_288_14]) ).
fof(f_288_16,plain,
! [U_1156] :
( ( ! [U_1158] :
( in(U_1158,sK240(U_1156))
| ! [U_1153] :
( U_1153 != U_1158
| ~ in(U_1153,succ(U_1156)) )
| ! [U_1152] :
( ( ! [U_1150] :
( ( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
& subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
& in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152)) )
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152)) )
& sK244(U_1156,U_1158,U_1152) != empty_set
& element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
& in(U_1152,omega) )
| U_1158 != U_1152
| ~ ordinal(U_1152) ) )
& ! [U_1157] :
( ( sK243(U_1156,U_1157) = U_1157
& in(sK243(U_1156,U_1157),succ(U_1156))
& ( ! [U_1146] :
( ( ! [U_1144] :
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146) )
& in(sK242(U_1156,U_1157,U_1146),U_1146) )
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157)))) )
| ~ in(sK241(U_1156,U_1157),omega) )
& U_1157 = sK241(U_1156,U_1157)
& ordinal(sK241(U_1156,U_1157)) )
| ~ in(U_1157,sK240(U_1156)) ) )
| ( sK234(U_1156) != sK235(U_1156)
& ( ! [U_1139] :
( ( ! [U_1137] :
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139) )
& in(sK239(U_1156,U_1139),U_1139) )
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156)))) )
| ~ in(sK238(U_1156),omega) )
& sK235(U_1156) = sK238(U_1156)
& ordinal(sK238(U_1156))
& sK233(U_1156) = sK235(U_1156)
& ( ! [U_1135] :
( ( ! [U_1133] :
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135) )
& in(sK237(U_1156,U_1135),U_1135) )
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156)))) )
| ~ in(sK236(U_1156),omega) )
& sK234(U_1156) = sK236(U_1156)
& ordinal(sK236(U_1156))
& sK233(U_1156) = sK234(U_1156) )
| ~ ordinal(U_1156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_1149,sK245(U_1156,U_1158,U_1152,U_1150))],[f_288_15]) ).
cnf(f_288_17,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_18,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_19,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_20,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_21,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_22,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_23,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_24,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_25,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_26,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_27,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_28,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_29,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_30,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_31,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_32,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_33,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_34,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_35,plain,
( in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_36,plain,
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_37,plain,
( in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_38,plain,
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_39,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_40,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_41,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_42,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_43,plain,
( in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_44,plain,
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_45,plain,
( in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_46,plain,
( U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_47,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_48,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_49,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_50,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_51,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_52,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_53,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_54,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_55,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_56,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_57,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_58,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_59,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_60,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_61,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_62,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_63,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_64,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_65,plain,
( in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_66,plain,
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_67,plain,
( in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_68,plain,
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_69,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_70,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_71,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_72,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_73,plain,
( in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_74,plain,
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_75,plain,
( in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_76,plain,
( U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_77,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_78,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_79,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_80,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_81,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_82,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK234(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_83,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_84,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_85,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_86,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_87,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_88,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK236(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_89,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_90,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_91,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_92,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_93,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_94,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) = sK236(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_95,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_96,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_97,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_98,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_99,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_100,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK237(U_1156,U_1135),U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_101,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_102,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_103,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_104,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_105,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_106,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1133 = sK237(U_1156,U_1135)
| ~ subset(sK237(U_1156,U_1135),U_1133)
| ~ in(U_1133,U_1135)
| U_1135 = empty_set
| ~ element(U_1135,powerset(powerset(sK236(U_1156))))
| ~ in(sK236(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_107,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_108,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_109,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_110,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_111,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_112,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK233(U_1156) = sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_113,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_114,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_115,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_116,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_117,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_118,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| ordinal(sK238(U_1156))
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_119,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_120,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_121,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_122,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_123,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_124,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK235(U_1156) = sK238(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_125,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_126,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_127,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_128,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_129,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_130,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| in(sK239(U_1156,U_1139),U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_131,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_132,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_133,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_134,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_135,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_136,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| U_1137 = sK239(U_1156,U_1139)
| ~ subset(sK239(U_1156,U_1139),U_1137)
| ~ in(U_1137,U_1139)
| U_1139 = empty_set
| ~ element(U_1139,powerset(powerset(sK238(U_1156))))
| ~ in(sK238(U_1156),omega)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_137,plain,
( ordinal(sK241(U_1156,U_1157))
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_138,plain,
( U_1157 = sK241(U_1156,U_1157)
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_139,plain,
( in(sK242(U_1156,U_1157,U_1146),U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_140,plain,
( U_1144 = sK242(U_1156,U_1157,U_1146)
| ~ subset(sK242(U_1156,U_1157,U_1146),U_1144)
| ~ in(U_1144,U_1146)
| U_1146 = empty_set
| ~ element(U_1146,powerset(powerset(sK241(U_1156,U_1157))))
| ~ in(sK241(U_1156,U_1157),omega)
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_141,plain,
( in(sK243(U_1156,U_1157),succ(U_1156))
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_142,plain,
( sK243(U_1156,U_1157) = U_1157
| ~ in(U_1157,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_143,plain,
( in(U_1152,omega)
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_144,plain,
( element(sK244(U_1156,U_1158,U_1152),powerset(powerset(U_1152)))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_145,plain,
( sK244(U_1156,U_1158,U_1152) != empty_set
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_146,plain,
( in(sK245(U_1156,U_1158,U_1152,U_1150),sK244(U_1156,U_1158,U_1152))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_147,plain,
( subset(U_1150,sK245(U_1156,U_1158,U_1152,U_1150))
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
cnf(f_288_148,plain,
( sK245(U_1156,U_1158,U_1152,U_1150) != U_1150
| ~ in(U_1150,sK244(U_1156,U_1158,U_1152))
| U_1158 != U_1152
| ~ ordinal(U_1152)
| U_1153 != U_1158
| ~ in(U_1153,succ(U_1156))
| in(U_1158,sK240(U_1156))
| sK234(U_1156) != sK235(U_1156)
| ~ ordinal(U_1156) ),
inference(clausify,[status(thm)],[f_288_16]) ).
fof(f_289_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_289_2,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
! [U_1168] :
( ( in(U_1168,U_1169)
| ! [U_1167] :
( ! [U_1166] :
( U_1168 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) )
| U_1167 != U_1168
| ~ in(U_1167,powerset(U_1171)) ) )
& ( ? [U_1165] :
( ? [U_1164] :
( U_1168 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) )
& U_1165 = U_1168
& in(U_1165,powerset(U_1171)) )
| ~ in(U_1168,U_1169) ) )
| ? [U_1163,U_1162,U_1161] :
( U_1162 != U_1161
& ? [U_1160] :
( U_1161 = set_difference(U_1160,singleton(U_1171))
& in(U_1160,U_1170) )
& U_1163 = U_1161
& ? [U_1159] :
( U_1162 = set_difference(U_1159,singleton(U_1171))
& in(U_1159,U_1170) )
& U_1163 = U_1162 )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
( ! [U_1173] :
( in(U_1173,U_1169)
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,U_1169) ) )
| ? [U_1163,U_1162,U_1161] :
( U_1162 != U_1161
& ? [U_1160] :
( U_1161 = set_difference(U_1160,singleton(U_1171))
& in(U_1160,U_1170) )
& U_1163 = U_1161
& ? [U_1159] :
( U_1162 = set_difference(U_1159,singleton(U_1171))
& in(U_1159,U_1170) )
& U_1163 = U_1162 )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(miniscope,[status(thm)],[f_289_2]) ).
fof(f_289_4,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
( ! [U_1173] :
( in(U_1173,U_1169)
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,U_1169) ) )
| ? [U_1162,U_1161] :
( U_1162 != U_1161
& ? [U_1160] :
( U_1161 = set_difference(U_1160,singleton(U_1171))
& in(U_1160,U_1170) )
& sK246(U_1171,U_1170) = U_1161
& ? [U_1159] :
( U_1162 = set_difference(U_1159,singleton(U_1171))
& in(U_1159,U_1170) )
& sK246(U_1171,U_1170) = U_1162 )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_1163,sK246(U_1171,U_1170))],[f_289_3]) ).
fof(f_289_5,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
( ! [U_1173] :
( in(U_1173,U_1169)
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,U_1169) ) )
| ? [U_1161] :
( sK247(U_1171,U_1170) != U_1161
& ? [U_1160] :
( U_1161 = set_difference(U_1160,singleton(U_1171))
& in(U_1160,U_1170) )
& sK246(U_1171,U_1170) = U_1161
& ? [U_1159] :
( sK247(U_1171,U_1170) = set_difference(U_1159,singleton(U_1171))
& in(U_1159,U_1170) )
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_1162,sK247(U_1171,U_1170))],[f_289_4]) ).
fof(f_289_6,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
( ! [U_1173] :
( in(U_1173,U_1169)
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,U_1169) ) )
| ( sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
& ? [U_1160] :
( sK248(U_1171,U_1170) = set_difference(U_1160,singleton(U_1171))
& in(U_1160,U_1170) )
& sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
& ? [U_1159] :
( sK247(U_1171,U_1170) = set_difference(U_1159,singleton(U_1171))
& in(U_1159,U_1170) )
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_1161,sK248(U_1171,U_1170))],[f_289_5]) ).
fof(f_289_7,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
( ! [U_1173] :
( in(U_1173,U_1169)
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,U_1169) ) )
| ( sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
& ? [U_1160] :
( sK248(U_1171,U_1170) = set_difference(U_1160,singleton(U_1171))
& in(U_1160,U_1170) )
& sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
& sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
& in(sK249(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_1159,sK249(U_1171,U_1170))],[f_289_6]) ).
fof(f_289_8,plain,
! [U_1171,U_1170] :
( ? [U_1169] :
( ! [U_1173] :
( in(U_1173,U_1169)
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,U_1169) ) )
| ( sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
& sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
& in(sK250(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
& sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
& in(sK249(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_1160,sK250(U_1171,U_1170))],[f_289_7]) ).
fof(f_289_9,plain,
! [U_1171,U_1170] :
( ( ! [U_1173] :
( in(U_1173,sK251(U_1171,U_1170))
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& ? [U_1164] :
( U_1172 = set_difference(U_1164,singleton(U_1171))
& in(U_1164,U_1170) ) )
| ~ in(U_1172,sK251(U_1171,U_1170)) ) )
| ( sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
& sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
& in(sK250(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
& sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
& in(sK249(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_1169,sK251(U_1171,U_1170))],[f_289_8]) ).
fof(f_289_10,plain,
! [U_1171,U_1170] :
( ( ! [U_1173] :
( in(U_1173,sK251(U_1171,U_1170))
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( ? [U_1165] :
( U_1165 = U_1172
& in(U_1165,powerset(U_1171)) )
& U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
& in(sK252(U_1171,U_1170,U_1172),U_1170) )
| ~ in(U_1172,sK251(U_1171,U_1170)) ) )
| ( sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
& sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
& in(sK250(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
& sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
& in(sK249(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_1164,sK252(U_1171,U_1170,U_1172))],[f_289_9]) ).
fof(f_289_11,plain,
! [U_1171,U_1170] :
( ( ! [U_1173] :
( in(U_1173,sK251(U_1171,U_1170))
| ! [U_1167] :
( U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171)) )
| ! [U_1166] :
( U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170) ) )
& ! [U_1172] :
( ( sK253(U_1171,U_1170,U_1172) = U_1172
& in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
& U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
& in(sK252(U_1171,U_1170,U_1172),U_1170) )
| ~ in(U_1172,sK251(U_1171,U_1170)) ) )
| ( sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
& sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
& in(sK250(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
& sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
& in(sK249(U_1171,U_1170),U_1170)
& sK246(U_1171,U_1170) = sK247(U_1171,U_1170) )
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_1165,sK253(U_1171,U_1170,U_1172))],[f_289_10]) ).
cnf(f_289_12,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK247(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_13,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK247(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_14,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK247(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_15,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK247(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_16,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK249(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_17,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK249(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_18,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK249(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_19,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK249(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_20,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_21,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_22,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_23,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_24,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_25,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_26,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_27,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_28,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK250(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_29,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK250(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_30,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK250(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_31,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| in(sK250(U_1171,U_1170),U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_32,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_33,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_34,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_35,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_36,plain,
( sK246(U_1171,U_1170) = sK247(U_1171,U_1170)
| in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_37,plain,
( in(sK249(U_1171,U_1170),U_1170)
| in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_38,plain,
( sK247(U_1171,U_1170) = set_difference(sK249(U_1171,U_1170),singleton(U_1171))
| in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_39,plain,
( sK246(U_1171,U_1170) = sK248(U_1171,U_1170)
| in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_40,plain,
( in(sK250(U_1171,U_1170),U_1170)
| in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_41,plain,
( sK248(U_1171,U_1170) = set_difference(sK250(U_1171,U_1170),singleton(U_1171))
| in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_42,plain,
( in(sK252(U_1171,U_1170,U_1172),U_1170)
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_43,plain,
( U_1172 = set_difference(sK252(U_1171,U_1170,U_1172),singleton(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_44,plain,
( in(sK253(U_1171,U_1170,U_1172),powerset(U_1171))
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_45,plain,
( sK253(U_1171,U_1170,U_1172) = U_1172
| ~ in(U_1172,sK251(U_1171,U_1170))
| sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
cnf(f_289_46,plain,
( in(U_1173,sK251(U_1171,U_1170))
| U_1167 != U_1173
| ~ in(U_1167,powerset(U_1171))
| U_1173 != set_difference(U_1166,singleton(U_1171))
| ~ in(U_1166,U_1170)
| sK247(U_1171,U_1170) != sK248(U_1171,U_1170)
| ~ element(U_1170,powerset(powerset(succ(U_1171))))
| ~ ordinal(U_1171) ),
inference(clausify,[status(thm)],[f_289_11]) ).
fof(f_290_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_290_2,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
! [U_1187] :
( ( in(U_1187,U_1188)
| ! [U_1186] :
( ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1187 != ordered_pair(U_1185,U_1184) )
| U_1186 != U_1187
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) ) )
& ( ? [U_1183] :
( ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1187 = ordered_pair(U_1182,U_1181) )
& U_1183 = U_1187
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
| ~ in(U_1187,U_1188) ) )
| ? [U_1180,U_1179,U_1178] :
( U_1179 != U_1178
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& U_1178 = ordered_pair(U_1177,U_1176) )
& U_1180 = U_1178
& ? [U_1175,U_1174] :
( in(ordered_pair(apply(U_1189,U_1175),apply(U_1189,U_1174)),U_1190)
& U_1179 = ordered_pair(U_1175,U_1174) )
& U_1180 = U_1179 )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ? [U_1180,U_1179,U_1178] :
( U_1179 != U_1178
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& U_1178 = ordered_pair(U_1177,U_1176) )
& U_1180 = U_1178
& ? [U_1175,U_1174] :
( in(ordered_pair(apply(U_1189,U_1175),apply(U_1189,U_1174)),U_1190)
& U_1179 = ordered_pair(U_1175,U_1174) )
& U_1180 = U_1179 )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(miniscope,[status(thm)],[f_290_2]) ).
fof(f_290_4,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ? [U_1179,U_1178] :
( U_1179 != U_1178
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& U_1178 = ordered_pair(U_1177,U_1176) )
& sK254(U_1191,U_1190,U_1189) = U_1178
& ? [U_1175,U_1174] :
( in(ordered_pair(apply(U_1189,U_1175),apply(U_1189,U_1174)),U_1190)
& U_1179 = ordered_pair(U_1175,U_1174) )
& sK254(U_1191,U_1190,U_1189) = U_1179 )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_1180,sK254(U_1191,U_1190,U_1189))],[f_290_3]) ).
fof(f_290_5,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ? [U_1178] :
( sK255(U_1191,U_1190,U_1189) != U_1178
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& U_1178 = ordered_pair(U_1177,U_1176) )
& sK254(U_1191,U_1190,U_1189) = U_1178
& ? [U_1175,U_1174] :
( in(ordered_pair(apply(U_1189,U_1175),apply(U_1189,U_1174)),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(U_1175,U_1174) )
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_1179,sK255(U_1191,U_1190,U_1189))],[f_290_4]) ).
fof(f_290_6,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(U_1177,U_1176) )
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& ? [U_1175,U_1174] :
( in(ordered_pair(apply(U_1189,U_1175),apply(U_1189,U_1174)),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(U_1175,U_1174) )
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_1178,sK256(U_1191,U_1190,U_1189))],[f_290_5]) ).
fof(f_290_7,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(U_1177,U_1176) )
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& ? [U_1174] :
( in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,U_1174)),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),U_1174) )
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_1175,sK257(U_1191,U_1190,U_1189))],[f_290_6]) ).
fof(f_290_8,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& ? [U_1177,U_1176] :
( in(ordered_pair(apply(U_1189,U_1177),apply(U_1189,U_1176)),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(U_1177,U_1176) )
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_1174,sK258(U_1191,U_1190,U_1189))],[f_290_7]) ).
fof(f_290_9,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& ? [U_1176] :
( in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,U_1176)),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),U_1176) )
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_1177,sK259(U_1191,U_1190,U_1189))],[f_290_8]) ).
fof(f_290_10,plain,
! [U_1191,U_1190,U_1189] :
( ? [U_1188] :
( ! [U_1193] :
( in(U_1193,U_1188)
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,U_1188) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_1176,sK260(U_1191,U_1190,U_1189))],[f_290_9]) ).
fof(f_290_11,plain,
! [U_1191,U_1190,U_1189] :
( ( ! [U_1193] :
( in(U_1193,sK261(U_1191,U_1190,U_1189))
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1182,U_1181] :
( in(ordered_pair(apply(U_1189,U_1182),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(U_1182,U_1181) ) )
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189)) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_1188,sK261(U_1191,U_1190,U_1189))],[f_290_10]) ).
fof(f_290_12,plain,
! [U_1191,U_1190,U_1189] :
( ( ! [U_1193] :
( in(U_1193,sK261(U_1191,U_1190,U_1189))
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& ? [U_1181] :
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,U_1181)),U_1190)
& U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),U_1181) ) )
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189)) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_1182,sK262(U_1191,U_1190,U_1189,U_1192))],[f_290_11]) ).
fof(f_290_13,plain,
! [U_1191,U_1190,U_1189] :
( ( ! [U_1193] :
( in(U_1193,sK261(U_1191,U_1190,U_1189))
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( ? [U_1183] :
( U_1183 = U_1192
& in(U_1183,cartesian_product2(U_1191,U_1191)) )
& in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
& U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192)) )
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189)) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_1181,sK263(U_1191,U_1190,U_1189,U_1192))],[f_290_12]) ).
fof(f_290_14,plain,
! [U_1191,U_1190,U_1189] :
( ( ! [U_1193] :
( in(U_1193,sK261(U_1191,U_1190,U_1189))
| ! [U_1186] :
( U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191)) )
| ! [U_1185,U_1184] :
( ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184) ) )
& ! [U_1192] :
( ( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
& in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
& in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
& U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192)) )
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189)) ) )
| ( sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
& sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
& in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
& sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
& sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189) )
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_1183,sK264(U_1191,U_1190,U_1189,U_1192))],[f_290_13]) ).
cnf(f_290_15,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_16,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_17,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_18,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_19,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_20,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_21,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_22,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_23,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_24,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_25,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_26,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_27,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_28,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_29,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_30,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_31,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_32,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_33,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_34,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_35,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_36,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_37,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_38,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_39,plain,
( sK254(U_1191,U_1190,U_1189) = sK255(U_1191,U_1190,U_1189)
| in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_40,plain,
( sK255(U_1191,U_1190,U_1189) = ordered_pair(sK257(U_1191,U_1190,U_1189),sK258(U_1191,U_1190,U_1189))
| in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_41,plain,
( in(ordered_pair(apply(U_1189,sK257(U_1191,U_1190,U_1189)),apply(U_1189,sK258(U_1191,U_1190,U_1189))),U_1190)
| in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_42,plain,
( sK254(U_1191,U_1190,U_1189) = sK256(U_1191,U_1190,U_1189)
| in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_43,plain,
( sK256(U_1191,U_1190,U_1189) = ordered_pair(sK259(U_1191,U_1190,U_1189),sK260(U_1191,U_1190,U_1189))
| in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_44,plain,
( in(ordered_pair(apply(U_1189,sK259(U_1191,U_1190,U_1189)),apply(U_1189,sK260(U_1191,U_1190,U_1189))),U_1190)
| in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_45,plain,
( U_1192 = ordered_pair(sK262(U_1191,U_1190,U_1189,U_1192),sK263(U_1191,U_1190,U_1189,U_1192))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_46,plain,
( in(ordered_pair(apply(U_1189,sK262(U_1191,U_1190,U_1189,U_1192)),apply(U_1189,sK263(U_1191,U_1190,U_1189,U_1192))),U_1190)
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_47,plain,
( in(sK264(U_1191,U_1190,U_1189,U_1192),cartesian_product2(U_1191,U_1191))
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_48,plain,
( sK264(U_1191,U_1190,U_1189,U_1192) = U_1192
| ~ in(U_1192,sK261(U_1191,U_1190,U_1189))
| sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
cnf(f_290_49,plain,
( in(U_1193,sK261(U_1191,U_1190,U_1189))
| U_1186 != U_1193
| ~ in(U_1186,cartesian_product2(U_1191,U_1191))
| ~ in(ordered_pair(apply(U_1189,U_1185),apply(U_1189,U_1184)),U_1190)
| U_1193 != ordered_pair(U_1185,U_1184)
| sK255(U_1191,U_1190,U_1189) != sK256(U_1191,U_1190,U_1189)
| ~ function(U_1189)
| ~ relation(U_1189)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_290_14]) ).
fof(f_291_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_291_2,plain,
! [U_1201] :
( ? [U_1200] :
! [U_1199] :
( ( in(U_1199,U_1200)
| ! [U_1198] :
( ~ ordinal(U_1199)
| U_1198 != U_1199
| ~ in(U_1198,U_1201) ) )
& ( ? [U_1197] :
( ordinal(U_1199)
& U_1197 = U_1199
& in(U_1197,U_1201) )
| ~ in(U_1199,U_1200) ) )
| ? [U_1196,U_1195,U_1194] :
( U_1195 != U_1194
& ordinal(U_1194)
& U_1196 = U_1194
& ordinal(U_1195)
& U_1196 = U_1195 ) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
( ! [U_1201] :
? [U_1200] :
( ! [U_1203] :
( in(U_1203,U_1200)
| ! [U_1198] :
( U_1198 != U_1203
| ~ in(U_1198,U_1201) )
| ~ ordinal(U_1203) )
& ! [U_1202] :
( ( ? [U_1197] :
( U_1197 = U_1202
& in(U_1197,U_1201) )
& ordinal(U_1202) )
| ~ in(U_1202,U_1200) ) )
| ? [U_1196,U_1195,U_1194] :
( U_1195 != U_1194
& ordinal(U_1194)
& U_1196 = U_1194
& ordinal(U_1195)
& U_1196 = U_1195 ) ),
inference(miniscope,[status(thm)],[f_291_2]) ).
fof(f_291_4,plain,
( ! [U_1201] :
? [U_1200] :
( ! [U_1203] :
( in(U_1203,U_1200)
| ! [U_1198] :
( U_1198 != U_1203
| ~ in(U_1198,U_1201) )
| ~ ordinal(U_1203) )
& ! [U_1202] :
( ( ? [U_1197] :
( U_1197 = U_1202
& in(U_1197,U_1201) )
& ordinal(U_1202) )
| ~ in(U_1202,U_1200) ) )
| ? [U_1195,U_1194] :
( U_1195 != U_1194
& ordinal(U_1194)
& sK265 = U_1194
& ordinal(U_1195)
& sK265 = U_1195 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_1196,sK265)],[f_291_3]) ).
fof(f_291_5,plain,
( ! [U_1201] :
? [U_1200] :
( ! [U_1203] :
( in(U_1203,U_1200)
| ! [U_1198] :
( U_1198 != U_1203
| ~ in(U_1198,U_1201) )
| ~ ordinal(U_1203) )
& ! [U_1202] :
( ( ? [U_1197] :
( U_1197 = U_1202
& in(U_1197,U_1201) )
& ordinal(U_1202) )
| ~ in(U_1202,U_1200) ) )
| ? [U_1194] :
( sK266 != U_1194
& ordinal(U_1194)
& sK265 = U_1194
& ordinal(sK266)
& sK265 = sK266 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_1195,sK266)],[f_291_4]) ).
fof(f_291_6,plain,
( ! [U_1201] :
? [U_1200] :
( ! [U_1203] :
( in(U_1203,U_1200)
| ! [U_1198] :
( U_1198 != U_1203
| ~ in(U_1198,U_1201) )
| ~ ordinal(U_1203) )
& ! [U_1202] :
( ( ? [U_1197] :
( U_1197 = U_1202
& in(U_1197,U_1201) )
& ordinal(U_1202) )
| ~ in(U_1202,U_1200) ) )
| ( sK266 != sK267
& ordinal(sK267)
& sK265 = sK267
& ordinal(sK266)
& sK265 = sK266 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_1194,sK267)],[f_291_5]) ).
fof(f_291_7,plain,
( ! [U_1201] :
( ! [U_1203] :
( in(U_1203,sK268(U_1201))
| ! [U_1198] :
( U_1198 != U_1203
| ~ in(U_1198,U_1201) )
| ~ ordinal(U_1203) )
& ! [U_1202] :
( ( ? [U_1197] :
( U_1197 = U_1202
& in(U_1197,U_1201) )
& ordinal(U_1202) )
| ~ in(U_1202,sK268(U_1201)) ) )
| ( sK266 != sK267
& ordinal(sK267)
& sK265 = sK267
& ordinal(sK266)
& sK265 = sK266 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_1200,sK268(U_1201))],[f_291_6]) ).
fof(f_291_8,plain,
( ! [U_1201] :
( ! [U_1203] :
( in(U_1203,sK268(U_1201))
| ! [U_1198] :
( U_1198 != U_1203
| ~ in(U_1198,U_1201) )
| ~ ordinal(U_1203) )
& ! [U_1202] :
( ( sK269(U_1201,U_1202) = U_1202
& in(sK269(U_1201,U_1202),U_1201)
& ordinal(U_1202) )
| ~ in(U_1202,sK268(U_1201)) ) )
| ( sK266 != sK267
& ordinal(sK267)
& sK265 = sK267
& ordinal(sK266)
& sK265 = sK266 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_1197,sK269(U_1201,U_1202))],[f_291_7]) ).
cnf(f_291_9,plain,
( ordinal(U_1202)
| ~ in(U_1202,sK268(U_1201))
| sK265 = sK266 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_10,plain,
( in(sK269(U_1201,U_1202),U_1201)
| ~ in(U_1202,sK268(U_1201))
| sK265 = sK266 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_11,plain,
( sK269(U_1201,U_1202) = U_1202
| ~ in(U_1202,sK268(U_1201))
| sK265 = sK266 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_12,plain,
( ordinal(U_1202)
| ~ in(U_1202,sK268(U_1201))
| ordinal(sK266) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_13,plain,
( in(sK269(U_1201,U_1202),U_1201)
| ~ in(U_1202,sK268(U_1201))
| ordinal(sK266) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_14,plain,
( sK269(U_1201,U_1202) = U_1202
| ~ in(U_1202,sK268(U_1201))
| ordinal(sK266) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_15,plain,
( ordinal(U_1202)
| ~ in(U_1202,sK268(U_1201))
| sK265 = sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_16,plain,
( in(sK269(U_1201,U_1202),U_1201)
| ~ in(U_1202,sK268(U_1201))
| sK265 = sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_17,plain,
( sK269(U_1201,U_1202) = U_1202
| ~ in(U_1202,sK268(U_1201))
| sK265 = sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_18,plain,
( ordinal(U_1202)
| ~ in(U_1202,sK268(U_1201))
| ordinal(sK267) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_19,plain,
( in(sK269(U_1201,U_1202),U_1201)
| ~ in(U_1202,sK268(U_1201))
| ordinal(sK267) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_20,plain,
( sK269(U_1201,U_1202) = U_1202
| ~ in(U_1202,sK268(U_1201))
| ordinal(sK267) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_21,plain,
( sK265 = sK266
| in(U_1203,sK268(U_1201))
| U_1198 != U_1203
| ~ in(U_1198,U_1201)
| ~ ordinal(U_1203) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_22,plain,
( ordinal(sK266)
| in(U_1203,sK268(U_1201))
| U_1198 != U_1203
| ~ in(U_1198,U_1201)
| ~ ordinal(U_1203) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_23,plain,
( sK265 = sK267
| in(U_1203,sK268(U_1201))
| U_1198 != U_1203
| ~ in(U_1198,U_1201)
| ~ ordinal(U_1203) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_24,plain,
( ordinal(sK267)
| in(U_1203,sK268(U_1201))
| U_1198 != U_1203
| ~ in(U_1198,U_1201)
| ~ ordinal(U_1203) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_25,plain,
( ordinal(U_1202)
| ~ in(U_1202,sK268(U_1201))
| sK266 != sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_26,plain,
( in(sK269(U_1201,U_1202),U_1201)
| ~ in(U_1202,sK268(U_1201))
| sK266 != sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_27,plain,
( sK269(U_1201,U_1202) = U_1202
| ~ in(U_1202,sK268(U_1201))
| sK266 != sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_28,plain,
( in(U_1203,sK268(U_1201))
| U_1198 != U_1203
| ~ in(U_1198,U_1201)
| ~ ordinal(U_1203)
| sK266 != sK267 ),
inference(clausify,[status(thm)],[f_291_8]) ).
fof(f_292_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_292_2,plain,
! [U_1213,U_1212,U_1211] :
( ? [U_1210] :
! [U_1209] :
( ( in(U_1209,U_1210)
| ! [U_1208] :
( ~ in(relation_image(U_1211,U_1209),U_1212)
| U_1208 != U_1209
| ~ in(U_1208,powerset(relation_dom(U_1211))) ) )
& ( ? [U_1207] :
( in(relation_image(U_1211,U_1209),U_1212)
& U_1207 = U_1209
& in(U_1207,powerset(relation_dom(U_1211))) )
| ~ in(U_1209,U_1210) ) )
| ? [U_1206,U_1205,U_1204] :
( U_1205 != U_1204
& in(relation_image(U_1211,U_1204),U_1212)
& U_1206 = U_1204
& in(relation_image(U_1211,U_1205),U_1212)
& U_1206 = U_1205 )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1213,U_1212,U_1211] :
( ? [U_1210] :
( ! [U_1215] :
( in(U_1215,U_1210)
| ! [U_1208] :
( U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211))) )
| ~ in(relation_image(U_1211,U_1215),U_1212) )
& ! [U_1214] :
( ( ? [U_1207] :
( U_1207 = U_1214
& in(U_1207,powerset(relation_dom(U_1211))) )
& in(relation_image(U_1211,U_1214),U_1212) )
| ~ in(U_1214,U_1210) ) )
| ? [U_1206,U_1205,U_1204] :
( U_1205 != U_1204
& in(relation_image(U_1211,U_1204),U_1212)
& U_1206 = U_1204
& in(relation_image(U_1211,U_1205),U_1212)
& U_1206 = U_1205 )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(miniscope,[status(thm)],[f_292_2]) ).
fof(f_292_4,plain,
! [U_1213,U_1212,U_1211] :
( ? [U_1210] :
( ! [U_1215] :
( in(U_1215,U_1210)
| ! [U_1208] :
( U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211))) )
| ~ in(relation_image(U_1211,U_1215),U_1212) )
& ! [U_1214] :
( ( ? [U_1207] :
( U_1207 = U_1214
& in(U_1207,powerset(relation_dom(U_1211))) )
& in(relation_image(U_1211,U_1214),U_1212) )
| ~ in(U_1214,U_1210) ) )
| ? [U_1205,U_1204] :
( U_1205 != U_1204
& in(relation_image(U_1211,U_1204),U_1212)
& sK270(U_1213,U_1212,U_1211) = U_1204
& in(relation_image(U_1211,U_1205),U_1212)
& sK270(U_1213,U_1212,U_1211) = U_1205 )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_1206,sK270(U_1213,U_1212,U_1211))],[f_292_3]) ).
fof(f_292_5,plain,
! [U_1213,U_1212,U_1211] :
( ? [U_1210] :
( ! [U_1215] :
( in(U_1215,U_1210)
| ! [U_1208] :
( U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211))) )
| ~ in(relation_image(U_1211,U_1215),U_1212) )
& ! [U_1214] :
( ( ? [U_1207] :
( U_1207 = U_1214
& in(U_1207,powerset(relation_dom(U_1211))) )
& in(relation_image(U_1211,U_1214),U_1212) )
| ~ in(U_1214,U_1210) ) )
| ? [U_1204] :
( sK271(U_1213,U_1212,U_1211) != U_1204
& in(relation_image(U_1211,U_1204),U_1212)
& sK270(U_1213,U_1212,U_1211) = U_1204
& in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211) )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_1205,sK271(U_1213,U_1212,U_1211))],[f_292_4]) ).
fof(f_292_6,plain,
! [U_1213,U_1212,U_1211] :
( ? [U_1210] :
( ! [U_1215] :
( in(U_1215,U_1210)
| ! [U_1208] :
( U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211))) )
| ~ in(relation_image(U_1211,U_1215),U_1212) )
& ! [U_1214] :
( ( ? [U_1207] :
( U_1207 = U_1214
& in(U_1207,powerset(relation_dom(U_1211))) )
& in(relation_image(U_1211,U_1214),U_1212) )
| ~ in(U_1214,U_1210) ) )
| ( sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
& in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
& in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211) )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_1204,sK272(U_1213,U_1212,U_1211))],[f_292_5]) ).
fof(f_292_7,plain,
! [U_1213,U_1212,U_1211] :
( ( ! [U_1215] :
( in(U_1215,sK273(U_1213,U_1212,U_1211))
| ! [U_1208] :
( U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211))) )
| ~ in(relation_image(U_1211,U_1215),U_1212) )
& ! [U_1214] :
( ( ? [U_1207] :
( U_1207 = U_1214
& in(U_1207,powerset(relation_dom(U_1211))) )
& in(relation_image(U_1211,U_1214),U_1212) )
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211)) ) )
| ( sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
& in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
& in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211) )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_1210,sK273(U_1213,U_1212,U_1211))],[f_292_6]) ).
fof(f_292_8,plain,
! [U_1213,U_1212,U_1211] :
( ( ! [U_1215] :
( in(U_1215,sK273(U_1213,U_1212,U_1211))
| ! [U_1208] :
( U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211))) )
| ~ in(relation_image(U_1211,U_1215),U_1212) )
& ! [U_1214] :
( ( sK274(U_1213,U_1212,U_1211,U_1214) = U_1214
& in(sK274(U_1213,U_1212,U_1211,U_1214),powerset(relation_dom(U_1211)))
& in(relation_image(U_1211,U_1214),U_1212) )
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211)) ) )
| ( sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
& in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
& in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
& sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211) )
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_1207,sK274(U_1213,U_1212,U_1211,U_1214))],[f_292_7]) ).
cnf(f_292_9,plain,
( in(relation_image(U_1211,U_1214),U_1212)
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_10,plain,
( in(sK274(U_1213,U_1212,U_1211,U_1214),powerset(relation_dom(U_1211)))
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_11,plain,
( sK274(U_1213,U_1212,U_1211,U_1214) = U_1214
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_12,plain,
( in(relation_image(U_1211,U_1214),U_1212)
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_13,plain,
( in(sK274(U_1213,U_1212,U_1211,U_1214),powerset(relation_dom(U_1211)))
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_14,plain,
( sK274(U_1213,U_1212,U_1211,U_1214) = U_1214
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_15,plain,
( in(relation_image(U_1211,U_1214),U_1212)
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_16,plain,
( in(sK274(U_1213,U_1212,U_1211,U_1214),powerset(relation_dom(U_1211)))
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_17,plain,
( sK274(U_1213,U_1212,U_1211,U_1214) = U_1214
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_18,plain,
( in(relation_image(U_1211,U_1214),U_1212)
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_19,plain,
( in(sK274(U_1213,U_1212,U_1211,U_1214),powerset(relation_dom(U_1211)))
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_20,plain,
( sK274(U_1213,U_1212,U_1211,U_1214) = U_1214
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_21,plain,
( sK270(U_1213,U_1212,U_1211) = sK271(U_1213,U_1212,U_1211)
| in(U_1215,sK273(U_1213,U_1212,U_1211))
| U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211)))
| ~ in(relation_image(U_1211,U_1215),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_22,plain,
( in(relation_image(U_1211,sK271(U_1213,U_1212,U_1211)),U_1212)
| in(U_1215,sK273(U_1213,U_1212,U_1211))
| U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211)))
| ~ in(relation_image(U_1211,U_1215),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_23,plain,
( sK270(U_1213,U_1212,U_1211) = sK272(U_1213,U_1212,U_1211)
| in(U_1215,sK273(U_1213,U_1212,U_1211))
| U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211)))
| ~ in(relation_image(U_1211,U_1215),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_24,plain,
( in(relation_image(U_1211,sK272(U_1213,U_1212,U_1211)),U_1212)
| in(U_1215,sK273(U_1213,U_1212,U_1211))
| U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211)))
| ~ in(relation_image(U_1211,U_1215),U_1212)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_25,plain,
( in(relation_image(U_1211,U_1214),U_1212)
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_26,plain,
( in(sK274(U_1213,U_1212,U_1211,U_1214),powerset(relation_dom(U_1211)))
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_27,plain,
( sK274(U_1213,U_1212,U_1211,U_1214) = U_1214
| ~ in(U_1214,sK273(U_1213,U_1212,U_1211))
| sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
cnf(f_292_28,plain,
( in(U_1215,sK273(U_1213,U_1212,U_1211))
| U_1208 != U_1215
| ~ in(U_1208,powerset(relation_dom(U_1211)))
| ~ in(relation_image(U_1211,U_1215),U_1212)
| sK271(U_1213,U_1212,U_1211) != sK272(U_1213,U_1212,U_1211)
| ~ function(U_1211)
| ~ relation(U_1211)
| ~ element(U_1212,powerset(powerset(U_1213))) ),
inference(clausify,[status(thm)],[f_292_8]) ).
fof(f_293_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_293_2,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
! [U_1225] :
( ( in(U_1225,U_1226)
| ! [U_1224] :
( ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1225 != U_1223
| ~ ordinal(U_1223) )
| U_1224 != U_1225
| ~ in(U_1224,succ(U_1227)) ) )
& ( ? [U_1222] :
( ? [U_1221] :
( in(U_1221,U_1228)
& U_1225 = U_1221
& ordinal(U_1221) )
& U_1222 = U_1225
& in(U_1222,succ(U_1227)) )
| ~ in(U_1225,U_1226) ) )
| ? [U_1220,U_1219,U_1218] :
( U_1219 != U_1218
& ? [U_1217] :
( in(U_1217,U_1228)
& U_1218 = U_1217
& ordinal(U_1217) )
& U_1220 = U_1218
& ? [U_1216] :
( in(U_1216,U_1228)
& U_1219 = U_1216
& ordinal(U_1216) )
& U_1220 = U_1219 )
| ~ ordinal(U_1227) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
( ! [U_1230] :
( in(U_1230,U_1226)
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,U_1226) ) )
| ? [U_1220,U_1219,U_1218] :
( U_1219 != U_1218
& ? [U_1217] :
( in(U_1217,U_1228)
& U_1218 = U_1217
& ordinal(U_1217) )
& U_1220 = U_1218
& ? [U_1216] :
( in(U_1216,U_1228)
& U_1219 = U_1216
& ordinal(U_1216) )
& U_1220 = U_1219 )
| ~ ordinal(U_1227) ),
inference(miniscope,[status(thm)],[f_293_2]) ).
fof(f_293_4,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
( ! [U_1230] :
( in(U_1230,U_1226)
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,U_1226) ) )
| ? [U_1219,U_1218] :
( U_1219 != U_1218
& ? [U_1217] :
( in(U_1217,U_1228)
& U_1218 = U_1217
& ordinal(U_1217) )
& sK275(U_1228,U_1227) = U_1218
& ? [U_1216] :
( in(U_1216,U_1228)
& U_1219 = U_1216
& ordinal(U_1216) )
& sK275(U_1228,U_1227) = U_1219 )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_1220,sK275(U_1228,U_1227))],[f_293_3]) ).
fof(f_293_5,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
( ! [U_1230] :
( in(U_1230,U_1226)
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,U_1226) ) )
| ? [U_1218] :
( sK276(U_1228,U_1227) != U_1218
& ? [U_1217] :
( in(U_1217,U_1228)
& U_1218 = U_1217
& ordinal(U_1217) )
& sK275(U_1228,U_1227) = U_1218
& ? [U_1216] :
( in(U_1216,U_1228)
& sK276(U_1228,U_1227) = U_1216
& ordinal(U_1216) )
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_1219,sK276(U_1228,U_1227))],[f_293_4]) ).
fof(f_293_6,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
( ! [U_1230] :
( in(U_1230,U_1226)
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,U_1226) ) )
| ( sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
& ? [U_1217] :
( in(U_1217,U_1228)
& sK277(U_1228,U_1227) = U_1217
& ordinal(U_1217) )
& sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
& ? [U_1216] :
( in(U_1216,U_1228)
& sK276(U_1228,U_1227) = U_1216
& ordinal(U_1216) )
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_1218,sK277(U_1228,U_1227))],[f_293_5]) ).
fof(f_293_7,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
( ! [U_1230] :
( in(U_1230,U_1226)
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,U_1226) ) )
| ( sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
& ? [U_1217] :
( in(U_1217,U_1228)
& sK277(U_1228,U_1227) = U_1217
& ordinal(U_1217) )
& sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
& in(sK278(U_1228,U_1227),U_1228)
& sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
& ordinal(sK278(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_1216,sK278(U_1228,U_1227))],[f_293_6]) ).
fof(f_293_8,plain,
! [U_1228,U_1227] :
( ? [U_1226] :
( ! [U_1230] :
( in(U_1230,U_1226)
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,U_1226) ) )
| ( sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
& in(sK279(U_1228,U_1227),U_1228)
& sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
& ordinal(sK279(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
& in(sK278(U_1228,U_1227),U_1228)
& sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
& ordinal(sK278(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_1217,sK279(U_1228,U_1227))],[f_293_7]) ).
fof(f_293_9,plain,
! [U_1228,U_1227] :
( ( ! [U_1230] :
( in(U_1230,sK280(U_1228,U_1227))
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& ? [U_1221] :
( in(U_1221,U_1228)
& U_1229 = U_1221
& ordinal(U_1221) ) )
| ~ in(U_1229,sK280(U_1228,U_1227)) ) )
| ( sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
& in(sK279(U_1228,U_1227),U_1228)
& sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
& ordinal(sK279(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
& in(sK278(U_1228,U_1227),U_1228)
& sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
& ordinal(sK278(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_1226,sK280(U_1228,U_1227))],[f_293_8]) ).
fof(f_293_10,plain,
! [U_1228,U_1227] :
( ( ! [U_1230] :
( in(U_1230,sK280(U_1228,U_1227))
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( ? [U_1222] :
( U_1222 = U_1229
& in(U_1222,succ(U_1227)) )
& in(sK281(U_1228,U_1227,U_1229),U_1228)
& U_1229 = sK281(U_1228,U_1227,U_1229)
& ordinal(sK281(U_1228,U_1227,U_1229)) )
| ~ in(U_1229,sK280(U_1228,U_1227)) ) )
| ( sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
& in(sK279(U_1228,U_1227),U_1228)
& sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
& ordinal(sK279(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
& in(sK278(U_1228,U_1227),U_1228)
& sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
& ordinal(sK278(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_1221,sK281(U_1228,U_1227,U_1229))],[f_293_9]) ).
fof(f_293_11,plain,
! [U_1228,U_1227] :
( ( ! [U_1230] :
( in(U_1230,sK280(U_1228,U_1227))
| ! [U_1224] :
( U_1224 != U_1230
| ~ in(U_1224,succ(U_1227)) )
| ! [U_1223] :
( ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223) ) )
& ! [U_1229] :
( ( sK282(U_1228,U_1227,U_1229) = U_1229
& in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
& in(sK281(U_1228,U_1227,U_1229),U_1228)
& U_1229 = sK281(U_1228,U_1227,U_1229)
& ordinal(sK281(U_1228,U_1227,U_1229)) )
| ~ in(U_1229,sK280(U_1228,U_1227)) ) )
| ( sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
& in(sK279(U_1228,U_1227),U_1228)
& sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
& ordinal(sK279(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
& in(sK278(U_1228,U_1227),U_1228)
& sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
& ordinal(sK278(U_1228,U_1227))
& sK275(U_1228,U_1227) = sK276(U_1228,U_1227) )
| ~ ordinal(U_1227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_1222,sK282(U_1228,U_1227,U_1229))],[f_293_10]) ).
cnf(f_293_12,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK276(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_13,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK276(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_14,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK276(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_15,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK276(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_16,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK276(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_17,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK278(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_18,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK278(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_19,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK278(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_20,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK278(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_21,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK278(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_22,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_23,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_24,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_25,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_26,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_27,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK278(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_28,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK278(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_29,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK278(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_30,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK278(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_31,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK278(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_32,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_33,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_34,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_35,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_36,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_37,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK279(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_38,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK279(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_39,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK279(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_40,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK279(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_41,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| ordinal(sK279(U_1228,U_1227))
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_42,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_43,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_44,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_45,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_46,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_47,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK279(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_48,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK279(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_49,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK279(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_50,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK279(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_51,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| in(sK279(U_1228,U_1227),U_1228)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_52,plain,
( sK275(U_1228,U_1227) = sK276(U_1228,U_1227)
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_53,plain,
( ordinal(sK278(U_1228,U_1227))
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_54,plain,
( sK276(U_1228,U_1227) = sK278(U_1228,U_1227)
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_55,plain,
( in(sK278(U_1228,U_1227),U_1228)
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_56,plain,
( sK275(U_1228,U_1227) = sK277(U_1228,U_1227)
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_57,plain,
( ordinal(sK279(U_1228,U_1227))
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_58,plain,
( sK277(U_1228,U_1227) = sK279(U_1228,U_1227)
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_59,plain,
( in(sK279(U_1228,U_1227),U_1228)
| in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_60,plain,
( ordinal(sK281(U_1228,U_1227,U_1229))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_61,plain,
( U_1229 = sK281(U_1228,U_1227,U_1229)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_62,plain,
( in(sK281(U_1228,U_1227,U_1229),U_1228)
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_63,plain,
( in(sK282(U_1228,U_1227,U_1229),succ(U_1227))
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_64,plain,
( sK282(U_1228,U_1227,U_1229) = U_1229
| ~ in(U_1229,sK280(U_1228,U_1227))
| sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
cnf(f_293_65,plain,
( in(U_1230,sK280(U_1228,U_1227))
| U_1224 != U_1230
| ~ in(U_1224,succ(U_1227))
| ~ in(U_1223,U_1228)
| U_1230 != U_1223
| ~ ordinal(U_1223)
| sK276(U_1228,U_1227) != sK277(U_1228,U_1227)
| ~ ordinal(U_1227) ),
inference(clausify,[status(thm)],[f_293_11]) ).
fof(f_294_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_294_2,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
? [U_1240] :
! [U_1239] :
( ( in(U_1239,U_1240)
| ! [U_1238,U_1237] :
( ! [U_1236] :
( ? [U_1235] :
( ~ in(ordered_pair(U_1237,U_1235),U_1242)
& in(U_1235,U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ~ in(U_1238,U_1243)
| ordered_pair(U_1238,U_1237) != U_1239 )
| ~ in(U_1239,cartesian_product2(U_1243,U_1241)) )
& ( ( ? [U_1234,U_1233] :
( ? [U_1232] :
( ! [U_1231] :
( in(ordered_pair(U_1233,U_1231),U_1242)
| ~ in(U_1231,U_1232) )
& in(U_1233,U_1232)
& U_1234 = U_1232 )
& in(U_1234,U_1243)
& ordered_pair(U_1234,U_1233) = U_1239 )
& in(U_1239,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1239,U_1240) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
? [U_1240] :
( ! [U_1245] :
( in(U_1245,U_1240)
| ! [U_1238] :
( ! [U_1237] :
( ! [U_1236] :
( ? [U_1235] :
( ~ in(ordered_pair(U_1237,U_1235),U_1242)
& in(U_1235,U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ordered_pair(U_1238,U_1237) != U_1245 )
| ~ in(U_1238,U_1243) )
| ~ in(U_1245,cartesian_product2(U_1243,U_1241)) )
& ! [U_1244] :
( ( ? [U_1234] :
( ? [U_1233] :
( ? [U_1232] :
( ! [U_1231] :
( in(ordered_pair(U_1233,U_1231),U_1242)
| ~ in(U_1231,U_1232) )
& in(U_1233,U_1232)
& U_1234 = U_1232 )
& ordered_pair(U_1234,U_1233) = U_1244 )
& in(U_1234,U_1243) )
& in(U_1244,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1244,U_1240) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(miniscope,[status(thm)],[f_294_2]) ).
fof(f_294_4,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
( ! [U_1245] :
( in(U_1245,sK283(U_1243,U_1242,U_1241))
| ! [U_1238] :
( ! [U_1237] :
( ! [U_1236] :
( ? [U_1235] :
( ~ in(ordered_pair(U_1237,U_1235),U_1242)
& in(U_1235,U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ordered_pair(U_1238,U_1237) != U_1245 )
| ~ in(U_1238,U_1243) )
| ~ in(U_1245,cartesian_product2(U_1243,U_1241)) )
& ! [U_1244] :
( ( ? [U_1234] :
( ? [U_1233] :
( ? [U_1232] :
( ! [U_1231] :
( in(ordered_pair(U_1233,U_1231),U_1242)
| ~ in(U_1231,U_1232) )
& in(U_1233,U_1232)
& U_1234 = U_1232 )
& ordered_pair(U_1234,U_1233) = U_1244 )
& in(U_1234,U_1243) )
& in(U_1244,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241)) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_1240,sK283(U_1243,U_1242,U_1241))],[f_294_3]) ).
fof(f_294_5,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
( ! [U_1245] :
( in(U_1245,sK283(U_1243,U_1242,U_1241))
| ! [U_1238] :
( ! [U_1237] :
( ! [U_1236] :
( ? [U_1235] :
( ~ in(ordered_pair(U_1237,U_1235),U_1242)
& in(U_1235,U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ordered_pair(U_1238,U_1237) != U_1245 )
| ~ in(U_1238,U_1243) )
| ~ in(U_1245,cartesian_product2(U_1243,U_1241)) )
& ! [U_1244] :
( ( ? [U_1233] :
( ? [U_1232] :
( ! [U_1231] :
( in(ordered_pair(U_1233,U_1231),U_1242)
| ~ in(U_1231,U_1232) )
& in(U_1233,U_1232)
& sK284(U_1243,U_1242,U_1241,U_1244) = U_1232 )
& ordered_pair(sK284(U_1243,U_1242,U_1241,U_1244),U_1233) = U_1244 )
& in(sK284(U_1243,U_1242,U_1241,U_1244),U_1243)
& in(U_1244,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241)) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_1234,sK284(U_1243,U_1242,U_1241,U_1244))],[f_294_4]) ).
fof(f_294_6,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
( ! [U_1245] :
( in(U_1245,sK283(U_1243,U_1242,U_1241))
| ! [U_1238] :
( ! [U_1237] :
( ! [U_1236] :
( ? [U_1235] :
( ~ in(ordered_pair(U_1237,U_1235),U_1242)
& in(U_1235,U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ordered_pair(U_1238,U_1237) != U_1245 )
| ~ in(U_1238,U_1243) )
| ~ in(U_1245,cartesian_product2(U_1243,U_1241)) )
& ! [U_1244] :
( ( ? [U_1232] :
( ! [U_1231] :
( in(ordered_pair(sK285(U_1243,U_1242,U_1241,U_1244),U_1231),U_1242)
| ~ in(U_1231,U_1232) )
& in(sK285(U_1243,U_1242,U_1241,U_1244),U_1232)
& sK284(U_1243,U_1242,U_1241,U_1244) = U_1232 )
& ordered_pair(sK284(U_1243,U_1242,U_1241,U_1244),sK285(U_1243,U_1242,U_1241,U_1244)) = U_1244
& in(sK284(U_1243,U_1242,U_1241,U_1244),U_1243)
& in(U_1244,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241)) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_1233,sK285(U_1243,U_1242,U_1241,U_1244))],[f_294_5]) ).
fof(f_294_7,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
( ! [U_1245] :
( in(U_1245,sK283(U_1243,U_1242,U_1241))
| ! [U_1238] :
( ! [U_1237] :
( ! [U_1236] :
( ? [U_1235] :
( ~ in(ordered_pair(U_1237,U_1235),U_1242)
& in(U_1235,U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ordered_pair(U_1238,U_1237) != U_1245 )
| ~ in(U_1238,U_1243) )
| ~ in(U_1245,cartesian_product2(U_1243,U_1241)) )
& ! [U_1244] :
( ( ! [U_1231] :
( in(ordered_pair(sK285(U_1243,U_1242,U_1241,U_1244),U_1231),U_1242)
| ~ in(U_1231,sK286(U_1243,U_1242,U_1241,U_1244)) )
& in(sK285(U_1243,U_1242,U_1241,U_1244),sK286(U_1243,U_1242,U_1241,U_1244))
& sK284(U_1243,U_1242,U_1241,U_1244) = sK286(U_1243,U_1242,U_1241,U_1244)
& ordered_pair(sK284(U_1243,U_1242,U_1241,U_1244),sK285(U_1243,U_1242,U_1241,U_1244)) = U_1244
& in(sK284(U_1243,U_1242,U_1241,U_1244),U_1243)
& in(U_1244,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241)) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_1232,sK286(U_1243,U_1242,U_1241,U_1244))],[f_294_6]) ).
fof(f_294_8,plain,
! [U_1243,U_1242] :
( ! [U_1241] :
( ! [U_1245] :
( in(U_1245,sK283(U_1243,U_1242,U_1241))
| ! [U_1238] :
( ! [U_1237] :
( ! [U_1236] :
( ( ~ in(ordered_pair(U_1237,sK287(U_1243,U_1242,U_1241,U_1245,U_1238,U_1237,U_1236)),U_1242)
& in(sK287(U_1243,U_1242,U_1241,U_1245,U_1238,U_1237,U_1236),U_1236) )
| ~ in(U_1237,U_1236)
| U_1238 != U_1236 )
| ordered_pair(U_1238,U_1237) != U_1245 )
| ~ in(U_1238,U_1243) )
| ~ in(U_1245,cartesian_product2(U_1243,U_1241)) )
& ! [U_1244] :
( ( ! [U_1231] :
( in(ordered_pair(sK285(U_1243,U_1242,U_1241,U_1244),U_1231),U_1242)
| ~ in(U_1231,sK286(U_1243,U_1242,U_1241,U_1244)) )
& in(sK285(U_1243,U_1242,U_1241,U_1244),sK286(U_1243,U_1242,U_1241,U_1244))
& sK284(U_1243,U_1242,U_1241,U_1244) = sK286(U_1243,U_1242,U_1241,U_1244)
& ordered_pair(sK284(U_1243,U_1242,U_1241,U_1244),sK285(U_1243,U_1242,U_1241,U_1244)) = U_1244
& in(sK284(U_1243,U_1242,U_1241,U_1244),U_1243)
& in(U_1244,cartesian_product2(U_1243,U_1241)) )
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241)) ) )
| ~ relation(U_1242)
| empty(U_1243) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_1235,sK287(U_1243,U_1242,U_1241,U_1245,U_1238,U_1237,U_1236))],[f_294_7]) ).
cnf(f_294_9,plain,
( in(U_1244,cartesian_product2(U_1243,U_1241))
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_10,plain,
( in(sK284(U_1243,U_1242,U_1241,U_1244),U_1243)
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_11,plain,
( ordered_pair(sK284(U_1243,U_1242,U_1241,U_1244),sK285(U_1243,U_1242,U_1241,U_1244)) = U_1244
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_12,plain,
( sK284(U_1243,U_1242,U_1241,U_1244) = sK286(U_1243,U_1242,U_1241,U_1244)
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_13,plain,
( in(sK285(U_1243,U_1242,U_1241,U_1244),sK286(U_1243,U_1242,U_1241,U_1244))
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_14,plain,
( in(ordered_pair(sK285(U_1243,U_1242,U_1241,U_1244),U_1231),U_1242)
| ~ in(U_1231,sK286(U_1243,U_1242,U_1241,U_1244))
| ~ in(U_1244,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_15,plain,
( in(sK287(U_1243,U_1242,U_1241,U_1245,U_1238,U_1237,U_1236),U_1236)
| ~ in(U_1237,U_1236)
| U_1238 != U_1236
| ordered_pair(U_1238,U_1237) != U_1245
| ~ in(U_1238,U_1243)
| ~ in(U_1245,cartesian_product2(U_1243,U_1241))
| in(U_1245,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
cnf(f_294_16,plain,
( ~ in(ordered_pair(U_1237,sK287(U_1243,U_1242,U_1241,U_1245,U_1238,U_1237,U_1236)),U_1242)
| ~ in(U_1237,U_1236)
| U_1238 != U_1236
| ordered_pair(U_1238,U_1237) != U_1245
| ~ in(U_1238,U_1243)
| ~ in(U_1245,cartesian_product2(U_1243,U_1241))
| in(U_1245,sK283(U_1243,U_1242,U_1241))
| ~ relation(U_1242)
| empty(U_1243) ),
inference(clausify,[status(thm)],[f_294_8]) ).
fof(f_295_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_295_2,plain,
! [U_1253,U_1252] :
? [U_1251] :
! [U_1250] :
( ( in(U_1250,U_1251)
| ! [U_1249,U_1248] :
( U_1248 != singleton(U_1249)
| ~ in(U_1249,U_1253)
| ordered_pair(U_1249,U_1248) != U_1250 )
| ~ in(U_1250,cartesian_product2(U_1253,U_1252)) )
& ( ( ? [U_1247,U_1246] :
( U_1246 = singleton(U_1247)
& in(U_1247,U_1253)
& ordered_pair(U_1247,U_1246) = U_1250 )
& in(U_1250,cartesian_product2(U_1253,U_1252)) )
| ~ in(U_1250,U_1251) ) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1253,U_1252] :
? [U_1251] :
( ! [U_1255] :
( in(U_1255,U_1251)
| ! [U_1249] :
( ! [U_1248] :
( U_1248 != singleton(U_1249)
| ordered_pair(U_1249,U_1248) != U_1255 )
| ~ in(U_1249,U_1253) )
| ~ in(U_1255,cartesian_product2(U_1253,U_1252)) )
& ! [U_1254] :
( ( ? [U_1247] :
( ? [U_1246] :
( U_1246 = singleton(U_1247)
& ordered_pair(U_1247,U_1246) = U_1254 )
& in(U_1247,U_1253) )
& in(U_1254,cartesian_product2(U_1253,U_1252)) )
| ~ in(U_1254,U_1251) ) ),
inference(miniscope,[status(thm)],[f_295_2]) ).
fof(f_295_4,plain,
! [U_1253,U_1252] :
( ! [U_1255] :
( in(U_1255,sK288(U_1253,U_1252))
| ! [U_1249] :
( ! [U_1248] :
( U_1248 != singleton(U_1249)
| ordered_pair(U_1249,U_1248) != U_1255 )
| ~ in(U_1249,U_1253) )
| ~ in(U_1255,cartesian_product2(U_1253,U_1252)) )
& ! [U_1254] :
( ( ? [U_1247] :
( ? [U_1246] :
( U_1246 = singleton(U_1247)
& ordered_pair(U_1247,U_1246) = U_1254 )
& in(U_1247,U_1253) )
& in(U_1254,cartesian_product2(U_1253,U_1252)) )
| ~ in(U_1254,sK288(U_1253,U_1252)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_1251,sK288(U_1253,U_1252))],[f_295_3]) ).
fof(f_295_5,plain,
! [U_1253,U_1252] :
( ! [U_1255] :
( in(U_1255,sK288(U_1253,U_1252))
| ! [U_1249] :
( ! [U_1248] :
( U_1248 != singleton(U_1249)
| ordered_pair(U_1249,U_1248) != U_1255 )
| ~ in(U_1249,U_1253) )
| ~ in(U_1255,cartesian_product2(U_1253,U_1252)) )
& ! [U_1254] :
( ( ? [U_1246] :
( U_1246 = singleton(sK289(U_1253,U_1252,U_1254))
& ordered_pair(sK289(U_1253,U_1252,U_1254),U_1246) = U_1254 )
& in(sK289(U_1253,U_1252,U_1254),U_1253)
& in(U_1254,cartesian_product2(U_1253,U_1252)) )
| ~ in(U_1254,sK288(U_1253,U_1252)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_1247,sK289(U_1253,U_1252,U_1254))],[f_295_4]) ).
fof(f_295_6,plain,
! [U_1253,U_1252] :
( ! [U_1255] :
( in(U_1255,sK288(U_1253,U_1252))
| ! [U_1249] :
( ! [U_1248] :
( U_1248 != singleton(U_1249)
| ordered_pair(U_1249,U_1248) != U_1255 )
| ~ in(U_1249,U_1253) )
| ~ in(U_1255,cartesian_product2(U_1253,U_1252)) )
& ! [U_1254] :
( ( sK290(U_1253,U_1252,U_1254) = singleton(sK289(U_1253,U_1252,U_1254))
& ordered_pair(sK289(U_1253,U_1252,U_1254),sK290(U_1253,U_1252,U_1254)) = U_1254
& in(sK289(U_1253,U_1252,U_1254),U_1253)
& in(U_1254,cartesian_product2(U_1253,U_1252)) )
| ~ in(U_1254,sK288(U_1253,U_1252)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_1246,sK290(U_1253,U_1252,U_1254))],[f_295_5]) ).
cnf(f_295_7,plain,
( in(U_1254,cartesian_product2(U_1253,U_1252))
| ~ in(U_1254,sK288(U_1253,U_1252)) ),
inference(clausify,[status(thm)],[f_295_6]) ).
cnf(f_295_8,plain,
( in(sK289(U_1253,U_1252,U_1254),U_1253)
| ~ in(U_1254,sK288(U_1253,U_1252)) ),
inference(clausify,[status(thm)],[f_295_6]) ).
cnf(f_295_9,plain,
( ordered_pair(sK289(U_1253,U_1252,U_1254),sK290(U_1253,U_1252,U_1254)) = U_1254
| ~ in(U_1254,sK288(U_1253,U_1252)) ),
inference(clausify,[status(thm)],[f_295_6]) ).
cnf(f_295_10,plain,
( sK290(U_1253,U_1252,U_1254) = singleton(sK289(U_1253,U_1252,U_1254))
| ~ in(U_1254,sK288(U_1253,U_1252)) ),
inference(clausify,[status(thm)],[f_295_6]) ).
cnf(f_295_11,plain,
( in(U_1255,sK288(U_1253,U_1252))
| U_1248 != singleton(U_1249)
| ordered_pair(U_1249,U_1248) != U_1255
| ~ in(U_1249,U_1253)
| ~ in(U_1255,cartesian_product2(U_1253,U_1252)) ),
inference(clausify,[status(thm)],[f_295_6]) ).
fof(f_296_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_296_2,plain,
! [U_1266] :
( ? [U_1265] :
! [U_1264] :
( ( in(U_1264,U_1265)
| ! [U_1263] :
( ( ? [U_1262] :
( ! [U_1261] :
( ? [U_1260] :
( U_1260 != U_1261
& subset(U_1261,U_1260)
& in(U_1260,U_1262) )
| ~ in(U_1261,U_1262) )
& U_1262 != empty_set
& element(U_1262,powerset(powerset(U_1263))) )
& in(U_1263,omega) )
| U_1264 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1264,succ(U_1266)) )
& ( ( ? [U_1259] :
( ( ! [U_1258] :
( ? [U_1257] :
( ! [U_1256] :
( U_1256 = U_1257
| ~ subset(U_1257,U_1256)
| ~ in(U_1256,U_1258) )
& in(U_1257,U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(U_1259))) )
| ~ in(U_1259,omega) )
& U_1264 = U_1259
& ordinal(U_1259) )
& in(U_1264,succ(U_1266)) )
| ~ in(U_1264,U_1265) ) )
| ~ ordinal(U_1266) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_1266] :
( ? [U_1265] :
( ! [U_1268] :
( in(U_1268,U_1265)
| ! [U_1263] :
( ( ? [U_1262] :
( ! [U_1261] :
( ? [U_1260] :
( U_1260 != U_1261
& subset(U_1261,U_1260)
& in(U_1260,U_1262) )
| ~ in(U_1261,U_1262) )
& U_1262 != empty_set
& element(U_1262,powerset(powerset(U_1263))) )
& in(U_1263,omega) )
| U_1268 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1268,succ(U_1266)) )
& ! [U_1267] :
( ( ? [U_1259] :
( ( ! [U_1258] :
( ? [U_1257] :
( ! [U_1256] :
( U_1256 = U_1257
| ~ subset(U_1257,U_1256)
| ~ in(U_1256,U_1258) )
& in(U_1257,U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(U_1259))) )
| ~ in(U_1259,omega) )
& U_1267 = U_1259
& ordinal(U_1259) )
& in(U_1267,succ(U_1266)) )
| ~ in(U_1267,U_1265) ) )
| ~ ordinal(U_1266) ),
inference(miniscope,[status(thm)],[f_296_2]) ).
fof(f_296_4,plain,
! [U_1266] :
( ( ! [U_1268] :
( in(U_1268,sK291(U_1266))
| ! [U_1263] :
( ( ? [U_1262] :
( ! [U_1261] :
( ? [U_1260] :
( U_1260 != U_1261
& subset(U_1261,U_1260)
& in(U_1260,U_1262) )
| ~ in(U_1261,U_1262) )
& U_1262 != empty_set
& element(U_1262,powerset(powerset(U_1263))) )
& in(U_1263,omega) )
| U_1268 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1268,succ(U_1266)) )
& ! [U_1267] :
( ( ? [U_1259] :
( ( ! [U_1258] :
( ? [U_1257] :
( ! [U_1256] :
( U_1256 = U_1257
| ~ subset(U_1257,U_1256)
| ~ in(U_1256,U_1258) )
& in(U_1257,U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(U_1259))) )
| ~ in(U_1259,omega) )
& U_1267 = U_1259
& ordinal(U_1259) )
& in(U_1267,succ(U_1266)) )
| ~ in(U_1267,sK291(U_1266)) ) )
| ~ ordinal(U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_1265,sK291(U_1266))],[f_296_3]) ).
fof(f_296_5,plain,
! [U_1266] :
( ( ! [U_1268] :
( in(U_1268,sK291(U_1266))
| ! [U_1263] :
( ( ? [U_1262] :
( ! [U_1261] :
( ? [U_1260] :
( U_1260 != U_1261
& subset(U_1261,U_1260)
& in(U_1260,U_1262) )
| ~ in(U_1261,U_1262) )
& U_1262 != empty_set
& element(U_1262,powerset(powerset(U_1263))) )
& in(U_1263,omega) )
| U_1268 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1268,succ(U_1266)) )
& ! [U_1267] :
( ( ( ! [U_1258] :
( ? [U_1257] :
( ! [U_1256] :
( U_1256 = U_1257
| ~ subset(U_1257,U_1256)
| ~ in(U_1256,U_1258) )
& in(U_1257,U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(sK292(U_1266,U_1267)))) )
| ~ in(sK292(U_1266,U_1267),omega) )
& U_1267 = sK292(U_1266,U_1267)
& ordinal(sK292(U_1266,U_1267))
& in(U_1267,succ(U_1266)) )
| ~ in(U_1267,sK291(U_1266)) ) )
| ~ ordinal(U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_1259,sK292(U_1266,U_1267))],[f_296_4]) ).
fof(f_296_6,plain,
! [U_1266] :
( ( ! [U_1268] :
( in(U_1268,sK291(U_1266))
| ! [U_1263] :
( ( ? [U_1262] :
( ! [U_1261] :
( ? [U_1260] :
( U_1260 != U_1261
& subset(U_1261,U_1260)
& in(U_1260,U_1262) )
| ~ in(U_1261,U_1262) )
& U_1262 != empty_set
& element(U_1262,powerset(powerset(U_1263))) )
& in(U_1263,omega) )
| U_1268 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1268,succ(U_1266)) )
& ! [U_1267] :
( ( ( ! [U_1258] :
( ( ! [U_1256] :
( U_1256 = sK293(U_1266,U_1267,U_1258)
| ~ subset(sK293(U_1266,U_1267,U_1258),U_1256)
| ~ in(U_1256,U_1258) )
& in(sK293(U_1266,U_1267,U_1258),U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(sK292(U_1266,U_1267)))) )
| ~ in(sK292(U_1266,U_1267),omega) )
& U_1267 = sK292(U_1266,U_1267)
& ordinal(sK292(U_1266,U_1267))
& in(U_1267,succ(U_1266)) )
| ~ in(U_1267,sK291(U_1266)) ) )
| ~ ordinal(U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_1257,sK293(U_1266,U_1267,U_1258))],[f_296_5]) ).
fof(f_296_7,plain,
! [U_1266] :
( ( ! [U_1268] :
( in(U_1268,sK291(U_1266))
| ! [U_1263] :
( ( ! [U_1261] :
( ? [U_1260] :
( U_1260 != U_1261
& subset(U_1261,U_1260)
& in(U_1260,sK294(U_1266,U_1268,U_1263)) )
| ~ in(U_1261,sK294(U_1266,U_1268,U_1263)) )
& sK294(U_1266,U_1268,U_1263) != empty_set
& element(sK294(U_1266,U_1268,U_1263),powerset(powerset(U_1263)))
& in(U_1263,omega) )
| U_1268 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1268,succ(U_1266)) )
& ! [U_1267] :
( ( ( ! [U_1258] :
( ( ! [U_1256] :
( U_1256 = sK293(U_1266,U_1267,U_1258)
| ~ subset(sK293(U_1266,U_1267,U_1258),U_1256)
| ~ in(U_1256,U_1258) )
& in(sK293(U_1266,U_1267,U_1258),U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(sK292(U_1266,U_1267)))) )
| ~ in(sK292(U_1266,U_1267),omega) )
& U_1267 = sK292(U_1266,U_1267)
& ordinal(sK292(U_1266,U_1267))
& in(U_1267,succ(U_1266)) )
| ~ in(U_1267,sK291(U_1266)) ) )
| ~ ordinal(U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_1262,sK294(U_1266,U_1268,U_1263))],[f_296_6]) ).
fof(f_296_8,plain,
! [U_1266] :
( ( ! [U_1268] :
( in(U_1268,sK291(U_1266))
| ! [U_1263] :
( ( ! [U_1261] :
( ( sK295(U_1266,U_1268,U_1263,U_1261) != U_1261
& subset(U_1261,sK295(U_1266,U_1268,U_1263,U_1261))
& in(sK295(U_1266,U_1268,U_1263,U_1261),sK294(U_1266,U_1268,U_1263)) )
| ~ in(U_1261,sK294(U_1266,U_1268,U_1263)) )
& sK294(U_1266,U_1268,U_1263) != empty_set
& element(sK294(U_1266,U_1268,U_1263),powerset(powerset(U_1263)))
& in(U_1263,omega) )
| U_1268 != U_1263
| ~ ordinal(U_1263) )
| ~ in(U_1268,succ(U_1266)) )
& ! [U_1267] :
( ( ( ! [U_1258] :
( ( ! [U_1256] :
( U_1256 = sK293(U_1266,U_1267,U_1258)
| ~ subset(sK293(U_1266,U_1267,U_1258),U_1256)
| ~ in(U_1256,U_1258) )
& in(sK293(U_1266,U_1267,U_1258),U_1258) )
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(sK292(U_1266,U_1267)))) )
| ~ in(sK292(U_1266,U_1267),omega) )
& U_1267 = sK292(U_1266,U_1267)
& ordinal(sK292(U_1266,U_1267))
& in(U_1267,succ(U_1266)) )
| ~ in(U_1267,sK291(U_1266)) ) )
| ~ ordinal(U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_1260,sK295(U_1266,U_1268,U_1263,U_1261))],[f_296_7]) ).
cnf(f_296_9,plain,
( in(U_1267,succ(U_1266))
| ~ in(U_1267,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_10,plain,
( ordinal(sK292(U_1266,U_1267))
| ~ in(U_1267,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_11,plain,
( U_1267 = sK292(U_1266,U_1267)
| ~ in(U_1267,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_12,plain,
( in(sK293(U_1266,U_1267,U_1258),U_1258)
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(sK292(U_1266,U_1267))))
| ~ in(sK292(U_1266,U_1267),omega)
| ~ in(U_1267,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_13,plain,
( U_1256 = sK293(U_1266,U_1267,U_1258)
| ~ subset(sK293(U_1266,U_1267,U_1258),U_1256)
| ~ in(U_1256,U_1258)
| U_1258 = empty_set
| ~ element(U_1258,powerset(powerset(sK292(U_1266,U_1267))))
| ~ in(sK292(U_1266,U_1267),omega)
| ~ in(U_1267,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_14,plain,
( in(U_1263,omega)
| U_1268 != U_1263
| ~ ordinal(U_1263)
| ~ in(U_1268,succ(U_1266))
| in(U_1268,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_15,plain,
( element(sK294(U_1266,U_1268,U_1263),powerset(powerset(U_1263)))
| U_1268 != U_1263
| ~ ordinal(U_1263)
| ~ in(U_1268,succ(U_1266))
| in(U_1268,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_16,plain,
( sK294(U_1266,U_1268,U_1263) != empty_set
| U_1268 != U_1263
| ~ ordinal(U_1263)
| ~ in(U_1268,succ(U_1266))
| in(U_1268,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_17,plain,
( in(sK295(U_1266,U_1268,U_1263,U_1261),sK294(U_1266,U_1268,U_1263))
| ~ in(U_1261,sK294(U_1266,U_1268,U_1263))
| U_1268 != U_1263
| ~ ordinal(U_1263)
| ~ in(U_1268,succ(U_1266))
| in(U_1268,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_18,plain,
( subset(U_1261,sK295(U_1266,U_1268,U_1263,U_1261))
| ~ in(U_1261,sK294(U_1266,U_1268,U_1263))
| U_1268 != U_1263
| ~ ordinal(U_1263)
| ~ in(U_1268,succ(U_1266))
| in(U_1268,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
cnf(f_296_19,plain,
( sK295(U_1266,U_1268,U_1263,U_1261) != U_1261
| ~ in(U_1261,sK294(U_1266,U_1268,U_1263))
| U_1268 != U_1263
| ~ ordinal(U_1263)
| ~ in(U_1268,succ(U_1266))
| in(U_1268,sK291(U_1266))
| ~ ordinal(U_1266) ),
inference(clausify,[status(thm)],[f_296_8]) ).
fof(f_297_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_297_2,plain,
! [U_1274,U_1273] :
( ? [U_1272] :
! [U_1271] :
( ( in(U_1271,U_1272)
| ! [U_1270] :
( U_1271 != set_difference(U_1270,singleton(U_1274))
| ~ in(U_1270,U_1273) )
| ~ in(U_1271,powerset(U_1274)) )
& ( ( ? [U_1269] :
( U_1271 = set_difference(U_1269,singleton(U_1274))
& in(U_1269,U_1273) )
& in(U_1271,powerset(U_1274)) )
| ~ in(U_1271,U_1272) ) )
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1274,U_1273] :
( ? [U_1272] :
( ! [U_1276] :
( in(U_1276,U_1272)
| ! [U_1270] :
( U_1276 != set_difference(U_1270,singleton(U_1274))
| ~ in(U_1270,U_1273) )
| ~ in(U_1276,powerset(U_1274)) )
& ! [U_1275] :
( ( ? [U_1269] :
( U_1275 = set_difference(U_1269,singleton(U_1274))
& in(U_1269,U_1273) )
& in(U_1275,powerset(U_1274)) )
| ~ in(U_1275,U_1272) ) )
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(miniscope,[status(thm)],[f_297_2]) ).
fof(f_297_4,plain,
! [U_1274,U_1273] :
( ( ! [U_1276] :
( in(U_1276,sK296(U_1274,U_1273))
| ! [U_1270] :
( U_1276 != set_difference(U_1270,singleton(U_1274))
| ~ in(U_1270,U_1273) )
| ~ in(U_1276,powerset(U_1274)) )
& ! [U_1275] :
( ( ? [U_1269] :
( U_1275 = set_difference(U_1269,singleton(U_1274))
& in(U_1269,U_1273) )
& in(U_1275,powerset(U_1274)) )
| ~ in(U_1275,sK296(U_1274,U_1273)) ) )
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_1272,sK296(U_1274,U_1273))],[f_297_3]) ).
fof(f_297_5,plain,
! [U_1274,U_1273] :
( ( ! [U_1276] :
( in(U_1276,sK296(U_1274,U_1273))
| ! [U_1270] :
( U_1276 != set_difference(U_1270,singleton(U_1274))
| ~ in(U_1270,U_1273) )
| ~ in(U_1276,powerset(U_1274)) )
& ! [U_1275] :
( ( U_1275 = set_difference(sK297(U_1274,U_1273,U_1275),singleton(U_1274))
& in(sK297(U_1274,U_1273,U_1275),U_1273)
& in(U_1275,powerset(U_1274)) )
| ~ in(U_1275,sK296(U_1274,U_1273)) ) )
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_1269,sK297(U_1274,U_1273,U_1275))],[f_297_4]) ).
cnf(f_297_6,plain,
( in(U_1275,powerset(U_1274))
| ~ in(U_1275,sK296(U_1274,U_1273))
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(clausify,[status(thm)],[f_297_5]) ).
cnf(f_297_7,plain,
( in(sK297(U_1274,U_1273,U_1275),U_1273)
| ~ in(U_1275,sK296(U_1274,U_1273))
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(clausify,[status(thm)],[f_297_5]) ).
cnf(f_297_8,plain,
( U_1275 = set_difference(sK297(U_1274,U_1273,U_1275),singleton(U_1274))
| ~ in(U_1275,sK296(U_1274,U_1273))
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(clausify,[status(thm)],[f_297_5]) ).
cnf(f_297_9,plain,
( in(U_1276,sK296(U_1274,U_1273))
| U_1276 != set_difference(U_1270,singleton(U_1274))
| ~ in(U_1270,U_1273)
| ~ in(U_1276,powerset(U_1274))
| ~ element(U_1273,powerset(powerset(succ(U_1274))))
| ~ ordinal(U_1274) ),
inference(clausify,[status(thm)],[f_297_5]) ).
fof(f_298_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_298_2,plain,
! [U_1285,U_1284,U_1283] :
( ? [U_1282] :
! [U_1281] :
( ( in(U_1281,U_1282)
| ! [U_1280,U_1279] :
( ~ in(ordered_pair(apply(U_1283,U_1280),apply(U_1283,U_1279)),U_1284)
| U_1281 != ordered_pair(U_1280,U_1279) )
| ~ in(U_1281,cartesian_product2(U_1285,U_1285)) )
& ( ( ? [U_1278,U_1277] :
( in(ordered_pair(apply(U_1283,U_1278),apply(U_1283,U_1277)),U_1284)
& U_1281 = ordered_pair(U_1278,U_1277) )
& in(U_1281,cartesian_product2(U_1285,U_1285)) )
| ~ in(U_1281,U_1282) ) )
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1285,U_1284,U_1283] :
( ? [U_1282] :
( ! [U_1287] :
( in(U_1287,U_1282)
| ! [U_1280,U_1279] :
( ~ in(ordered_pair(apply(U_1283,U_1280),apply(U_1283,U_1279)),U_1284)
| U_1287 != ordered_pair(U_1280,U_1279) )
| ~ in(U_1287,cartesian_product2(U_1285,U_1285)) )
& ! [U_1286] :
( ( ? [U_1278,U_1277] :
( in(ordered_pair(apply(U_1283,U_1278),apply(U_1283,U_1277)),U_1284)
& U_1286 = ordered_pair(U_1278,U_1277) )
& in(U_1286,cartesian_product2(U_1285,U_1285)) )
| ~ in(U_1286,U_1282) ) )
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(miniscope,[status(thm)],[f_298_2]) ).
fof(f_298_4,plain,
! [U_1285,U_1284,U_1283] :
( ( ! [U_1287] :
( in(U_1287,sK298(U_1285,U_1284,U_1283))
| ! [U_1280,U_1279] :
( ~ in(ordered_pair(apply(U_1283,U_1280),apply(U_1283,U_1279)),U_1284)
| U_1287 != ordered_pair(U_1280,U_1279) )
| ~ in(U_1287,cartesian_product2(U_1285,U_1285)) )
& ! [U_1286] :
( ( ? [U_1278,U_1277] :
( in(ordered_pair(apply(U_1283,U_1278),apply(U_1283,U_1277)),U_1284)
& U_1286 = ordered_pair(U_1278,U_1277) )
& in(U_1286,cartesian_product2(U_1285,U_1285)) )
| ~ in(U_1286,sK298(U_1285,U_1284,U_1283)) ) )
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_1282,sK298(U_1285,U_1284,U_1283))],[f_298_3]) ).
fof(f_298_5,plain,
! [U_1285,U_1284,U_1283] :
( ( ! [U_1287] :
( in(U_1287,sK298(U_1285,U_1284,U_1283))
| ! [U_1280,U_1279] :
( ~ in(ordered_pair(apply(U_1283,U_1280),apply(U_1283,U_1279)),U_1284)
| U_1287 != ordered_pair(U_1280,U_1279) )
| ~ in(U_1287,cartesian_product2(U_1285,U_1285)) )
& ! [U_1286] :
( ( ? [U_1277] :
( in(ordered_pair(apply(U_1283,sK299(U_1285,U_1284,U_1283,U_1286)),apply(U_1283,U_1277)),U_1284)
& U_1286 = ordered_pair(sK299(U_1285,U_1284,U_1283,U_1286),U_1277) )
& in(U_1286,cartesian_product2(U_1285,U_1285)) )
| ~ in(U_1286,sK298(U_1285,U_1284,U_1283)) ) )
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_1278,sK299(U_1285,U_1284,U_1283,U_1286))],[f_298_4]) ).
fof(f_298_6,plain,
! [U_1285,U_1284,U_1283] :
( ( ! [U_1287] :
( in(U_1287,sK298(U_1285,U_1284,U_1283))
| ! [U_1280,U_1279] :
( ~ in(ordered_pair(apply(U_1283,U_1280),apply(U_1283,U_1279)),U_1284)
| U_1287 != ordered_pair(U_1280,U_1279) )
| ~ in(U_1287,cartesian_product2(U_1285,U_1285)) )
& ! [U_1286] :
( ( in(ordered_pair(apply(U_1283,sK299(U_1285,U_1284,U_1283,U_1286)),apply(U_1283,sK300(U_1285,U_1284,U_1283,U_1286))),U_1284)
& U_1286 = ordered_pair(sK299(U_1285,U_1284,U_1283,U_1286),sK300(U_1285,U_1284,U_1283,U_1286))
& in(U_1286,cartesian_product2(U_1285,U_1285)) )
| ~ in(U_1286,sK298(U_1285,U_1284,U_1283)) ) )
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_1277,sK300(U_1285,U_1284,U_1283,U_1286))],[f_298_5]) ).
cnf(f_298_7,plain,
( in(U_1286,cartesian_product2(U_1285,U_1285))
| ~ in(U_1286,sK298(U_1285,U_1284,U_1283))
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(clausify,[status(thm)],[f_298_6]) ).
cnf(f_298_8,plain,
( U_1286 = ordered_pair(sK299(U_1285,U_1284,U_1283,U_1286),sK300(U_1285,U_1284,U_1283,U_1286))
| ~ in(U_1286,sK298(U_1285,U_1284,U_1283))
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(clausify,[status(thm)],[f_298_6]) ).
cnf(f_298_9,plain,
( in(ordered_pair(apply(U_1283,sK299(U_1285,U_1284,U_1283,U_1286)),apply(U_1283,sK300(U_1285,U_1284,U_1283,U_1286))),U_1284)
| ~ in(U_1286,sK298(U_1285,U_1284,U_1283))
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(clausify,[status(thm)],[f_298_6]) ).
cnf(f_298_10,plain,
( in(U_1287,sK298(U_1285,U_1284,U_1283))
| ~ in(ordered_pair(apply(U_1283,U_1280),apply(U_1283,U_1279)),U_1284)
| U_1287 != ordered_pair(U_1280,U_1279)
| ~ in(U_1287,cartesian_product2(U_1285,U_1285))
| ~ function(U_1283)
| ~ relation(U_1283)
| ~ relation(U_1284) ),
inference(clausify,[status(thm)],[f_298_6]) ).
fof(f_299_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_299_2,plain,
! [U_1290] :
? [U_1289] :
! [U_1288] :
( ( in(U_1288,U_1289)
| ~ ordinal(U_1288)
| ~ in(U_1288,U_1290) )
& ( ( ordinal(U_1288)
& in(U_1288,U_1290) )
| ~ in(U_1288,U_1289) ) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_1290] :
? [U_1289] :
( ! [U_1292] :
( in(U_1292,U_1289)
| ~ ordinal(U_1292)
| ~ in(U_1292,U_1290) )
& ! [U_1291] :
( ( ordinal(U_1291)
& in(U_1291,U_1290) )
| ~ in(U_1291,U_1289) ) ),
inference(miniscope,[status(thm)],[f_299_2]) ).
fof(f_299_4,plain,
! [U_1290] :
( ! [U_1292] :
( in(U_1292,sK301(U_1290))
| ~ ordinal(U_1292)
| ~ in(U_1292,U_1290) )
& ! [U_1291] :
( ( ordinal(U_1291)
& in(U_1291,U_1290) )
| ~ in(U_1291,sK301(U_1290)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_1289,sK301(U_1290))],[f_299_3]) ).
cnf(f_299_5,plain,
( in(U_1291,U_1290)
| ~ in(U_1291,sK301(U_1290)) ),
inference(clausify,[status(thm)],[f_299_4]) ).
cnf(f_299_6,plain,
( ordinal(U_1291)
| ~ in(U_1291,sK301(U_1290)) ),
inference(clausify,[status(thm)],[f_299_4]) ).
cnf(f_299_7,plain,
( in(U_1292,sK301(U_1290))
| ~ ordinal(U_1292)
| ~ in(U_1292,U_1290) ),
inference(clausify,[status(thm)],[f_299_4]) ).
fof(f_300_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_300_2,plain,
! [U_1297,U_1296,U_1295] :
( ? [U_1294] :
! [U_1293] :
( ( in(U_1293,U_1294)
| ~ in(relation_image(U_1295,U_1293),U_1296)
| ~ in(U_1293,powerset(relation_dom(U_1295))) )
& ( ( in(relation_image(U_1295,U_1293),U_1296)
& in(U_1293,powerset(relation_dom(U_1295))) )
| ~ in(U_1293,U_1294) ) )
| ~ function(U_1295)
| ~ relation(U_1295)
| ~ element(U_1296,powerset(powerset(U_1297))) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1297,U_1296,U_1295] :
( ? [U_1294] :
( ! [U_1299] :
( in(U_1299,U_1294)
| ~ in(relation_image(U_1295,U_1299),U_1296)
| ~ in(U_1299,powerset(relation_dom(U_1295))) )
& ! [U_1298] :
( ( in(relation_image(U_1295,U_1298),U_1296)
& in(U_1298,powerset(relation_dom(U_1295))) )
| ~ in(U_1298,U_1294) ) )
| ~ function(U_1295)
| ~ relation(U_1295)
| ~ element(U_1296,powerset(powerset(U_1297))) ),
inference(miniscope,[status(thm)],[f_300_2]) ).
fof(f_300_4,plain,
! [U_1297,U_1296,U_1295] :
( ( ! [U_1299] :
( in(U_1299,sK302(U_1297,U_1296,U_1295))
| ~ in(relation_image(U_1295,U_1299),U_1296)
| ~ in(U_1299,powerset(relation_dom(U_1295))) )
& ! [U_1298] :
( ( in(relation_image(U_1295,U_1298),U_1296)
& in(U_1298,powerset(relation_dom(U_1295))) )
| ~ in(U_1298,sK302(U_1297,U_1296,U_1295)) ) )
| ~ function(U_1295)
| ~ relation(U_1295)
| ~ element(U_1296,powerset(powerset(U_1297))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_1294,sK302(U_1297,U_1296,U_1295))],[f_300_3]) ).
cnf(f_300_5,plain,
( in(U_1298,powerset(relation_dom(U_1295)))
| ~ in(U_1298,sK302(U_1297,U_1296,U_1295))
| ~ function(U_1295)
| ~ relation(U_1295)
| ~ element(U_1296,powerset(powerset(U_1297))) ),
inference(clausify,[status(thm)],[f_300_4]) ).
cnf(f_300_6,plain,
( in(relation_image(U_1295,U_1298),U_1296)
| ~ in(U_1298,sK302(U_1297,U_1296,U_1295))
| ~ function(U_1295)
| ~ relation(U_1295)
| ~ element(U_1296,powerset(powerset(U_1297))) ),
inference(clausify,[status(thm)],[f_300_4]) ).
cnf(f_300_7,plain,
( in(U_1299,sK302(U_1297,U_1296,U_1295))
| ~ in(relation_image(U_1295,U_1299),U_1296)
| ~ in(U_1299,powerset(relation_dom(U_1295)))
| ~ function(U_1295)
| ~ relation(U_1295)
| ~ element(U_1296,powerset(powerset(U_1297))) ),
inference(clausify,[status(thm)],[f_300_4]) ).
fof(f_301_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_301_2,plain,
! [U_1305,U_1304] :
( ? [U_1303] :
! [U_1302] :
( ( in(U_1302,U_1303)
| ! [U_1301] :
( ~ in(U_1301,U_1305)
| U_1302 != U_1301
| ~ ordinal(U_1301) )
| ~ in(U_1302,succ(U_1304)) )
& ( ( ? [U_1300] :
( in(U_1300,U_1305)
& U_1302 = U_1300
& ordinal(U_1300) )
& in(U_1302,succ(U_1304)) )
| ~ in(U_1302,U_1303) ) )
| ~ ordinal(U_1304) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1305,U_1304] :
( ? [U_1303] :
( ! [U_1307] :
( in(U_1307,U_1303)
| ! [U_1301] :
( ~ in(U_1301,U_1305)
| U_1307 != U_1301
| ~ ordinal(U_1301) )
| ~ in(U_1307,succ(U_1304)) )
& ! [U_1306] :
( ( ? [U_1300] :
( in(U_1300,U_1305)
& U_1306 = U_1300
& ordinal(U_1300) )
& in(U_1306,succ(U_1304)) )
| ~ in(U_1306,U_1303) ) )
| ~ ordinal(U_1304) ),
inference(miniscope,[status(thm)],[f_301_2]) ).
fof(f_301_4,plain,
! [U_1305,U_1304] :
( ( ! [U_1307] :
( in(U_1307,sK303(U_1305,U_1304))
| ! [U_1301] :
( ~ in(U_1301,U_1305)
| U_1307 != U_1301
| ~ ordinal(U_1301) )
| ~ in(U_1307,succ(U_1304)) )
& ! [U_1306] :
( ( ? [U_1300] :
( in(U_1300,U_1305)
& U_1306 = U_1300
& ordinal(U_1300) )
& in(U_1306,succ(U_1304)) )
| ~ in(U_1306,sK303(U_1305,U_1304)) ) )
| ~ ordinal(U_1304) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_1303,sK303(U_1305,U_1304))],[f_301_3]) ).
fof(f_301_5,plain,
! [U_1305,U_1304] :
( ( ! [U_1307] :
( in(U_1307,sK303(U_1305,U_1304))
| ! [U_1301] :
( ~ in(U_1301,U_1305)
| U_1307 != U_1301
| ~ ordinal(U_1301) )
| ~ in(U_1307,succ(U_1304)) )
& ! [U_1306] :
( ( in(sK304(U_1305,U_1304,U_1306),U_1305)
& U_1306 = sK304(U_1305,U_1304,U_1306)
& ordinal(sK304(U_1305,U_1304,U_1306))
& in(U_1306,succ(U_1304)) )
| ~ in(U_1306,sK303(U_1305,U_1304)) ) )
| ~ ordinal(U_1304) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_1300,sK304(U_1305,U_1304,U_1306))],[f_301_4]) ).
cnf(f_301_6,plain,
( in(U_1306,succ(U_1304))
| ~ in(U_1306,sK303(U_1305,U_1304))
| ~ ordinal(U_1304) ),
inference(clausify,[status(thm)],[f_301_5]) ).
cnf(f_301_7,plain,
( ordinal(sK304(U_1305,U_1304,U_1306))
| ~ in(U_1306,sK303(U_1305,U_1304))
| ~ ordinal(U_1304) ),
inference(clausify,[status(thm)],[f_301_5]) ).
cnf(f_301_8,plain,
( U_1306 = sK304(U_1305,U_1304,U_1306)
| ~ in(U_1306,sK303(U_1305,U_1304))
| ~ ordinal(U_1304) ),
inference(clausify,[status(thm)],[f_301_5]) ).
cnf(f_301_9,plain,
( in(sK304(U_1305,U_1304,U_1306),U_1305)
| ~ in(U_1306,sK303(U_1305,U_1304))
| ~ ordinal(U_1304) ),
inference(clausify,[status(thm)],[f_301_5]) ).
cnf(f_301_10,plain,
( in(U_1307,sK303(U_1305,U_1304))
| ~ in(U_1301,U_1305)
| U_1307 != U_1301
| ~ ordinal(U_1301)
| ~ in(U_1307,succ(U_1304))
| ~ ordinal(U_1304) ),
inference(clausify,[status(thm)],[f_301_5]) ).
fof(f_302_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_302_2,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ? [U_1318] :
( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| U_1318 != U_1316 )
& in(U_1318,U_1324) )
| ? [U_1314,U_1313,U_1312] :
( U_1313 != U_1312
& ? [U_1311] :
( ! [U_1310] :
( in(ordered_pair(U_1312,U_1310),U_1323)
| ~ in(U_1310,U_1311) )
& in(U_1312,U_1311)
& U_1314 = U_1311 )
& ? [U_1309] :
( ! [U_1308] :
( in(ordered_pair(U_1313,U_1308),U_1323)
| ~ in(U_1308,U_1309) )
& in(U_1313,U_1309)
& U_1314 = U_1309 )
& in(U_1314,U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ? [U_1318] :
( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| U_1318 != U_1316 )
& in(U_1318,U_1324) )
| ? [U_1313,U_1312] :
( U_1313 != U_1312
& ? [U_1311] :
( ! [U_1310] :
( in(ordered_pair(U_1312,U_1310),U_1323)
| ~ in(U_1310,U_1311) )
& in(U_1312,U_1311)
& sK305(U_1324,U_1323) = U_1311 )
& ? [U_1309] :
( ! [U_1308] :
( in(ordered_pair(U_1313,U_1308),U_1323)
| ~ in(U_1308,U_1309) )
& in(U_1313,U_1309)
& sK305(U_1324,U_1323) = U_1309 )
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_1314,sK305(U_1324,U_1323))],[f_302_2]) ).
fof(f_302_4,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ? [U_1318] :
( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| U_1318 != U_1316 )
& in(U_1318,U_1324) )
| ? [U_1312] :
( sK306(U_1324,U_1323) != U_1312
& ? [U_1311] :
( ! [U_1310] :
( in(ordered_pair(U_1312,U_1310),U_1323)
| ~ in(U_1310,U_1311) )
& in(U_1312,U_1311)
& sK305(U_1324,U_1323) = U_1311 )
& ? [U_1309] :
( ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,U_1309) )
& in(sK306(U_1324,U_1323),U_1309)
& sK305(U_1324,U_1323) = U_1309 )
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_1313,sK306(U_1324,U_1323))],[f_302_3]) ).
fof(f_302_5,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ? [U_1318] :
( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| U_1318 != U_1316 )
& in(U_1318,U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ? [U_1311] :
( ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,U_1311) )
& in(sK307(U_1324,U_1323),U_1311)
& sK305(U_1324,U_1323) = U_1311 )
& ? [U_1309] :
( ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,U_1309) )
& in(sK306(U_1324,U_1323),U_1309)
& sK305(U_1324,U_1323) = U_1309 )
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_1312,sK307(U_1324,U_1323))],[f_302_4]) ).
fof(f_302_6,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ? [U_1318] :
( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| U_1318 != U_1316 )
& in(U_1318,U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ? [U_1311] :
( ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,U_1311) )
& in(sK307(U_1324,U_1323),U_1311)
& sK305(U_1324,U_1323) = U_1311 )
& ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323)) )
& in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_1309,sK308(U_1324,U_1323))],[f_302_5]) ).
fof(f_302_7,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ? [U_1318] :
( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| U_1318 != U_1316 )
& in(U_1318,U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323)) )
& in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
& ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323)) )
& in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_1311,sK309(U_1324,U_1323))],[f_302_6]) ).
fof(f_302_8,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ( ! [U_1317,U_1316] :
( ? [U_1315] :
( ~ in(ordered_pair(U_1317,U_1315),U_1323)
& in(U_1315,U_1316) )
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316 )
& in(sK310(U_1324,U_1323),U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323)) )
& in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
& ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323)) )
& in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_1318,sK310(U_1324,U_1323))],[f_302_7]) ).
fof(f_302_9,plain,
! [U_1324,U_1323] :
( ? [U_1322] :
( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(U_1322,U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(U_1322,U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(U_1322) = U_1324
& function(U_1322)
& relation(U_1322) )
| ( ! [U_1317,U_1316] :
( ( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
& in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316) )
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316 )
& in(sK310(U_1324,U_1323),U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323)) )
& in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
& ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323)) )
& in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_1315,sK311(U_1324,U_1323,U_1317,U_1316))],[f_302_8]) ).
fof(f_302_10,plain,
! [U_1324,U_1323] :
( ( ! [U_1321] :
( ? [U_1320] :
( ! [U_1319] :
( in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,U_1320) )
& in(apply(sK312(U_1324,U_1323),U_1321),U_1320)
& U_1321 = U_1320 )
| ~ in(U_1321,U_1324) )
& relation_dom(sK312(U_1324,U_1323)) = U_1324
& function(sK312(U_1324,U_1323))
& relation(sK312(U_1324,U_1323)) )
| ( ! [U_1317,U_1316] :
( ( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
& in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316) )
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316 )
& in(sK310(U_1324,U_1323),U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323)) )
& in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
& ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323)) )
& in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_1322,sK312(U_1324,U_1323))],[f_302_9]) ).
fof(f_302_11,plain,
! [U_1324,U_1323] :
( ( ! [U_1321] :
( ( ! [U_1319] :
( in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321)) )
& in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
& U_1321 = sK313(U_1324,U_1323,U_1321) )
| ~ in(U_1321,U_1324) )
& relation_dom(sK312(U_1324,U_1323)) = U_1324
& function(sK312(U_1324,U_1323))
& relation(sK312(U_1324,U_1323)) )
| ( ! [U_1317,U_1316] :
( ( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
& in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316) )
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316 )
& in(sK310(U_1324,U_1323),U_1324) )
| ( sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
& ! [U_1310] :
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323)) )
& in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
& ! [U_1308] :
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323)) )
& in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
& sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
& in(sK305(U_1324,U_1323),U_1324) )
| ~ relation(U_1323)
| empty(U_1324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_1320,sK313(U_1324,U_1323,U_1321))],[f_302_10]) ).
cnf(f_302_12,plain,
( in(sK305(U_1324,U_1323),U_1324)
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_13,plain,
( sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_14,plain,
( in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_15,plain,
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_16,plain,
( sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_17,plain,
( in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_18,plain,
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_19,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_20,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_21,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_22,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_23,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_24,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_25,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_26,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_27,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_28,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_29,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_30,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_31,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_32,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_33,plain,
( in(sK310(U_1324,U_1323),U_1324)
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_34,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_35,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| relation(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_36,plain,
( in(sK305(U_1324,U_1323),U_1324)
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_37,plain,
( sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_38,plain,
( in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_39,plain,
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_40,plain,
( sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_41,plain,
( in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_42,plain,
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_43,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_44,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_45,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_46,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_47,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_48,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_49,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_50,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_51,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_52,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_53,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_54,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_55,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_56,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_57,plain,
( in(sK310(U_1324,U_1323),U_1324)
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_58,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_59,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| function(sK312(U_1324,U_1323))
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_60,plain,
( in(sK305(U_1324,U_1323),U_1324)
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_61,plain,
( sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_62,plain,
( in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_63,plain,
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_64,plain,
( sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_65,plain,
( in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_66,plain,
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_67,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_68,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_69,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_70,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_71,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_72,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_73,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_74,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_75,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_76,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_77,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_78,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_79,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_80,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_81,plain,
( in(sK310(U_1324,U_1323),U_1324)
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_82,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_83,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| relation_dom(sK312(U_1324,U_1323)) = U_1324
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_84,plain,
( in(sK305(U_1324,U_1323),U_1324)
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_85,plain,
( sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_86,plain,
( in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_87,plain,
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_88,plain,
( sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_89,plain,
( in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_90,plain,
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_91,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_92,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_93,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_94,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_95,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_96,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_97,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_98,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_99,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_100,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_101,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_102,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_103,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_104,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_105,plain,
( in(sK305(U_1324,U_1323),U_1324)
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_106,plain,
( sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_107,plain,
( in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_108,plain,
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_109,plain,
( sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_110,plain,
( in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_111,plain,
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_112,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_113,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_114,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_115,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_116,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_117,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_118,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_119,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_120,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_121,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_122,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_123,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_124,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_125,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_126,plain,
( in(sK305(U_1324,U_1323),U_1324)
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_127,plain,
( sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_128,plain,
( in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_129,plain,
( in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_130,plain,
( sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_131,plain,
( in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_132,plain,
( in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(sK310(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_133,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_134,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK305(U_1324,U_1323),U_1324)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_135,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_136,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK308(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_137,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_138,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK306(U_1324,U_1323),sK308(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_139,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_140,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK306(U_1324,U_1323),U_1308),U_1323)
| ~ in(U_1308,sK308(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_141,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_142,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK305(U_1324,U_1323) = sK309(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_143,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_144,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(sK307(U_1324,U_1323),sK309(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_145,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_146,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| in(ordered_pair(sK307(U_1324,U_1323),U_1310),U_1323)
| ~ in(U_1310,sK309(U_1324,U_1323))
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_147,plain,
( in(sK310(U_1324,U_1323),U_1324)
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_148,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_149,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| U_1321 = sK313(U_1324,U_1323,U_1321)
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_150,plain,
( in(sK310(U_1324,U_1323),U_1324)
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_151,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_152,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| in(apply(sK312(U_1324,U_1323),U_1321),sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_153,plain,
( in(sK310(U_1324,U_1323),U_1324)
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_154,plain,
( in(sK311(U_1324,U_1323,U_1317,U_1316),U_1316)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
cnf(f_302_155,plain,
( ~ in(ordered_pair(U_1317,sK311(U_1324,U_1323,U_1317,U_1316)),U_1323)
| ~ in(U_1317,U_1316)
| sK310(U_1324,U_1323) != U_1316
| sK306(U_1324,U_1323) != sK307(U_1324,U_1323)
| in(ordered_pair(apply(sK312(U_1324,U_1323),U_1321),U_1319),U_1323)
| ~ in(U_1319,sK313(U_1324,U_1323,U_1321))
| ~ in(U_1321,U_1324)
| ~ relation(U_1323)
| empty(U_1324) ),
inference(clausify,[status(thm)],[f_302_11]) ).
fof(f_303_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_303_2,plain,
! [U_1332] :
( ? [U_1331] :
( ! [U_1330] :
( apply(U_1331,U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) )
& relation_dom(U_1331) = U_1332
& function(U_1331)
& relation(U_1331) )
| ? [U_1329] :
( ! [U_1328] : U_1328 != singleton(U_1329)
& in(U_1329,U_1332) )
| ? [U_1327,U_1326,U_1325] :
( U_1326 != U_1325
& U_1325 = singleton(U_1327)
& U_1326 = singleton(U_1327)
& in(U_1327,U_1332) ) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_1332] :
( ? [U_1331] :
( ! [U_1330] :
( apply(U_1331,U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) )
& relation_dom(U_1331) = U_1332
& function(U_1331)
& relation(U_1331) )
| ? [U_1329] :
( ! [U_1328] : U_1328 != singleton(U_1329)
& in(U_1329,U_1332) )
| ? [U_1326,U_1325] :
( U_1326 != U_1325
& U_1325 = singleton(sK314(U_1332))
& U_1326 = singleton(sK314(U_1332))
& in(sK314(U_1332),U_1332) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_1327,sK314(U_1332))],[f_303_2]) ).
fof(f_303_4,plain,
! [U_1332] :
( ? [U_1331] :
( ! [U_1330] :
( apply(U_1331,U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) )
& relation_dom(U_1331) = U_1332
& function(U_1331)
& relation(U_1331) )
| ? [U_1329] :
( ! [U_1328] : U_1328 != singleton(U_1329)
& in(U_1329,U_1332) )
| ? [U_1325] :
( sK315(U_1332) != U_1325
& U_1325 = singleton(sK314(U_1332))
& sK315(U_1332) = singleton(sK314(U_1332))
& in(sK314(U_1332),U_1332) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_1326,sK315(U_1332))],[f_303_3]) ).
fof(f_303_5,plain,
! [U_1332] :
( ? [U_1331] :
( ! [U_1330] :
( apply(U_1331,U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) )
& relation_dom(U_1331) = U_1332
& function(U_1331)
& relation(U_1331) )
| ? [U_1329] :
( ! [U_1328] : U_1328 != singleton(U_1329)
& in(U_1329,U_1332) )
| ( sK315(U_1332) != sK316(U_1332)
& sK316(U_1332) = singleton(sK314(U_1332))
& sK315(U_1332) = singleton(sK314(U_1332))
& in(sK314(U_1332),U_1332) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_1325,sK316(U_1332))],[f_303_4]) ).
fof(f_303_6,plain,
! [U_1332] :
( ? [U_1331] :
( ! [U_1330] :
( apply(U_1331,U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) )
& relation_dom(U_1331) = U_1332
& function(U_1331)
& relation(U_1331) )
| ( ! [U_1328] : U_1328 != singleton(sK317(U_1332))
& in(sK317(U_1332),U_1332) )
| ( sK315(U_1332) != sK316(U_1332)
& sK316(U_1332) = singleton(sK314(U_1332))
& sK315(U_1332) = singleton(sK314(U_1332))
& in(sK314(U_1332),U_1332) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_1329,sK317(U_1332))],[f_303_5]) ).
fof(f_303_7,plain,
! [U_1332] :
( ( ! [U_1330] :
( apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) )
& relation_dom(sK318(U_1332)) = U_1332
& function(sK318(U_1332))
& relation(sK318(U_1332)) )
| ( ! [U_1328] : U_1328 != singleton(sK317(U_1332))
& in(sK317(U_1332),U_1332) )
| ( sK315(U_1332) != sK316(U_1332)
& sK316(U_1332) = singleton(sK314(U_1332))
& sK315(U_1332) = singleton(sK314(U_1332))
& in(sK314(U_1332),U_1332) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_1331,sK318(U_1332))],[f_303_6]) ).
cnf(f_303_8,plain,
( in(sK314(U_1332),U_1332)
| in(sK317(U_1332),U_1332)
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_9,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_10,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_11,plain,
( in(sK314(U_1332),U_1332)
| U_1328 != singleton(sK317(U_1332))
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_12,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_13,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_14,plain,
( in(sK317(U_1332),U_1332)
| sK315(U_1332) != sK316(U_1332)
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_15,plain,
( U_1328 != singleton(sK317(U_1332))
| sK315(U_1332) != sK316(U_1332)
| relation(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_16,plain,
( in(sK314(U_1332),U_1332)
| in(sK317(U_1332),U_1332)
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_17,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_18,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_19,plain,
( in(sK314(U_1332),U_1332)
| U_1328 != singleton(sK317(U_1332))
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_20,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_21,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_22,plain,
( in(sK317(U_1332),U_1332)
| sK315(U_1332) != sK316(U_1332)
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_23,plain,
( U_1328 != singleton(sK317(U_1332))
| sK315(U_1332) != sK316(U_1332)
| function(sK318(U_1332)) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_24,plain,
( in(sK314(U_1332),U_1332)
| in(sK317(U_1332),U_1332)
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_25,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_26,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_27,plain,
( in(sK314(U_1332),U_1332)
| U_1328 != singleton(sK317(U_1332))
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_28,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_29,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_30,plain,
( in(sK317(U_1332),U_1332)
| sK315(U_1332) != sK316(U_1332)
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_31,plain,
( U_1328 != singleton(sK317(U_1332))
| sK315(U_1332) != sK316(U_1332)
| relation_dom(sK318(U_1332)) = U_1332 ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_32,plain,
( in(sK314(U_1332),U_1332)
| in(sK317(U_1332),U_1332)
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_33,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_34,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| in(sK317(U_1332),U_1332)
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_35,plain,
( in(sK314(U_1332),U_1332)
| U_1328 != singleton(sK317(U_1332))
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_36,plain,
( sK315(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_37,plain,
( sK316(U_1332) = singleton(sK314(U_1332))
| U_1328 != singleton(sK317(U_1332))
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_38,plain,
( in(sK317(U_1332),U_1332)
| sK315(U_1332) != sK316(U_1332)
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
cnf(f_303_39,plain,
( U_1328 != singleton(sK317(U_1332))
| sK315(U_1332) != sK316(U_1332)
| apply(sK318(U_1332),U_1330) = singleton(U_1330)
| ~ in(U_1330,U_1332) ),
inference(clausify,[status(thm)],[f_303_7]) ).
fof(f_304_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_304_2,plain,
( ! [U_1344] :
( ! [U_1343] :
( ? [U_1342] :
( ! [U_1341] :
( U_1341 = U_1342
| ~ subset(U_1342,U_1341)
| ~ in(U_1341,U_1343) )
& in(U_1342,U_1343) )
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344))) )
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) )
| ? [U_1340] :
( ? [U_1339] :
( ! [U_1338] :
( ? [U_1337] :
( U_1337 != U_1338
& subset(U_1338,U_1337)
& in(U_1337,U_1339) )
| ~ in(U_1338,U_1339) )
& U_1339 != empty_set
& element(U_1339,powerset(powerset(U_1340))) )
& in(U_1340,omega)
& ! [U_1336] :
( ! [U_1335] :
( ? [U_1334] :
( ! [U_1333] :
( U_1333 = U_1334
| ~ subset(U_1334,U_1333)
| ~ in(U_1333,U_1335) )
& in(U_1334,U_1335) )
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336))) )
| ~ in(U_1336,omega)
| ~ in(U_1336,U_1340)
| ~ ordinal(U_1336) )
& ordinal(U_1340) ) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
( ! [U_1344] :
( ! [U_1343] :
( ? [U_1342] :
( ! [U_1341] :
( U_1341 = U_1342
| ~ subset(U_1342,U_1341)
| ~ in(U_1341,U_1343) )
& in(U_1342,U_1343) )
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344))) )
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) )
| ( ? [U_1339] :
( ! [U_1338] :
( ? [U_1337] :
( U_1337 != U_1338
& subset(U_1338,U_1337)
& in(U_1337,U_1339) )
| ~ in(U_1338,U_1339) )
& U_1339 != empty_set
& element(U_1339,powerset(powerset(sK319))) )
& in(sK319,omega)
& ! [U_1336] :
( ! [U_1335] :
( ? [U_1334] :
( ! [U_1333] :
( U_1333 = U_1334
| ~ subset(U_1334,U_1333)
| ~ in(U_1333,U_1335) )
& in(U_1334,U_1335) )
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336))) )
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336) )
& ordinal(sK319) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_1340,sK319)],[f_304_2]) ).
fof(f_304_4,plain,
( ! [U_1344] :
( ! [U_1343] :
( ? [U_1342] :
( ! [U_1341] :
( U_1341 = U_1342
| ~ subset(U_1342,U_1341)
| ~ in(U_1341,U_1343) )
& in(U_1342,U_1343) )
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344))) )
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) )
| ( ? [U_1339] :
( ! [U_1338] :
( ? [U_1337] :
( U_1337 != U_1338
& subset(U_1338,U_1337)
& in(U_1337,U_1339) )
| ~ in(U_1338,U_1339) )
& U_1339 != empty_set
& element(U_1339,powerset(powerset(sK319))) )
& in(sK319,omega)
& ! [U_1336] :
( ! [U_1335] :
( ( ! [U_1333] :
( U_1333 = sK320(U_1336,U_1335)
| ~ subset(sK320(U_1336,U_1335),U_1333)
| ~ in(U_1333,U_1335) )
& in(sK320(U_1336,U_1335),U_1335) )
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336))) )
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336) )
& ordinal(sK319) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_1334,sK320(U_1336,U_1335))],[f_304_3]) ).
fof(f_304_5,plain,
( ! [U_1344] :
( ! [U_1343] :
( ? [U_1342] :
( ! [U_1341] :
( U_1341 = U_1342
| ~ subset(U_1342,U_1341)
| ~ in(U_1341,U_1343) )
& in(U_1342,U_1343) )
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344))) )
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) )
| ( ! [U_1338] :
( ? [U_1337] :
( U_1337 != U_1338
& subset(U_1338,U_1337)
& in(U_1337,sK321) )
| ~ in(U_1338,sK321) )
& sK321 != empty_set
& element(sK321,powerset(powerset(sK319)))
& in(sK319,omega)
& ! [U_1336] :
( ! [U_1335] :
( ( ! [U_1333] :
( U_1333 = sK320(U_1336,U_1335)
| ~ subset(sK320(U_1336,U_1335),U_1333)
| ~ in(U_1333,U_1335) )
& in(sK320(U_1336,U_1335),U_1335) )
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336))) )
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336) )
& ordinal(sK319) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_1339,sK321)],[f_304_4]) ).
fof(f_304_6,plain,
( ! [U_1344] :
( ! [U_1343] :
( ? [U_1342] :
( ! [U_1341] :
( U_1341 = U_1342
| ~ subset(U_1342,U_1341)
| ~ in(U_1341,U_1343) )
& in(U_1342,U_1343) )
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344))) )
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) )
| ( ! [U_1338] :
( ( sK322(U_1338) != U_1338
& subset(U_1338,sK322(U_1338))
& in(sK322(U_1338),sK321) )
| ~ in(U_1338,sK321) )
& sK321 != empty_set
& element(sK321,powerset(powerset(sK319)))
& in(sK319,omega)
& ! [U_1336] :
( ! [U_1335] :
( ( ! [U_1333] :
( U_1333 = sK320(U_1336,U_1335)
| ~ subset(sK320(U_1336,U_1335),U_1333)
| ~ in(U_1333,U_1335) )
& in(sK320(U_1336,U_1335),U_1335) )
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336))) )
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336) )
& ordinal(sK319) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_1337,sK322(U_1338))],[f_304_5]) ).
fof(f_304_7,plain,
( ! [U_1344] :
( ! [U_1343] :
( ( ! [U_1341] :
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343) )
& in(sK323(U_1344,U_1343),U_1343) )
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344))) )
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) )
| ( ! [U_1338] :
( ( sK322(U_1338) != U_1338
& subset(U_1338,sK322(U_1338))
& in(sK322(U_1338),sK321) )
| ~ in(U_1338,sK321) )
& sK321 != empty_set
& element(sK321,powerset(powerset(sK319)))
& in(sK319,omega)
& ! [U_1336] :
( ! [U_1335] :
( ( ! [U_1333] :
( U_1333 = sK320(U_1336,U_1335)
| ~ subset(sK320(U_1336,U_1335),U_1333)
| ~ in(U_1333,U_1335) )
& in(sK320(U_1336,U_1335),U_1335) )
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336))) )
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336) )
& ordinal(sK319) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_1342,sK323(U_1344,U_1343))],[f_304_6]) ).
cnf(f_304_8,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| ordinal(sK319) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_9,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| ordinal(sK319) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_10,plain,
( in(sK320(U_1336,U_1335),U_1335)
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336)))
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336)
| in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_11,plain,
( U_1333 = sK320(U_1336,U_1335)
| ~ subset(sK320(U_1336,U_1335),U_1333)
| ~ in(U_1333,U_1335)
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336)))
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336)
| in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_12,plain,
( in(sK320(U_1336,U_1335),U_1335)
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336)))
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336)
| U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_13,plain,
( U_1333 = sK320(U_1336,U_1335)
| ~ subset(sK320(U_1336,U_1335),U_1333)
| ~ in(U_1333,U_1335)
| U_1335 = empty_set
| ~ element(U_1335,powerset(powerset(U_1336)))
| ~ in(U_1336,omega)
| ~ in(U_1336,sK319)
| ~ ordinal(U_1336)
| U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_14,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| in(sK319,omega) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_15,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| in(sK319,omega) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_16,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| element(sK321,powerset(powerset(sK319))) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_17,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| element(sK321,powerset(powerset(sK319))) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_18,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| sK321 != empty_set ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_19,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| sK321 != empty_set ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_20,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| in(sK322(U_1338),sK321)
| ~ in(U_1338,sK321) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_21,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| in(sK322(U_1338),sK321)
| ~ in(U_1338,sK321) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_22,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| subset(U_1338,sK322(U_1338))
| ~ in(U_1338,sK321) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_23,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| subset(U_1338,sK322(U_1338))
| ~ in(U_1338,sK321) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_24,plain,
( in(sK323(U_1344,U_1343),U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| sK322(U_1338) != U_1338
| ~ in(U_1338,sK321) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_25,plain,
( U_1341 = sK323(U_1344,U_1343)
| ~ subset(sK323(U_1344,U_1343),U_1341)
| ~ in(U_1341,U_1343)
| U_1343 = empty_set
| ~ element(U_1343,powerset(powerset(U_1344)))
| ~ in(U_1344,omega)
| ~ ordinal(U_1344)
| sK322(U_1338) != U_1338
| ~ in(U_1338,sK321) ),
inference(clausify,[status(thm)],[f_304_7]) ).
fof(f_305_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_305_2,plain,
! [U_1347] :
? [U_1346] :
( ! [U_1345] :
( apply(U_1346,U_1345) = singleton(U_1345)
| ~ in(U_1345,U_1347) )
& relation_dom(U_1346) = U_1347
& function(U_1346)
& relation(U_1346) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_1347] :
( ! [U_1345] :
( apply(sK324(U_1347),U_1345) = singleton(U_1345)
| ~ in(U_1345,U_1347) )
& relation_dom(sK324(U_1347)) = U_1347
& function(sK324(U_1347))
& relation(sK324(U_1347)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_1346,sK324(U_1347))],[f_305_2]) ).
cnf(f_305_4,plain,
relation(sK324(U_1347)),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_5,plain,
function(sK324(U_1347)),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_6,plain,
relation_dom(sK324(U_1347)) = U_1347,
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_7,plain,
( apply(sK324(U_1347),U_1345) = singleton(U_1345)
| ~ in(U_1345,U_1347) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_306_2,plain,
! [U_1349,U_1348] :
( disjoint(U_1348,U_1349)
| ~ disjoint(U_1349,U_1348) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( disjoint(U_1348,U_1349)
| ~ disjoint(U_1349,U_1348) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [A,B] :
( equipotent(B,A)
| ~ equipotent(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r2_wellord2]) ).
fof(f_307_2,plain,
! [U_1351,U_1350] :
( equipotent(U_1350,U_1351)
| ~ equipotent(U_1351,U_1350) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( equipotent(U_1350,U_1351)
| ~ equipotent(U_1351,U_1350) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_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_308_2,plain,
! [U_1355,U_1354,U_1353,U_1352] :
( ( in(ordered_pair(U_1355,U_1354),cartesian_product2(U_1353,U_1352))
| ~ in(U_1354,U_1352)
| ~ in(U_1355,U_1353) )
& ( ( in(U_1354,U_1352)
& in(U_1355,U_1353) )
| ~ in(ordered_pair(U_1355,U_1354),cartesian_product2(U_1353,U_1352)) ) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_1363,U_1361,U_1359,U_1357] :
( in(ordered_pair(U_1363,U_1361),cartesian_product2(U_1359,U_1357))
| ~ in(U_1361,U_1357)
| ~ in(U_1363,U_1359) )
& ! [U_1362,U_1360,U_1358,U_1356] :
( ( in(U_1360,U_1356)
& in(U_1362,U_1358) )
| ~ in(ordered_pair(U_1362,U_1360),cartesian_product2(U_1358,U_1356)) ) ),
inference(miniscope,[status(thm)],[f_308_2]) ).
cnf(f_308_4,plain,
( in(U_1362,U_1358)
| ~ in(ordered_pair(U_1362,U_1360),cartesian_product2(U_1358,U_1356)) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( in(U_1360,U_1356)
| ~ in(ordered_pair(U_1362,U_1360),cartesian_product2(U_1358,U_1356)) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( in(ordered_pair(U_1363,U_1361),cartesian_product2(U_1359,U_1357))
| ~ in(U_1361,U_1357)
| ~ in(U_1363,U_1359) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_309_2,plain,
! [U_1364] : in(U_1364,succ(U_1364)),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
in(U_1364,succ(U_1364)),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_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_310_2,plain,
! [U_1368,U_1367,U_1366,U_1365] :
( U_1368 = U_1365
| U_1368 = U_1366
| unordered_pair(U_1368,U_1367) != unordered_pair(U_1366,U_1365) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1368,U_1367,U_1366] :
( ! [U_1365] :
( U_1368 = U_1365
| unordered_pair(U_1368,U_1367) != unordered_pair(U_1366,U_1365) )
| U_1368 = U_1366 ),
inference(miniscope,[status(thm)],[f_310_2]) ).
cnf(f_310_4,plain,
( U_1368 = U_1365
| unordered_pair(U_1368,U_1367) != unordered_pair(U_1366,U_1365)
| U_1368 = U_1366 ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_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_311_2,plain,
! [U_1371,U_1370,U_1369] :
( ( ( in(U_1371,relation_rng(relation_rng_restriction(U_1370,U_1369)))
| ~ in(U_1371,relation_rng(U_1369))
| ~ in(U_1371,U_1370) )
& ( ( in(U_1371,relation_rng(U_1369))
& in(U_1371,U_1370) )
| ~ in(U_1371,relation_rng(relation_rng_restriction(U_1370,U_1369))) ) )
| ~ relation(U_1369) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( in(U_1371,U_1370)
| ~ in(U_1371,relation_rng(relation_rng_restriction(U_1370,U_1369)))
| ~ relation(U_1369) ),
inference(clausify,[status(thm)],[f_311_2]) ).
cnf(f_311_4,plain,
( in(U_1371,relation_rng(U_1369))
| ~ in(U_1371,relation_rng(relation_rng_restriction(U_1370,U_1369)))
| ~ relation(U_1369) ),
inference(clausify,[status(thm)],[f_311_2]) ).
cnf(f_311_5,plain,
( in(U_1371,relation_rng(relation_rng_restriction(U_1370,U_1369)))
| ~ in(U_1371,relation_rng(U_1369))
| ~ in(U_1371,U_1370)
| ~ relation(U_1369) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_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_312_2,plain,
! [U_1373,U_1372] :
( subset(relation_rng(relation_rng_restriction(U_1373,U_1372)),U_1373)
| ~ relation(U_1372) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
( subset(relation_rng(relation_rng_restriction(U_1373,U_1372)),U_1373)
| ~ relation(U_1372) ),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_313_2,plain,
! [U_1375,U_1374] :
( subset(relation_rng_restriction(U_1375,U_1374),U_1374)
| ~ relation(U_1374) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( subset(relation_rng_restriction(U_1375,U_1374),U_1374)
| ~ relation(U_1374) ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_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_314_2,plain,
! [U_1377,U_1376] :
( subset(relation_rng(relation_rng_restriction(U_1377,U_1376)),relation_rng(U_1376))
| ~ relation(U_1376) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( subset(relation_rng(relation_rng_restriction(U_1377,U_1376)),relation_rng(U_1376))
| ~ relation(U_1376) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_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_315_2,plain,
! [U_1380,U_1379,U_1378] :
( ( subset(cartesian_product2(U_1378,U_1380),cartesian_product2(U_1378,U_1379))
& subset(cartesian_product2(U_1380,U_1378),cartesian_product2(U_1379,U_1378)) )
| ~ subset(U_1380,U_1379) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
! [U_1380,U_1379] :
( ( ! [U_1382] : subset(cartesian_product2(U_1382,U_1380),cartesian_product2(U_1382,U_1379))
& ! [U_1381] : subset(cartesian_product2(U_1380,U_1381),cartesian_product2(U_1379,U_1381)) )
| ~ subset(U_1380,U_1379) ),
inference(miniscope,[status(thm)],[f_315_2]) ).
cnf(f_315_4,plain,
( subset(cartesian_product2(U_1380,U_1381),cartesian_product2(U_1379,U_1381))
| ~ subset(U_1380,U_1379) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_5,plain,
( subset(cartesian_product2(U_1382,U_1380),cartesian_product2(U_1382,U_1379))
| ~ subset(U_1380,U_1379) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_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_316_2,plain,
! [U_1384,U_1383] :
( relation_rng(relation_rng_restriction(U_1384,U_1383)) = set_intersection2(relation_rng(U_1383),U_1384)
| ~ relation(U_1383) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( relation_rng(relation_rng_restriction(U_1384,U_1383)) = set_intersection2(relation_rng(U_1383),U_1384)
| ~ relation(U_1383) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_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_317_2,plain,
! [U_1388,U_1387,U_1386,U_1385] :
( subset(cartesian_product2(U_1388,U_1386),cartesian_product2(U_1387,U_1385))
| ~ subset(U_1386,U_1385)
| ~ subset(U_1388,U_1387) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( subset(cartesian_product2(U_1388,U_1386),cartesian_product2(U_1387,U_1385))
| ~ subset(U_1386,U_1385)
| ~ subset(U_1388,U_1387) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_1,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
inference(negate,[status(cth)],[t12_pre_topc]) ).
fof(f_318_2,negated_conjecture,
? [A] :
( cast_as_carrier_subset(A) != the_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[f_318_1]) ).
fof(f_318_3,negated_conjecture,
? [U_1389] :
( cast_as_carrier_subset(U_1389) != the_carrier(U_1389)
& one_sorted_str(U_1389) ),
inference(variable_rename,[status(thm)],[f_318_2]) ).
fof(f_318_4,negated_conjecture,
( cast_as_carrier_subset(sK325) != the_carrier(sK325)
& one_sorted_str(sK325) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_1389,sK325)],[f_318_3]) ).
fof(f_318_5,negated_conjecture,
( cast_as_carrier_subset(sK325) != the_carrier(sK325)
& one_sorted_str(sK325) ),
inference(definitional_conversion,[status(esa)],[f_318_4]) ).
cnf(f_318_6,negated_conjecture,
one_sorted_str(sK325),
inference(clausify,[status(thm)],[f_318_5]) ).
cnf(f_318_7,negated_conjecture,
cast_as_carrier_subset(sK325) != the_carrier(sK325),
inference(clausify,[status(thm)],[f_318_5]) ).
fof(f_319_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_319_2,plain,
! [U_1392,U_1391,U_1390] :
( ( subset(relation_rng(U_1390),U_1391)
& subset(relation_dom(U_1390),U_1392) )
| ~ relation_of2_as_subset(U_1390,U_1392,U_1391) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
( subset(relation_dom(U_1390),U_1392)
| ~ relation_of2_as_subset(U_1390,U_1392,U_1391) ),
inference(clausify,[status(thm)],[f_319_2]) ).
cnf(f_319_4,plain,
( subset(relation_rng(U_1390),U_1391)
| ~ relation_of2_as_subset(U_1390,U_1392,U_1391) ),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_320_2,plain,
! [U_1394,U_1393] :
( set_union2(U_1394,U_1393) = U_1393
| ~ subset(U_1394,U_1393) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( set_union2(U_1394,U_1393) = U_1393
| ~ subset(U_1394,U_1393) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_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_321_2,plain,
! [U_1400] :
? [U_1399] :
( ! [U_1398] :
( in(U_1398,U_1399)
| are_equipotent(U_1398,U_1399)
| ~ subset(U_1398,U_1399) )
& ! [U_1397] :
( in(powerset(U_1397),U_1399)
| ~ in(U_1397,U_1399) )
& ! [U_1396,U_1395] :
( in(U_1395,U_1399)
| ~ subset(U_1395,U_1396)
| ~ in(U_1396,U_1399) )
& in(U_1400,U_1399) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1400] :
( ! [U_1398] :
( in(U_1398,sK326(U_1400))
| are_equipotent(U_1398,sK326(U_1400))
| ~ subset(U_1398,sK326(U_1400)) )
& ! [U_1397] :
( in(powerset(U_1397),sK326(U_1400))
| ~ in(U_1397,sK326(U_1400)) )
& ! [U_1396,U_1395] :
( in(U_1395,sK326(U_1400))
| ~ subset(U_1395,U_1396)
| ~ in(U_1396,sK326(U_1400)) )
& in(U_1400,sK326(U_1400)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_1399,sK326(U_1400))],[f_321_2]) ).
cnf(f_321_4,plain,
in(U_1400,sK326(U_1400)),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_5,plain,
( in(U_1395,sK326(U_1400))
| ~ subset(U_1395,U_1396)
| ~ in(U_1396,sK326(U_1400)) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_6,plain,
( in(powerset(U_1397),sK326(U_1400))
| ~ in(U_1397,sK326(U_1400)) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_7,plain,
( in(U_1398,sK326(U_1400))
| are_equipotent(U_1398,sK326(U_1400))
| ~ subset(U_1398,sK326(U_1400)) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [A,B] :
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t13_finset_1]) ).
fof(f_322_2,plain,
! [U_1402,U_1401] :
( finite(U_1402)
| ~ finite(U_1401)
| ~ subset(U_1402,U_1401) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_1402] :
( ! [U_1401] :
( ~ finite(U_1401)
| ~ subset(U_1402,U_1401) )
| finite(U_1402) ),
inference(miniscope,[status(thm)],[f_322_2]) ).
cnf(f_322_4,plain,
( ~ finite(U_1401)
| ~ subset(U_1402,U_1401)
| finite(U_1402) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_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_323_2,plain,
! [U_1405,U_1404,U_1403] :
( relation_dom_restriction(relation_rng_restriction(U_1405,U_1403),U_1404) = relation_rng_restriction(U_1405,relation_dom_restriction(U_1403,U_1404))
| ~ relation(U_1403) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_1405,U_1403),U_1404) = relation_rng_restriction(U_1405,relation_dom_restriction(U_1403,U_1404))
| ~ relation(U_1403) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_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_324_2,plain,
! [U_1410,U_1409,U_1408] :
( ( ( in(U_1410,relation_image(U_1408,U_1409))
| ! [U_1407] :
( ~ in(U_1407,U_1409)
| ~ in(ordered_pair(U_1407,U_1410),U_1408)
| ~ in(U_1407,relation_dom(U_1408)) ) )
& ( ? [U_1406] :
( in(U_1406,U_1409)
& in(ordered_pair(U_1406,U_1410),U_1408)
& in(U_1406,relation_dom(U_1408)) )
| ~ in(U_1410,relation_image(U_1408,U_1409)) ) )
| ~ relation(U_1408) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_1410,U_1409,U_1408] :
( ( ( in(U_1410,relation_image(U_1408,U_1409))
| ! [U_1407] :
( ~ in(U_1407,U_1409)
| ~ in(ordered_pair(U_1407,U_1410),U_1408)
| ~ in(U_1407,relation_dom(U_1408)) ) )
& ( ( in(sK327(U_1410,U_1409,U_1408),U_1409)
& in(ordered_pair(sK327(U_1410,U_1409,U_1408),U_1410),U_1408)
& in(sK327(U_1410,U_1409,U_1408),relation_dom(U_1408)) )
| ~ in(U_1410,relation_image(U_1408,U_1409)) ) )
| ~ relation(U_1408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_1406,sK327(U_1410,U_1409,U_1408))],[f_324_2]) ).
cnf(f_324_4,plain,
( in(sK327(U_1410,U_1409,U_1408),relation_dom(U_1408))
| ~ in(U_1410,relation_image(U_1408,U_1409))
| ~ relation(U_1408) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_5,plain,
( in(ordered_pair(sK327(U_1410,U_1409,U_1408),U_1410),U_1408)
| ~ in(U_1410,relation_image(U_1408,U_1409))
| ~ relation(U_1408) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_6,plain,
( in(sK327(U_1410,U_1409,U_1408),U_1409)
| ~ in(U_1410,relation_image(U_1408,U_1409))
| ~ relation(U_1408) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_7,plain,
( in(U_1410,relation_image(U_1408,U_1409))
| ~ in(U_1407,U_1409)
| ~ in(ordered_pair(U_1407,U_1410),U_1408)
| ~ in(U_1407,relation_dom(U_1408))
| ~ relation(U_1408) ),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_325_2,plain,
! [U_1412,U_1411] :
( subset(relation_image(U_1411,U_1412),relation_rng(U_1411))
| ~ relation(U_1411) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( subset(relation_image(U_1411,U_1412),relation_rng(U_1411))
| ~ relation(U_1411) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_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_326_2,plain,
! [U_1414,U_1413] :
( subset(relation_image(U_1413,relation_inverse_image(U_1413,U_1414)),U_1414)
| ~ function(U_1413)
| ~ relation(U_1413) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( subset(relation_image(U_1413,relation_inverse_image(U_1413,U_1414)),U_1414)
| ~ function(U_1413)
| ~ relation(U_1413) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_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_327_2,plain,
! [U_1416,U_1415] :
( relation_image(U_1415,U_1416) = relation_image(U_1415,set_intersection2(relation_dom(U_1415),U_1416))
| ~ relation(U_1415) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( relation_image(U_1415,U_1416) = relation_image(U_1415,set_intersection2(relation_dom(U_1415),U_1416))
| ~ relation(U_1415) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_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_328_2,plain,
! [U_1418,U_1417] :
( subset(U_1418,relation_inverse_image(U_1417,relation_image(U_1417,U_1418)))
| ~ subset(U_1418,relation_dom(U_1417))
| ~ relation(U_1417) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( subset(U_1418,relation_inverse_image(U_1417,relation_image(U_1417,U_1418)))
| ~ subset(U_1418,relation_dom(U_1417))
| ~ relation(U_1417) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_329_2,plain,
! [U_1419] :
( relation_image(U_1419,relation_dom(U_1419)) = relation_rng(U_1419)
| ~ relation(U_1419) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( relation_image(U_1419,relation_dom(U_1419)) = relation_rng(U_1419)
| ~ relation(U_1419) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_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_330_2,plain,
! [U_1421,U_1420] :
( relation_image(U_1420,relation_inverse_image(U_1420,U_1421)) = U_1421
| ~ subset(U_1421,relation_rng(U_1420))
| ~ function(U_1420)
| ~ relation(U_1420) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
( relation_image(U_1420,relation_inverse_image(U_1420,U_1421)) = U_1421
| ~ subset(U_1421,relation_rng(U_1420))
| ~ function(U_1420)
| ~ relation(U_1420) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_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_331_2,plain,
! [U_1425,U_1424,U_1423,U_1422] :
( relation_of2_as_subset(U_1422,U_1423,U_1424)
| ~ subset(relation_rng(U_1422),U_1424)
| ~ relation_of2_as_subset(U_1422,U_1423,U_1425) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( relation_of2_as_subset(U_1422,U_1423,U_1424)
| ~ subset(relation_rng(U_1422),U_1424)
| ~ relation_of2_as_subset(U_1422,U_1423,U_1425) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[t15_finset_1]) ).
fof(f_332_2,plain,
! [U_1427,U_1426] :
( finite(set_intersection2(U_1427,U_1426))
| ~ finite(U_1427) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1427] :
( ! [U_1426] : finite(set_intersection2(U_1427,U_1426))
| ~ finite(U_1427) ),
inference(miniscope,[status(thm)],[f_332_2]) ).
cnf(f_332_4,plain,
( finite(set_intersection2(U_1427,U_1426))
| ~ finite(U_1427) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_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_333_2,plain,
! [U_1429] :
( ! [U_1428] :
( relation_rng(relation_composition(U_1429,U_1428)) = relation_image(U_1428,relation_rng(U_1429))
| ~ relation(U_1428) )
| ~ relation(U_1429) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( relation_rng(relation_composition(U_1429,U_1428)) = relation_image(U_1428,relation_rng(U_1429))
| ~ relation(U_1428)
| ~ relation(U_1429) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_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_334_2,plain,
! [U_1434,U_1433,U_1432] :
( ( ( in(U_1434,relation_inverse_image(U_1432,U_1433))
| ! [U_1431] :
( ~ in(U_1431,U_1433)
| ~ in(ordered_pair(U_1434,U_1431),U_1432)
| ~ in(U_1431,relation_rng(U_1432)) ) )
& ( ? [U_1430] :
( in(U_1430,U_1433)
& in(ordered_pair(U_1434,U_1430),U_1432)
& in(U_1430,relation_rng(U_1432)) )
| ~ in(U_1434,relation_inverse_image(U_1432,U_1433)) ) )
| ~ relation(U_1432) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1434,U_1433,U_1432] :
( ( ( in(U_1434,relation_inverse_image(U_1432,U_1433))
| ! [U_1431] :
( ~ in(U_1431,U_1433)
| ~ in(ordered_pair(U_1434,U_1431),U_1432)
| ~ in(U_1431,relation_rng(U_1432)) ) )
& ( ( in(sK328(U_1434,U_1433,U_1432),U_1433)
& in(ordered_pair(U_1434,sK328(U_1434,U_1433,U_1432)),U_1432)
& in(sK328(U_1434,U_1433,U_1432),relation_rng(U_1432)) )
| ~ in(U_1434,relation_inverse_image(U_1432,U_1433)) ) )
| ~ relation(U_1432) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_1430,sK328(U_1434,U_1433,U_1432))],[f_334_2]) ).
cnf(f_334_4,plain,
( in(sK328(U_1434,U_1433,U_1432),relation_rng(U_1432))
| ~ in(U_1434,relation_inverse_image(U_1432,U_1433))
| ~ relation(U_1432) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_5,plain,
( in(ordered_pair(U_1434,sK328(U_1434,U_1433,U_1432)),U_1432)
| ~ in(U_1434,relation_inverse_image(U_1432,U_1433))
| ~ relation(U_1432) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_6,plain,
( in(sK328(U_1434,U_1433,U_1432),U_1433)
| ~ in(U_1434,relation_inverse_image(U_1432,U_1433))
| ~ relation(U_1432) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_7,plain,
( in(U_1434,relation_inverse_image(U_1432,U_1433))
| ~ in(U_1431,U_1433)
| ~ in(ordered_pair(U_1434,U_1431),U_1432)
| ~ in(U_1431,relation_rng(U_1432))
| ~ relation(U_1432) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_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_335_2,plain,
! [U_1436,U_1435] :
( subset(relation_inverse_image(U_1435,U_1436),relation_dom(U_1435))
| ~ relation(U_1435) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( subset(relation_inverse_image(U_1435,U_1436),relation_dom(U_1435))
| ~ relation(U_1435) ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_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_336_2,plain,
! [U_1440,U_1439,U_1438,U_1437] :
( relation_of2_as_subset(U_1437,U_1438,U_1439)
| ~ subset(U_1440,U_1439)
| ~ relation_of2_as_subset(U_1437,U_1438,U_1440) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( relation_of2_as_subset(U_1437,U_1438,U_1439)
| ~ subset(U_1440,U_1439)
| ~ relation_of2_as_subset(U_1437,U_1438,U_1440) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_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_337_2,plain,
! [U_1443,U_1442,U_1441] :
( ( ( in(U_1443,relation_restriction(U_1441,U_1442))
| ~ in(U_1443,cartesian_product2(U_1442,U_1442))
| ~ in(U_1443,U_1441) )
& ( ( in(U_1443,cartesian_product2(U_1442,U_1442))
& in(U_1443,U_1441) )
| ~ in(U_1443,relation_restriction(U_1441,U_1442)) ) )
| ~ relation(U_1441) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( in(U_1443,U_1441)
| ~ in(U_1443,relation_restriction(U_1441,U_1442))
| ~ relation(U_1441) ),
inference(clausify,[status(thm)],[f_337_2]) ).
cnf(f_337_4,plain,
( in(U_1443,cartesian_product2(U_1442,U_1442))
| ~ in(U_1443,relation_restriction(U_1441,U_1442))
| ~ relation(U_1441) ),
inference(clausify,[status(thm)],[f_337_2]) ).
cnf(f_337_5,plain,
( in(U_1443,relation_restriction(U_1441,U_1442))
| ~ in(U_1443,cartesian_product2(U_1442,U_1442))
| ~ in(U_1443,U_1441)
| ~ relation(U_1441) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_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_338_2,plain,
! [U_1445,U_1444] :
( relation_inverse_image(U_1444,U_1445) != empty_set
| ~ subset(U_1445,relation_rng(U_1444))
| U_1445 = empty_set
| ~ relation(U_1444) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
( relation_inverse_image(U_1444,U_1445) != empty_set
| ~ subset(U_1445,relation_rng(U_1444))
| U_1445 = empty_set
| ~ relation(U_1444) ),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_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_339_2,plain,
! [U_1448,U_1447,U_1446] :
( subset(relation_inverse_image(U_1446,U_1448),relation_inverse_image(U_1446,U_1447))
| ~ subset(U_1448,U_1447)
| ~ relation(U_1446) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
( subset(relation_inverse_image(U_1446,U_1448),relation_inverse_image(U_1446,U_1447))
| ~ subset(U_1448,U_1447)
| ~ relation(U_1446) ),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_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_340_2,plain,
! [U_1450,U_1449] :
( finite(relation_image(U_1449,U_1450))
| ~ finite(U_1450)
| ~ function(U_1449)
| ~ relation(U_1449) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( finite(relation_image(U_1449,U_1450))
| ~ finite(U_1450)
| ~ function(U_1449)
| ~ relation(U_1449) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_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_341_2,plain,
! [U_1452,U_1451] :
( relation_restriction(U_1451,U_1452) = relation_dom_restriction(relation_rng_restriction(U_1452,U_1451),U_1452)
| ~ relation(U_1451) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( relation_restriction(U_1451,U_1452) = relation_dom_restriction(relation_rng_restriction(U_1452,U_1451),U_1452)
| ~ relation(U_1451) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_342_2,plain,
! [U_1454,U_1453] : subset(set_intersection2(U_1454,U_1453),U_1454),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
subset(set_intersection2(U_1454,U_1453),U_1454),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_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_343_2,plain,
! [U_1458] :
( ! [U_1457] :
( ? [U_1456] :
( ! [U_1455] :
( U_1455 = U_1456
| ~ subset(U_1456,U_1455)
| ~ in(U_1455,U_1457) )
& in(U_1456,U_1457) )
| U_1457 = empty_set
| ~ element(U_1457,powerset(powerset(U_1458))) )
| ~ finite(U_1458) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1458] :
( ! [U_1457] :
( ( ! [U_1455] :
( U_1455 = sK329(U_1458,U_1457)
| ~ subset(sK329(U_1458,U_1457),U_1455)
| ~ in(U_1455,U_1457) )
& in(sK329(U_1458,U_1457),U_1457) )
| U_1457 = empty_set
| ~ element(U_1457,powerset(powerset(U_1458))) )
| ~ finite(U_1458) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_1456,sK329(U_1458,U_1457))],[f_343_2]) ).
cnf(f_343_4,plain,
( in(sK329(U_1458,U_1457),U_1457)
| U_1457 = empty_set
| ~ element(U_1457,powerset(powerset(U_1458)))
| ~ finite(U_1458) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_5,plain,
( U_1455 = sK329(U_1458,U_1457)
| ~ subset(sK329(U_1458,U_1457),U_1455)
| ~ in(U_1455,U_1457)
| U_1457 = empty_set
| ~ element(U_1457,powerset(powerset(U_1458)))
| ~ finite(U_1458) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_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_344_2,plain,
! [U_1460,U_1459] :
( relation_restriction(U_1459,U_1460) = relation_rng_restriction(U_1460,relation_dom_restriction(U_1459,U_1460))
| ~ relation(U_1459) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( relation_restriction(U_1459,U_1460) = relation_rng_restriction(U_1460,relation_dom_restriction(U_1459,U_1460))
| ~ relation(U_1459) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_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_345_2,plain,
! [U_1463,U_1462,U_1461] :
( ( in(U_1463,U_1462)
& in(U_1463,relation_field(U_1461)) )
| ~ in(U_1463,relation_field(relation_restriction(U_1461,U_1462)))
| ~ relation(U_1461) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( in(U_1463,relation_field(U_1461))
| ~ in(U_1463,relation_field(relation_restriction(U_1461,U_1462)))
| ~ relation(U_1461) ),
inference(clausify,[status(thm)],[f_345_2]) ).
cnf(f_345_4,plain,
( in(U_1463,U_1462)
| ~ in(U_1463,relation_field(relation_restriction(U_1461,U_1462)))
| ~ relation(U_1461) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_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_346_2,plain,
! [U_1466,U_1465,U_1464] :
( subset(U_1466,set_intersection2(U_1465,U_1464))
| ~ subset(U_1466,U_1464)
| ~ subset(U_1466,U_1465) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( subset(U_1466,set_intersection2(U_1465,U_1464))
| ~ subset(U_1466,U_1464)
| ~ subset(U_1466,U_1465) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_347_2,plain,
! [U_1467] : set_union2(U_1467,empty_set) = U_1467,
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
set_union2(U_1467,empty_set) = U_1467,
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_348_2,plain,
! [U_1469,U_1468] :
( element(U_1469,U_1468)
| ~ in(U_1469,U_1468) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
( element(U_1469,U_1468)
| ~ in(U_1469,U_1468) ),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_349_2,plain,
! [U_1472,U_1471,U_1470] :
( subset(U_1472,U_1470)
| ~ subset(U_1471,U_1470)
| ~ subset(U_1472,U_1471) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
( subset(U_1472,U_1470)
| ~ subset(U_1471,U_1470)
| ~ subset(U_1472,U_1471) ),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_350_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_350_1]) ).
fof(f_351_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_351_2,plain,
! [U_1475,U_1474,U_1473] :
( ( in(U_1474,relation_rng(U_1473))
& in(U_1475,relation_dom(U_1473)) )
| ~ in(ordered_pair(U_1475,U_1474),U_1473)
| ~ relation(U_1473) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( in(U_1475,relation_dom(U_1473))
| ~ in(ordered_pair(U_1475,U_1474),U_1473)
| ~ relation(U_1473) ),
inference(clausify,[status(thm)],[f_351_2]) ).
cnf(f_351_4,plain,
( in(U_1474,relation_rng(U_1473))
| ~ in(ordered_pair(U_1475,U_1474),U_1473)
| ~ relation(U_1473) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_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_352_2,plain,
! [U_1477,U_1476] :
( ( subset(relation_field(relation_restriction(U_1476,U_1477)),U_1477)
& subset(relation_field(relation_restriction(U_1476,U_1477)),relation_field(U_1476)) )
| ~ relation(U_1476) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( subset(relation_field(relation_restriction(U_1476,U_1477)),relation_field(U_1476))
| ~ relation(U_1476) ),
inference(clausify,[status(thm)],[f_352_2]) ).
cnf(f_352_4,plain,
( subset(relation_field(relation_restriction(U_1476,U_1477)),U_1477)
| ~ relation(U_1476) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_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_353_2,plain,
! [U_1480,U_1479] :
( ! [U_1478] :
( ( ( in(U_1480,relation_dom(relation_composition(U_1478,U_1479)))
| ~ in(apply(U_1478,U_1480),relation_dom(U_1479))
| ~ in(U_1480,relation_dom(U_1478)) )
& ( ( in(apply(U_1478,U_1480),relation_dom(U_1479))
& in(U_1480,relation_dom(U_1478)) )
| ~ in(U_1480,relation_dom(relation_composition(U_1478,U_1479))) ) )
| ~ function(U_1478)
| ~ relation(U_1478) )
| ~ function(U_1479)
| ~ relation(U_1479) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( in(U_1480,relation_dom(U_1478))
| ~ in(U_1480,relation_dom(relation_composition(U_1478,U_1479)))
| ~ function(U_1478)
| ~ relation(U_1478)
| ~ function(U_1479)
| ~ relation(U_1479) ),
inference(clausify,[status(thm)],[f_353_2]) ).
cnf(f_353_4,plain,
( in(apply(U_1478,U_1480),relation_dom(U_1479))
| ~ in(U_1480,relation_dom(relation_composition(U_1478,U_1479)))
| ~ function(U_1478)
| ~ relation(U_1478)
| ~ function(U_1479)
| ~ relation(U_1479) ),
inference(clausify,[status(thm)],[f_353_2]) ).
cnf(f_353_5,plain,
( in(U_1480,relation_dom(relation_composition(U_1478,U_1479)))
| ~ in(apply(U_1478,U_1480),relation_dom(U_1479))
| ~ in(U_1480,relation_dom(U_1478))
| ~ function(U_1478)
| ~ relation(U_1478)
| ~ function(U_1479)
| ~ relation(U_1479) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_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_354_2,plain,
! [U_1485,U_1484,U_1483,U_1482] :
( ! [U_1481] :
( apply(relation_composition(U_1482,U_1481),U_1483) = apply(U_1481,apply(U_1482,U_1483))
| U_1484 = empty_set
| ~ in(U_1483,U_1485)
| ~ function(U_1481)
| ~ relation(U_1481) )
| ~ relation_of2_as_subset(U_1482,U_1485,U_1484)
| ~ quasi_total(U_1482,U_1485,U_1484)
| ~ function(U_1482) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( apply(relation_composition(U_1482,U_1481),U_1483) = apply(U_1481,apply(U_1482,U_1483))
| U_1484 = empty_set
| ~ in(U_1483,U_1485)
| ~ function(U_1481)
| ~ relation(U_1481)
| ~ relation_of2_as_subset(U_1482,U_1485,U_1484)
| ~ quasi_total(U_1482,U_1485,U_1484)
| ~ function(U_1482) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_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_355_2,plain,
! [U_1487] :
( ! [U_1486] :
( in(U_1487,U_1486)
| ~ proper_subset(U_1487,U_1486)
| ~ ordinal(U_1486) )
| ~ epsilon_transitive(U_1487) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( in(U_1487,U_1486)
| ~ proper_subset(U_1487,U_1486)
| ~ ordinal(U_1486)
| ~ epsilon_transitive(U_1487) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_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_356_2,plain,
! [U_1488] :
( subset(U_1488,cartesian_product2(relation_dom(U_1488),relation_rng(U_1488)))
| ~ relation(U_1488) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( subset(U_1488,cartesian_product2(relation_dom(U_1488),relation_rng(U_1488)))
| ~ relation(U_1488) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_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_357_2,plain,
! [U_1491,U_1490,U_1489] :
( subset(fiber(relation_restriction(U_1489,U_1491),U_1490),fiber(U_1489,U_1490))
| ~ relation(U_1489) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( subset(fiber(relation_restriction(U_1489,U_1491),U_1490),fiber(U_1489,U_1490))
| ~ relation(U_1489) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_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_358_2,plain,
! [U_1494,U_1493] :
( ! [U_1492] :
( apply(relation_composition(U_1492,U_1493),U_1494) = apply(U_1493,apply(U_1492,U_1494))
| ~ in(U_1494,relation_dom(relation_composition(U_1492,U_1493)))
| ~ function(U_1492)
| ~ relation(U_1492) )
| ~ function(U_1493)
| ~ relation(U_1493) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( apply(relation_composition(U_1492,U_1493),U_1494) = apply(U_1493,apply(U_1492,U_1494))
| ~ in(U_1494,relation_dom(relation_composition(U_1492,U_1493)))
| ~ function(U_1492)
| ~ relation(U_1492)
| ~ function(U_1493)
| ~ relation(U_1493) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_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_359_2,plain,
! [U_1501,U_1500,U_1499] :
( ( ( ! [U_1498] :
( ? [U_1497] : in(ordered_pair(U_1498,U_1497),U_1499)
| ~ in(U_1498,U_1500) )
| relation_dom_as_subset(U_1500,U_1501,U_1499) != U_1500 )
& ( relation_dom_as_subset(U_1500,U_1501,U_1499) = U_1500
| ? [U_1496] :
( ! [U_1495] : ~ in(ordered_pair(U_1496,U_1495),U_1499)
& in(U_1496,U_1500) ) ) )
| ~ relation_of2_as_subset(U_1499,U_1500,U_1501) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_1501,U_1500,U_1499] :
( ( ( ! [U_1498] :
( ? [U_1497] : in(ordered_pair(U_1498,U_1497),U_1499)
| ~ in(U_1498,U_1500) )
| relation_dom_as_subset(U_1500,U_1501,U_1499) != U_1500 )
& ( relation_dom_as_subset(U_1500,U_1501,U_1499) = U_1500
| ( ! [U_1495] : ~ in(ordered_pair(sK330(U_1501,U_1500,U_1499),U_1495),U_1499)
& in(sK330(U_1501,U_1500,U_1499),U_1500) ) ) )
| ~ relation_of2_as_subset(U_1499,U_1500,U_1501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_1496,sK330(U_1501,U_1500,U_1499))],[f_359_2]) ).
fof(f_359_4,plain,
! [U_1501,U_1500,U_1499] :
( ( ( ! [U_1498] :
( in(ordered_pair(U_1498,sK331(U_1501,U_1500,U_1499,U_1498)),U_1499)
| ~ in(U_1498,U_1500) )
| relation_dom_as_subset(U_1500,U_1501,U_1499) != U_1500 )
& ( relation_dom_as_subset(U_1500,U_1501,U_1499) = U_1500
| ( ! [U_1495] : ~ in(ordered_pair(sK330(U_1501,U_1500,U_1499),U_1495),U_1499)
& in(sK330(U_1501,U_1500,U_1499),U_1500) ) ) )
| ~ relation_of2_as_subset(U_1499,U_1500,U_1501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_1497,sK331(U_1501,U_1500,U_1499,U_1498))],[f_359_3]) ).
cnf(f_359_5,plain,
( in(sK330(U_1501,U_1500,U_1499),U_1500)
| relation_dom_as_subset(U_1500,U_1501,U_1499) = U_1500
| ~ relation_of2_as_subset(U_1499,U_1500,U_1501) ),
inference(clausify,[status(thm)],[f_359_4]) ).
cnf(f_359_6,plain,
( ~ in(ordered_pair(sK330(U_1501,U_1500,U_1499),U_1495),U_1499)
| relation_dom_as_subset(U_1500,U_1501,U_1499) = U_1500
| ~ relation_of2_as_subset(U_1499,U_1500,U_1501) ),
inference(clausify,[status(thm)],[f_359_4]) ).
cnf(f_359_7,plain,
( in(ordered_pair(U_1498,sK331(U_1501,U_1500,U_1499,U_1498)),U_1499)
| ~ in(U_1498,U_1500)
| relation_dom_as_subset(U_1500,U_1501,U_1499) != U_1500
| ~ relation_of2_as_subset(U_1499,U_1500,U_1501) ),
inference(clausify,[status(thm)],[f_359_4]) ).
fof(f_360_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_360_2,plain,
! [U_1503,U_1502] :
( reflexive(relation_restriction(U_1502,U_1503))
| ~ reflexive(U_1502)
| ~ relation(U_1502) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
cnf(f_360_3,plain,
( reflexive(relation_restriction(U_1502,U_1503))
| ~ reflexive(U_1502)
| ~ relation(U_1502) ),
inference(clausify,[status(thm)],[f_360_2]) ).
fof(f_361_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_361_2,plain,
! [U_1506,U_1505] :
( ! [U_1504] :
( apply(relation_composition(U_1505,U_1504),U_1506) = apply(U_1504,apply(U_1505,U_1506))
| ~ in(U_1506,relation_dom(U_1505))
| ~ function(U_1504)
| ~ relation(U_1504) )
| ~ function(U_1505)
| ~ relation(U_1505) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
cnf(f_361_3,plain,
( apply(relation_composition(U_1505,U_1504),U_1506) = apply(U_1504,apply(U_1505,U_1506))
| ~ in(U_1506,relation_dom(U_1505))
| ~ function(U_1504)
| ~ relation(U_1504)
| ~ function(U_1505)
| ~ relation(U_1505) ),
inference(clausify,[status(thm)],[f_361_2]) ).
fof(f_362_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_362_2,plain,
! [U_1509] :
( ! [U_1508] :
( ! [U_1507] :
( below(U_1509,meet_commut(U_1509,U_1508,U_1507),U_1508)
| ~ element(U_1507,the_carrier(U_1509)) )
| ~ element(U_1508,the_carrier(U_1509)) )
| ~ latt_str(U_1509)
| ~ meet_absorbing(U_1509)
| ~ meet_commutative(U_1509)
| empty_carrier(U_1509) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
( below(U_1509,meet_commut(U_1509,U_1508,U_1507),U_1508)
| ~ element(U_1507,the_carrier(U_1509))
| ~ element(U_1508,the_carrier(U_1509))
| ~ latt_str(U_1509)
| ~ meet_absorbing(U_1509)
| ~ meet_commutative(U_1509)
| empty_carrier(U_1509) ),
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_363_2,plain,
! [U_1511,U_1510] :
( ordinal(U_1511)
| ~ in(U_1511,U_1510)
| ~ ordinal(U_1510) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( ordinal(U_1511)
| ~ in(U_1511,U_1510)
| ~ ordinal(U_1510) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_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_364_2,plain,
! [U_1518,U_1517,U_1516] :
( ( ( ! [U_1515] :
( ? [U_1514] : in(ordered_pair(U_1514,U_1515),U_1516)
| ~ in(U_1515,U_1517) )
| relation_rng_as_subset(U_1518,U_1517,U_1516) != U_1517 )
& ( relation_rng_as_subset(U_1518,U_1517,U_1516) = U_1517
| ? [U_1513] :
( ! [U_1512] : ~ in(ordered_pair(U_1512,U_1513),U_1516)
& in(U_1513,U_1517) ) ) )
| ~ relation_of2_as_subset(U_1516,U_1518,U_1517) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_1518,U_1517,U_1516] :
( ( ( ! [U_1515] :
( ? [U_1514] : in(ordered_pair(U_1514,U_1515),U_1516)
| ~ in(U_1515,U_1517) )
| relation_rng_as_subset(U_1518,U_1517,U_1516) != U_1517 )
& ( relation_rng_as_subset(U_1518,U_1517,U_1516) = U_1517
| ( ! [U_1512] : ~ in(ordered_pair(U_1512,sK332(U_1518,U_1517,U_1516)),U_1516)
& in(sK332(U_1518,U_1517,U_1516),U_1517) ) ) )
| ~ relation_of2_as_subset(U_1516,U_1518,U_1517) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_1513,sK332(U_1518,U_1517,U_1516))],[f_364_2]) ).
fof(f_364_4,plain,
! [U_1518,U_1517,U_1516] :
( ( ( ! [U_1515] :
( in(ordered_pair(sK333(U_1518,U_1517,U_1516,U_1515),U_1515),U_1516)
| ~ in(U_1515,U_1517) )
| relation_rng_as_subset(U_1518,U_1517,U_1516) != U_1517 )
& ( relation_rng_as_subset(U_1518,U_1517,U_1516) = U_1517
| ( ! [U_1512] : ~ in(ordered_pair(U_1512,sK332(U_1518,U_1517,U_1516)),U_1516)
& in(sK332(U_1518,U_1517,U_1516),U_1517) ) ) )
| ~ relation_of2_as_subset(U_1516,U_1518,U_1517) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_1514,sK333(U_1518,U_1517,U_1516,U_1515))],[f_364_3]) ).
cnf(f_364_5,plain,
( in(sK332(U_1518,U_1517,U_1516),U_1517)
| relation_rng_as_subset(U_1518,U_1517,U_1516) = U_1517
| ~ relation_of2_as_subset(U_1516,U_1518,U_1517) ),
inference(clausify,[status(thm)],[f_364_4]) ).
cnf(f_364_6,plain,
( ~ in(ordered_pair(U_1512,sK332(U_1518,U_1517,U_1516)),U_1516)
| relation_rng_as_subset(U_1518,U_1517,U_1516) = U_1517
| ~ relation_of2_as_subset(U_1516,U_1518,U_1517) ),
inference(clausify,[status(thm)],[f_364_4]) ).
cnf(f_364_7,plain,
( in(ordered_pair(sK333(U_1518,U_1517,U_1516,U_1515),U_1515),U_1516)
| ~ in(U_1515,U_1517)
| relation_rng_as_subset(U_1518,U_1517,U_1516) != U_1517
| ~ relation_of2_as_subset(U_1516,U_1518,U_1517) ),
inference(clausify,[status(thm)],[f_364_4]) ).
fof(f_365_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_365_2,plain,
! [U_1520,U_1519] :
( connected(relation_restriction(U_1519,U_1520))
| ~ connected(U_1519)
| ~ relation(U_1519) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
( connected(relation_restriction(U_1519,U_1520))
| ~ connected(U_1519)
| ~ relation(U_1519) ),
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_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_366_2,plain,
! [U_1522] :
( ! [U_1521] :
( in(U_1521,U_1522)
| U_1522 = U_1521
| in(U_1522,U_1521)
| ~ ordinal(U_1521) )
| ~ ordinal(U_1522) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
( in(U_1521,U_1522)
| U_1522 = U_1521
| in(U_1522,U_1521)
| ~ ordinal(U_1521)
| ~ ordinal(U_1522) ),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_367_2,plain,
! [U_1524,U_1523] :
( transitive(relation_restriction(U_1523,U_1524))
| ~ transitive(U_1523)
| ~ relation(U_1523) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
( transitive(relation_restriction(U_1523,U_1524))
| ~ transitive(U_1523)
| ~ relation(U_1523) ),
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_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_368_2,plain,
! [U_1526] :
( ! [U_1525] :
( ( subset(relation_rng(U_1526),relation_rng(U_1525))
& subset(relation_dom(U_1526),relation_dom(U_1525)) )
| ~ subset(U_1526,U_1525)
| ~ relation(U_1525) )
| ~ relation(U_1526) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
cnf(f_368_3,plain,
( subset(relation_dom(U_1526),relation_dom(U_1525))
| ~ subset(U_1526,U_1525)
| ~ relation(U_1525)
| ~ relation(U_1526) ),
inference(clausify,[status(thm)],[f_368_2]) ).
cnf(f_368_4,plain,
( subset(relation_rng(U_1526),relation_rng(U_1525))
| ~ subset(U_1526,U_1525)
| ~ relation(U_1525)
| ~ relation(U_1526) ),
inference(clausify,[status(thm)],[f_368_2]) ).
fof(f_369_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_369_2,plain,
! [U_1528,U_1527] :
( antisymmetric(relation_restriction(U_1527,U_1528))
| ~ antisymmetric(U_1527)
| ~ relation(U_1527) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( antisymmetric(relation_restriction(U_1527,U_1528))
| ~ antisymmetric(U_1527)
| ~ relation(U_1527) ),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_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_370_2,plain,
! [U_1530,U_1529] :
( ( well_ordering(relation_restriction(U_1529,U_1530))
& relation_field(relation_restriction(U_1529,U_1530)) = U_1530 )
| ~ well_orders(U_1529,U_1530)
| ~ relation(U_1529) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
( relation_field(relation_restriction(U_1529,U_1530)) = U_1530
| ~ well_orders(U_1529,U_1530)
| ~ relation(U_1529) ),
inference(clausify,[status(thm)],[f_370_2]) ).
cnf(f_370_4,plain,
( well_ordering(relation_restriction(U_1529,U_1530))
| ~ well_orders(U_1529,U_1530)
| ~ relation(U_1529) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_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_371_2,plain,
! [U_1531] :
( finite(relation_rng(U_1531))
| ~ finite(relation_dom(U_1531))
| ~ function(U_1531)
| ~ relation(U_1531) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( finite(relation_rng(U_1531))
| ~ finite(relation_dom(U_1531))
| ~ function(U_1531)
| ~ relation(U_1531) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_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_372_2,plain,
! [U_1534] :
( ! [U_1533] :
( ! [U_1532] :
( U_1533 = U_1532
| ~ below(U_1534,U_1532,U_1533)
| ~ below(U_1534,U_1533,U_1532)
| ~ element(U_1532,the_carrier(U_1534)) )
| ~ element(U_1533,the_carrier(U_1534)) )
| ~ join_semilatt_str(U_1534)
| ~ join_commutative(U_1534)
| empty_carrier(U_1534) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( U_1533 = U_1532
| ~ below(U_1534,U_1532,U_1533)
| ~ below(U_1534,U_1533,U_1532)
| ~ element(U_1532,the_carrier(U_1534))
| ~ element(U_1533,the_carrier(U_1534))
| ~ join_semilatt_str(U_1534)
| ~ join_commutative(U_1534)
| empty_carrier(U_1534) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
! [A] :
? [B] :
( well_orders(B,A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t26_wellord2]) ).
fof(f_373_2,plain,
! [U_1536] :
? [U_1535] :
( well_orders(U_1535,U_1536)
& relation(U_1535) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_1536] :
( well_orders(sK334(U_1536),U_1536)
& relation(sK334(U_1536)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_1535,sK334(U_1536))],[f_373_2]) ).
cnf(f_373_4,plain,
relation(sK334(U_1536)),
inference(clausify,[status(thm)],[f_373_3]) ).
cnf(f_373_5,plain,
well_orders(sK334(U_1536),U_1536),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_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_374_2,plain,
! [U_1539,U_1538,U_1537] :
( subset(set_intersection2(U_1539,U_1537),set_intersection2(U_1538,U_1537))
| ~ subset(U_1539,U_1538) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
! [U_1539,U_1538] :
( ! [U_1537] : subset(set_intersection2(U_1539,U_1537),set_intersection2(U_1538,U_1537))
| ~ subset(U_1539,U_1538) ),
inference(miniscope,[status(thm)],[f_374_2]) ).
cnf(f_374_4,plain,
( subset(set_intersection2(U_1539,U_1537),set_intersection2(U_1538,U_1537))
| ~ subset(U_1539,U_1538) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_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_375_2,plain,
! [U_1543] :
( ? [U_1542] :
( ! [U_1541] :
( in(apply(U_1542,U_1541),U_1541)
| ~ in(U_1541,U_1543) )
& relation_dom(U_1542) = U_1543
& function(U_1542)
& relation(U_1542) )
| ? [U_1540] :
( U_1540 = empty_set
& in(U_1540,U_1543) )
| empty(U_1543) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
! [U_1543] :
( ? [U_1542] :
( ! [U_1541] :
( in(apply(U_1542,U_1541),U_1541)
| ~ in(U_1541,U_1543) )
& relation_dom(U_1542) = U_1543
& function(U_1542)
& relation(U_1542) )
| ( sK335(U_1543) = empty_set
& in(sK335(U_1543),U_1543) )
| empty(U_1543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_1540,sK335(U_1543))],[f_375_2]) ).
fof(f_375_4,plain,
! [U_1543] :
( ( ! [U_1541] :
( in(apply(sK336(U_1543),U_1541),U_1541)
| ~ in(U_1541,U_1543) )
& relation_dom(sK336(U_1543)) = U_1543
& function(sK336(U_1543))
& relation(sK336(U_1543)) )
| ( sK335(U_1543) = empty_set
& in(sK335(U_1543),U_1543) )
| empty(U_1543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_1542,sK336(U_1543))],[f_375_3]) ).
cnf(f_375_5,plain,
( relation(sK336(U_1543))
| in(sK335(U_1543),U_1543)
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_6,plain,
( function(sK336(U_1543))
| in(sK335(U_1543),U_1543)
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_7,plain,
( relation_dom(sK336(U_1543)) = U_1543
| in(sK335(U_1543),U_1543)
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_8,plain,
( in(apply(sK336(U_1543),U_1541),U_1541)
| ~ in(U_1541,U_1543)
| in(sK335(U_1543),U_1543)
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_9,plain,
( relation(sK336(U_1543))
| sK335(U_1543) = empty_set
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_10,plain,
( function(sK336(U_1543))
| sK335(U_1543) = empty_set
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_11,plain,
( relation_dom(sK336(U_1543)) = U_1543
| sK335(U_1543) = empty_set
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_12,plain,
( in(apply(sK336(U_1543),U_1541),U_1541)
| ~ in(U_1541,U_1543)
| sK335(U_1543) = empty_set
| empty(U_1543) ),
inference(clausify,[status(thm)],[f_375_4]) ).
fof(f_376_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_376_2,plain,
! [U_1545,U_1544] :
( set_intersection2(U_1545,U_1544) = U_1545
| ~ subset(U_1545,U_1544) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( set_intersection2(U_1545,U_1544) = U_1545
| ~ subset(U_1545,U_1544) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_377_2,plain,
! [U_1546] : set_intersection2(U_1546,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
set_intersection2(U_1546,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_378_2,plain,
! [U_1548,U_1547] :
( in(U_1548,U_1547)
| empty(U_1547)
| ~ element(U_1548,U_1547) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
( in(U_1548,U_1547)
| empty(U_1547)
| ~ element(U_1548,U_1547) ),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_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_379_2,plain,
! [U_1551,U_1550] :
( U_1551 = U_1550
| ? [U_1549] :
( ( ~ in(U_1549,U_1551)
& in(U_1549,U_1550) )
| ( ~ in(U_1549,U_1550)
& in(U_1549,U_1551) ) ) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1551,U_1550] :
( U_1551 = U_1550
| ? [U_1553] :
( ~ in(U_1553,U_1551)
& in(U_1553,U_1550) )
| ? [U_1552] :
( ~ in(U_1552,U_1550)
& in(U_1552,U_1551) ) ),
inference(miniscope,[status(thm)],[f_379_2]) ).
fof(f_379_4,plain,
! [U_1551,U_1550] :
( U_1551 = U_1550
| ? [U_1553] :
( ~ in(U_1553,U_1551)
& in(U_1553,U_1550) )
| ( ~ in(sK337(U_1551,U_1550),U_1550)
& in(sK337(U_1551,U_1550),U_1551) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_1552,sK337(U_1551,U_1550))],[f_379_3]) ).
fof(f_379_5,plain,
! [U_1551,U_1550] :
( U_1551 = U_1550
| ( ~ in(sK338(U_1551,U_1550),U_1551)
& in(sK338(U_1551,U_1550),U_1550) )
| ( ~ in(sK337(U_1551,U_1550),U_1550)
& in(sK337(U_1551,U_1550),U_1551) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_1553,sK338(U_1551,U_1550))],[f_379_4]) ).
cnf(f_379_6,plain,
( in(sK338(U_1551,U_1550),U_1550)
| in(sK337(U_1551,U_1550),U_1551)
| U_1551 = U_1550 ),
inference(clausify,[status(thm)],[f_379_5]) ).
cnf(f_379_7,plain,
( ~ in(sK338(U_1551,U_1550),U_1551)
| in(sK337(U_1551,U_1550),U_1551)
| U_1551 = U_1550 ),
inference(clausify,[status(thm)],[f_379_5]) ).
cnf(f_379_8,plain,
( in(sK338(U_1551,U_1550),U_1550)
| ~ in(sK337(U_1551,U_1550),U_1550)
| U_1551 = U_1550 ),
inference(clausify,[status(thm)],[f_379_5]) ).
cnf(f_379_9,plain,
( ~ in(sK338(U_1551,U_1550),U_1551)
| ~ in(sK337(U_1551,U_1550),U_1550)
| U_1551 = U_1550 ),
inference(clausify,[status(thm)],[f_379_5]) ).
fof(f_380_1,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t2_wellord2]) ).
fof(f_380_2,plain,
! [U_1554] : reflexive(inclusion_relation(U_1554)),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
reflexive(inclusion_relation(U_1554)),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_381_2,plain,
! [U_1555] : subset(empty_set,U_1555),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
subset(empty_set,U_1555),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_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_382_2,plain,
! [U_1558,U_1557,U_1556] :
( ( in(U_1557,relation_field(U_1556))
& in(U_1558,relation_field(U_1556)) )
| ~ in(ordered_pair(U_1558,U_1557),U_1556)
| ~ relation(U_1556) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
( in(U_1558,relation_field(U_1556))
| ~ in(ordered_pair(U_1558,U_1557),U_1556)
| ~ relation(U_1556) ),
inference(clausify,[status(thm)],[f_382_2]) ).
cnf(f_382_4,plain,
( in(U_1557,relation_field(U_1556))
| ~ in(ordered_pair(U_1558,U_1557),U_1556)
| ~ relation(U_1556) ),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_383_2,plain,
! [U_1560] :
( ordinal(U_1560)
| ? [U_1559] :
( ( ~ subset(U_1559,U_1560)
| ~ ordinal(U_1559) )
& in(U_1559,U_1560) ) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_1560] :
( ordinal(U_1560)
| ( ( ~ subset(sK339(U_1560),U_1560)
| ~ ordinal(sK339(U_1560)) )
& in(sK339(U_1560),U_1560) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_1559,sK339(U_1560))],[f_383_2]) ).
cnf(f_383_4,plain,
( in(sK339(U_1560),U_1560)
| ordinal(U_1560) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_5,plain,
( ~ subset(sK339(U_1560),U_1560)
| ~ ordinal(sK339(U_1560))
| ordinal(U_1560) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_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_384_2,plain,
! [U_1562,U_1561] :
( well_founded_relation(relation_restriction(U_1561,U_1562))
| ~ well_founded_relation(U_1561)
| ~ relation(U_1561) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
( well_founded_relation(relation_restriction(U_1561,U_1562))
| ~ well_founded_relation(U_1561)
| ~ relation(U_1561) ),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_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_385_2,plain,
! [U_1566,U_1565] :
( ? [U_1564] :
( ! [U_1563] :
( ordinal_subset(U_1564,U_1563)
| ~ in(U_1563,U_1566)
| ~ ordinal(U_1563) )
& in(U_1564,U_1566)
& ordinal(U_1564) )
| U_1566 = empty_set
| ~ subset(U_1566,U_1565)
| ~ ordinal(U_1565) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_1566,U_1565] :
( ( ! [U_1563] :
( ordinal_subset(sK340(U_1566,U_1565),U_1563)
| ~ in(U_1563,U_1566)
| ~ ordinal(U_1563) )
& in(sK340(U_1566,U_1565),U_1566)
& ordinal(sK340(U_1566,U_1565)) )
| U_1566 = empty_set
| ~ subset(U_1566,U_1565)
| ~ ordinal(U_1565) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_1564,sK340(U_1566,U_1565))],[f_385_2]) ).
cnf(f_385_4,plain,
( ordinal(sK340(U_1566,U_1565))
| U_1566 = empty_set
| ~ subset(U_1566,U_1565)
| ~ ordinal(U_1565) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_5,plain,
( in(sK340(U_1566,U_1565),U_1566)
| U_1566 = empty_set
| ~ subset(U_1566,U_1565)
| ~ ordinal(U_1565) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_6,plain,
( ordinal_subset(sK340(U_1566,U_1565),U_1563)
| ~ in(U_1563,U_1566)
| ~ ordinal(U_1563)
| U_1566 = empty_set
| ~ subset(U_1566,U_1565)
| ~ ordinal(U_1565) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_1,plain,
! [A,B] :
( well_ordering(relation_restriction(B,A))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1]) ).
fof(f_386_2,plain,
! [U_1568,U_1567] :
( well_ordering(relation_restriction(U_1567,U_1568))
| ~ well_ordering(U_1567)
| ~ relation(U_1567) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
( well_ordering(relation_restriction(U_1567,U_1568))
| ~ well_ordering(U_1567)
| ~ relation(U_1567) ),
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_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_387_2,plain,
! [U_1570] :
( ! [U_1569] :
( ( ( in(U_1570,U_1569)
| ~ ordinal_subset(succ(U_1570),U_1569) )
& ( ordinal_subset(succ(U_1570),U_1569)
| ~ in(U_1570,U_1569) ) )
| ~ ordinal(U_1569) )
| ~ ordinal(U_1570) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
( ordinal_subset(succ(U_1570),U_1569)
| ~ in(U_1570,U_1569)
| ~ ordinal(U_1569)
| ~ ordinal(U_1570) ),
inference(clausify,[status(thm)],[f_387_2]) ).
cnf(f_387_4,plain,
( in(U_1570,U_1569)
| ~ ordinal_subset(succ(U_1570),U_1569)
| ~ ordinal(U_1569)
| ~ ordinal(U_1570) ),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_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_388_2,plain,
! [U_1573,U_1572,U_1571] :
( subset(set_difference(U_1573,U_1571),set_difference(U_1572,U_1571))
| ~ subset(U_1573,U_1572) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_1573,U_1572] :
( ! [U_1571] : subset(set_difference(U_1573,U_1571),set_difference(U_1572,U_1571))
| ~ subset(U_1573,U_1572) ),
inference(miniscope,[status(thm)],[f_388_2]) ).
cnf(f_388_4,plain,
( subset(set_difference(U_1573,U_1571),set_difference(U_1572,U_1571))
| ~ subset(U_1573,U_1572) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_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_389_2,plain,
! [U_1577,U_1576,U_1575,U_1574] :
( ( U_1576 = U_1574
& U_1577 = U_1575 )
| ordered_pair(U_1577,U_1576) != ordered_pair(U_1575,U_1574) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
( U_1577 = U_1575
| ordered_pair(U_1577,U_1576) != ordered_pair(U_1575,U_1574) ),
inference(clausify,[status(thm)],[f_389_2]) ).
cnf(f_389_4,plain,
( U_1576 = U_1574
| ordered_pair(U_1577,U_1576) != ordered_pair(U_1575,U_1574) ),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_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_390_2,plain,
! [U_1581,U_1580] :
( ( ( U_1580 = identity_relation(U_1581)
| ? [U_1579] :
( apply(U_1580,U_1579) != U_1579
& in(U_1579,U_1581) )
| relation_dom(U_1580) != U_1581 )
& ( ( ! [U_1578] :
( apply(U_1580,U_1578) = U_1578
| ~ in(U_1578,U_1581) )
& relation_dom(U_1580) = U_1581 )
| U_1580 != identity_relation(U_1581) ) )
| ~ function(U_1580)
| ~ relation(U_1580) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
! [U_1581,U_1580] :
( ( ( U_1580 = identity_relation(U_1581)
| ( apply(U_1580,sK341(U_1581,U_1580)) != sK341(U_1581,U_1580)
& in(sK341(U_1581,U_1580),U_1581) )
| relation_dom(U_1580) != U_1581 )
& ( ( ! [U_1578] :
( apply(U_1580,U_1578) = U_1578
| ~ in(U_1578,U_1581) )
& relation_dom(U_1580) = U_1581 )
| U_1580 != identity_relation(U_1581) ) )
| ~ function(U_1580)
| ~ relation(U_1580) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_1579,sK341(U_1581,U_1580))],[f_390_2]) ).
cnf(f_390_4,plain,
( relation_dom(U_1580) = U_1581
| U_1580 != identity_relation(U_1581)
| ~ function(U_1580)
| ~ relation(U_1580) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_5,plain,
( apply(U_1580,U_1578) = U_1578
| ~ in(U_1578,U_1581)
| U_1580 != identity_relation(U_1581)
| ~ function(U_1580)
| ~ relation(U_1580) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_6,plain,
( in(sK341(U_1581,U_1580),U_1581)
| relation_dom(U_1580) != U_1581
| U_1580 = identity_relation(U_1581)
| ~ function(U_1580)
| ~ relation(U_1580) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_7,plain,
( apply(U_1580,sK341(U_1581,U_1580)) != sK341(U_1581,U_1580)
| relation_dom(U_1580) != U_1581
| U_1580 = identity_relation(U_1581)
| ~ function(U_1580)
| ~ relation(U_1580) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_391_2,plain,
! [U_1583,U_1582] :
( apply(identity_relation(U_1583),U_1582) = U_1582
| ~ in(U_1582,U_1583) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( apply(identity_relation(U_1583),U_1582) = U_1582
| ~ in(U_1582,U_1583) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_392_2,plain,
! [U_1585,U_1584] : subset(set_difference(U_1585,U_1584),U_1585),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
subset(set_difference(U_1585,U_1584),U_1585),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_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_393_2,plain,
! [U_1586] :
( ( relation_dom(U_1586) = relation_rng(relation_inverse(U_1586))
& relation_rng(U_1586) = relation_dom(relation_inverse(U_1586)) )
| ~ relation(U_1586) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
( relation_rng(U_1586) = relation_dom(relation_inverse(U_1586))
| ~ relation(U_1586) ),
inference(clausify,[status(thm)],[f_393_2]) ).
cnf(f_393_4,plain,
( relation_dom(U_1586) = relation_rng(relation_inverse(U_1586))
| ~ relation(U_1586) ),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_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_394_2,plain,
! [U_1588,U_1587] :
( ( set_difference(U_1588,U_1587) = empty_set
| ~ subset(U_1588,U_1587) )
& ( subset(U_1588,U_1587)
| set_difference(U_1588,U_1587) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
( ! [U_1592,U_1590] :
( set_difference(U_1592,U_1590) = empty_set
| ~ subset(U_1592,U_1590) )
& ! [U_1591,U_1589] :
( subset(U_1591,U_1589)
| set_difference(U_1591,U_1589) != empty_set ) ),
inference(miniscope,[status(thm)],[f_394_2]) ).
cnf(f_394_4,plain,
( subset(U_1591,U_1589)
| set_difference(U_1591,U_1589) != empty_set ),
inference(clausify,[status(thm)],[f_394_3]) ).
cnf(f_394_5,plain,
( set_difference(U_1592,U_1590) = empty_set
| ~ subset(U_1592,U_1590) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_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_395_2,plain,
! [U_1594,U_1593] :
( ( subset(singleton(U_1594),U_1593)
| ~ in(U_1594,U_1593) )
& ( in(U_1594,U_1593)
| ~ subset(singleton(U_1594),U_1593) ) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
( ! [U_1598,U_1596] :
( subset(singleton(U_1598),U_1596)
| ~ in(U_1598,U_1596) )
& ! [U_1597,U_1595] :
( in(U_1597,U_1595)
| ~ subset(singleton(U_1597),U_1595) ) ),
inference(miniscope,[status(thm)],[f_395_2]) ).
cnf(f_395_4,plain,
( in(U_1597,U_1595)
| ~ subset(singleton(U_1597),U_1595) ),
inference(clausify,[status(thm)],[f_395_3]) ).
cnf(f_395_5,plain,
( subset(singleton(U_1598),U_1596)
| ~ in(U_1598,U_1596) ),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_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_396_2,plain,
! [U_1601,U_1600,U_1599] :
( ( subset(unordered_pair(U_1601,U_1600),U_1599)
| ~ in(U_1600,U_1599)
| ~ in(U_1601,U_1599) )
& ( ( in(U_1600,U_1599)
& in(U_1601,U_1599) )
| ~ subset(unordered_pair(U_1601,U_1600),U_1599) ) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
( ! [U_1607,U_1605,U_1603] :
( subset(unordered_pair(U_1607,U_1605),U_1603)
| ~ in(U_1605,U_1603)
| ~ in(U_1607,U_1603) )
& ! [U_1606,U_1604,U_1602] :
( ( in(U_1604,U_1602)
& in(U_1606,U_1602) )
| ~ subset(unordered_pair(U_1606,U_1604),U_1602) ) ),
inference(miniscope,[status(thm)],[f_396_2]) ).
cnf(f_396_4,plain,
( in(U_1606,U_1602)
| ~ subset(unordered_pair(U_1606,U_1604),U_1602) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_5,plain,
( in(U_1604,U_1602)
| ~ subset(unordered_pair(U_1606,U_1604),U_1602) ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_6,plain,
( subset(unordered_pair(U_1607,U_1605),U_1603)
| ~ in(U_1605,U_1603)
| ~ in(U_1607,U_1603) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_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_397_2,plain,
! [U_1609,U_1608] :
( relation_field(relation_restriction(U_1608,U_1609)) = U_1609
| ~ subset(U_1609,relation_field(U_1608))
| ~ well_ordering(U_1608)
| ~ relation(U_1608) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( relation_field(relation_restriction(U_1608,U_1609)) = U_1609
| ~ subset(U_1609,relation_field(U_1608))
| ~ well_ordering(U_1608)
| ~ relation(U_1608) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_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_398_2,plain,
! [U_1611,U_1610] : set_union2(U_1611,set_difference(U_1610,U_1611)) = set_union2(U_1611,U_1610),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
set_union2(U_1611,set_difference(U_1610,U_1611)) = set_union2(U_1611,U_1610),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_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_399_2,plain,
! [U_1613,U_1612] :
( ( subset(U_1613,singleton(U_1612))
| ( U_1613 != singleton(U_1612)
& U_1613 != empty_set ) )
& ( U_1613 = singleton(U_1612)
| U_1613 = empty_set
| ~ subset(U_1613,singleton(U_1612)) ) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
( ! [U_1617,U_1615] :
( subset(U_1617,singleton(U_1615))
| ( U_1617 != singleton(U_1615)
& U_1617 != empty_set ) )
& ! [U_1616,U_1614] :
( U_1616 = singleton(U_1614)
| U_1616 = empty_set
| ~ subset(U_1616,singleton(U_1614)) ) ),
inference(miniscope,[status(thm)],[f_399_2]) ).
cnf(f_399_4,plain,
( U_1616 = singleton(U_1614)
| U_1616 = empty_set
| ~ subset(U_1616,singleton(U_1614)) ),
inference(clausify,[status(thm)],[f_399_3]) ).
cnf(f_399_5,plain,
( U_1617 != empty_set
| subset(U_1617,singleton(U_1615)) ),
inference(clausify,[status(thm)],[f_399_3]) ).
cnf(f_399_6,plain,
( U_1617 != singleton(U_1615)
| subset(U_1617,singleton(U_1615)) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_400_2,plain,
! [U_1618] : set_difference(U_1618,empty_set) = U_1618,
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
set_difference(U_1618,empty_set) = U_1618,
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_401_2,plain,
! [U_1621,U_1620,U_1619] :
( ~ in(U_1619,U_1621)
| ~ in(U_1620,U_1619)
| ~ in(U_1621,U_1620) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_1621,U_1620] :
( ! [U_1619] :
( ~ in(U_1619,U_1621)
| ~ in(U_1620,U_1619) )
| ~ in(U_1621,U_1620) ),
inference(miniscope,[status(thm)],[f_401_2]) ).
cnf(f_401_4,plain,
( ~ in(U_1619,U_1621)
| ~ in(U_1620,U_1619)
| ~ in(U_1621,U_1620) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_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_402_2,plain,
! [U_1623,U_1622] :
( ( element(U_1623,powerset(U_1622))
| ~ subset(U_1623,U_1622) )
& ( subset(U_1623,U_1622)
| ~ element(U_1623,powerset(U_1622)) ) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
( ! [U_1627,U_1625] :
( element(U_1627,powerset(U_1625))
| ~ subset(U_1627,U_1625) )
& ! [U_1626,U_1624] :
( subset(U_1626,U_1624)
| ~ element(U_1626,powerset(U_1624)) ) ),
inference(miniscope,[status(thm)],[f_402_2]) ).
cnf(f_402_4,plain,
( subset(U_1626,U_1624)
| ~ element(U_1626,powerset(U_1624)) ),
inference(clausify,[status(thm)],[f_402_3]) ).
cnf(f_402_5,plain,
( element(U_1627,powerset(U_1625))
| ~ subset(U_1627,U_1625) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_1,plain,
! [A] : transitive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t3_wellord2]) ).
fof(f_403_2,plain,
! [U_1628] : transitive(inclusion_relation(U_1628)),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
transitive(inclusion_relation(U_1628)),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_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_404_2,plain,
! [U_1632,U_1631] :
( ( ~ disjoint(U_1632,U_1631)
| ! [U_1630] :
( ~ in(U_1630,U_1631)
| ~ in(U_1630,U_1632) ) )
& ( ? [U_1629] :
( in(U_1629,U_1631)
& in(U_1629,U_1632) )
| disjoint(U_1632,U_1631) ) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
( ! [U_1636,U_1634] :
( ~ disjoint(U_1636,U_1634)
| ! [U_1630] :
( ~ in(U_1630,U_1634)
| ~ in(U_1630,U_1636) ) )
& ! [U_1635,U_1633] :
( ? [U_1629] :
( in(U_1629,U_1633)
& in(U_1629,U_1635) )
| disjoint(U_1635,U_1633) ) ),
inference(miniscope,[status(thm)],[f_404_2]) ).
fof(f_404_4,plain,
( ! [U_1636,U_1634] :
( ~ disjoint(U_1636,U_1634)
| ! [U_1630] :
( ~ in(U_1630,U_1634)
| ~ in(U_1630,U_1636) ) )
& ! [U_1635,U_1633] :
( ( in(sK342(U_1635,U_1633),U_1633)
& in(sK342(U_1635,U_1633),U_1635) )
| disjoint(U_1635,U_1633) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_1629,sK342(U_1635,U_1633))],[f_404_3]) ).
cnf(f_404_5,plain,
( in(sK342(U_1635,U_1633),U_1635)
| disjoint(U_1635,U_1633) ),
inference(clausify,[status(thm)],[f_404_4]) ).
cnf(f_404_6,plain,
( in(sK342(U_1635,U_1633),U_1633)
| disjoint(U_1635,U_1633) ),
inference(clausify,[status(thm)],[f_404_4]) ).
cnf(f_404_7,plain,
( ~ disjoint(U_1636,U_1634)
| ~ in(U_1630,U_1634)
| ~ in(U_1630,U_1636) ),
inference(clausify,[status(thm)],[f_404_4]) ).
fof(f_405_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_405_2,plain,
! [U_1637] :
( U_1637 = empty_set
| ~ subset(U_1637,empty_set) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( U_1637 = empty_set
| ~ subset(U_1637,empty_set) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_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_406_2,plain,
! [U_1639,U_1638] : set_difference(set_union2(U_1639,U_1638),U_1638) = set_difference(U_1639,U_1638),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
set_difference(set_union2(U_1639,U_1638),U_1638) = set_difference(U_1639,U_1638),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_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_407_2,plain,
! [U_1642] :
( ( ( being_limit_ordinal(U_1642)
| ? [U_1641] :
( ~ in(succ(U_1641),U_1642)
& in(U_1641,U_1642)
& ordinal(U_1641) ) )
& ( ! [U_1640] :
( in(succ(U_1640),U_1642)
| ~ in(U_1640,U_1642)
| ~ ordinal(U_1640) )
| ~ being_limit_ordinal(U_1642) ) )
| ~ ordinal(U_1642) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_1642] :
( ( ( being_limit_ordinal(U_1642)
| ( ~ in(succ(sK343(U_1642)),U_1642)
& in(sK343(U_1642),U_1642)
& ordinal(sK343(U_1642)) ) )
& ( ! [U_1640] :
( in(succ(U_1640),U_1642)
| ~ in(U_1640,U_1642)
| ~ ordinal(U_1640) )
| ~ being_limit_ordinal(U_1642) ) )
| ~ ordinal(U_1642) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_1641,sK343(U_1642))],[f_407_2]) ).
cnf(f_407_4,plain,
( in(succ(U_1640),U_1642)
| ~ in(U_1640,U_1642)
| ~ ordinal(U_1640)
| ~ being_limit_ordinal(U_1642)
| ~ ordinal(U_1642) ),
inference(clausify,[status(thm)],[f_407_3]) ).
cnf(f_407_5,plain,
( ordinal(sK343(U_1642))
| being_limit_ordinal(U_1642)
| ~ ordinal(U_1642) ),
inference(clausify,[status(thm)],[f_407_3]) ).
cnf(f_407_6,plain,
( in(sK343(U_1642),U_1642)
| being_limit_ordinal(U_1642)
| ~ ordinal(U_1642) ),
inference(clausify,[status(thm)],[f_407_3]) ).
cnf(f_407_7,plain,
( ~ in(succ(sK343(U_1642)),U_1642)
| being_limit_ordinal(U_1642)
| ~ ordinal(U_1642) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_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_408_2,plain,
! [U_1645] :
( ( ( ~ being_limit_ordinal(U_1645)
| ! [U_1644] :
( U_1645 != succ(U_1644)
| ~ ordinal(U_1644) ) )
& ( ? [U_1643] :
( U_1645 = succ(U_1643)
& ordinal(U_1643) )
| being_limit_ordinal(U_1645) ) )
| ~ ordinal(U_1645) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
! [U_1645] :
( ( ( ~ being_limit_ordinal(U_1645)
| ! [U_1644] :
( U_1645 != succ(U_1644)
| ~ ordinal(U_1644) ) )
& ( ( U_1645 = succ(sK344(U_1645))
& ordinal(sK344(U_1645)) )
| being_limit_ordinal(U_1645) ) )
| ~ ordinal(U_1645) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_1643,sK344(U_1645))],[f_408_2]) ).
cnf(f_408_4,plain,
( ordinal(sK344(U_1645))
| being_limit_ordinal(U_1645)
| ~ ordinal(U_1645) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_5,plain,
( U_1645 = succ(sK344(U_1645))
| being_limit_ordinal(U_1645)
| ~ ordinal(U_1645) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_6,plain,
( ~ being_limit_ordinal(U_1645)
| U_1645 != succ(U_1644)
| ~ ordinal(U_1644)
| ~ ordinal(U_1645) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_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_409_2,plain,
! [U_1648,U_1647] :
( ! [U_1646] :
( ( ( disjoint(U_1647,U_1646)
| ~ subset(U_1647,subset_complement(U_1648,U_1646)) )
& ( subset(U_1647,subset_complement(U_1648,U_1646))
| ~ disjoint(U_1647,U_1646) ) )
| ~ element(U_1646,powerset(U_1648)) )
| ~ element(U_1647,powerset(U_1648)) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( subset(U_1647,subset_complement(U_1648,U_1646))
| ~ disjoint(U_1647,U_1646)
| ~ element(U_1646,powerset(U_1648))
| ~ element(U_1647,powerset(U_1648)) ),
inference(clausify,[status(thm)],[f_409_2]) ).
cnf(f_409_4,plain,
( disjoint(U_1647,U_1646)
| ~ subset(U_1647,subset_complement(U_1648,U_1646))
| ~ element(U_1646,powerset(U_1648))
| ~ element(U_1647,powerset(U_1648)) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_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_410_2,plain,
! [U_1650] :
( ! [U_1649] :
( subset(relation_dom(relation_composition(U_1650,U_1649)),relation_dom(U_1650))
| ~ relation(U_1649) )
| ~ relation(U_1650) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
cnf(f_410_3,plain,
( subset(relation_dom(relation_composition(U_1650,U_1649)),relation_dom(U_1650))
| ~ relation(U_1649)
| ~ relation(U_1650) ),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_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_411_2,plain,
! [U_1652] :
( ! [U_1651] :
( subset(relation_rng(relation_composition(U_1652,U_1651)),relation_rng(U_1651))
| ~ relation(U_1651) )
| ~ relation(U_1652) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( subset(relation_rng(relation_composition(U_1652,U_1651)),relation_rng(U_1651))
| ~ relation(U_1651)
| ~ relation(U_1652) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_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_412_2,plain,
! [U_1654,U_1653] :
( U_1653 = set_union2(U_1654,set_difference(U_1653,U_1654))
| ~ subset(U_1654,U_1653) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( U_1653 = set_union2(U_1654,set_difference(U_1653,U_1654))
| ~ subset(U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_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_413_2,plain,
! [U_1659,U_1658,U_1657,U_1656] :
( ! [U_1655] :
( ( in(U_1655,relation_inverse_image(U_1656,U_1657))
| ~ in(apply(U_1656,U_1655),U_1657)
| ~ in(U_1655,U_1659) )
& ( ( in(apply(U_1656,U_1655),U_1657)
& in(U_1655,U_1659) )
| ~ in(U_1655,relation_inverse_image(U_1656,U_1657)) ) )
| U_1658 = empty_set
| ~ relation_of2_as_subset(U_1656,U_1659,U_1658)
| ~ quasi_total(U_1656,U_1659,U_1658)
| ~ function(U_1656) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
! [U_1659,U_1658,U_1657,U_1656] :
( ( ! [U_1661] :
( in(U_1661,relation_inverse_image(U_1656,U_1657))
| ~ in(apply(U_1656,U_1661),U_1657)
| ~ in(U_1661,U_1659) )
& ! [U_1660] :
( ( in(apply(U_1656,U_1660),U_1657)
& in(U_1660,U_1659) )
| ~ in(U_1660,relation_inverse_image(U_1656,U_1657)) ) )
| U_1658 = empty_set
| ~ relation_of2_as_subset(U_1656,U_1659,U_1658)
| ~ quasi_total(U_1656,U_1659,U_1658)
| ~ function(U_1656) ),
inference(miniscope,[status(thm)],[f_413_2]) ).
cnf(f_413_4,plain,
( in(U_1660,U_1659)
| ~ in(U_1660,relation_inverse_image(U_1656,U_1657))
| U_1658 = empty_set
| ~ relation_of2_as_subset(U_1656,U_1659,U_1658)
| ~ quasi_total(U_1656,U_1659,U_1658)
| ~ function(U_1656) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_5,plain,
( in(apply(U_1656,U_1660),U_1657)
| ~ in(U_1660,relation_inverse_image(U_1656,U_1657))
| U_1658 = empty_set
| ~ relation_of2_as_subset(U_1656,U_1659,U_1658)
| ~ quasi_total(U_1656,U_1659,U_1658)
| ~ function(U_1656) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_6,plain,
( in(U_1661,relation_inverse_image(U_1656,U_1657))
| ~ in(apply(U_1656,U_1661),U_1657)
| ~ in(U_1661,U_1659)
| U_1658 = empty_set
| ~ relation_of2_as_subset(U_1656,U_1659,U_1658)
| ~ quasi_total(U_1656,U_1659,U_1658)
| ~ function(U_1656) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_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_414_2,plain,
! [U_1663] :
( ! [U_1662] :
( relation_dom(relation_composition(U_1663,U_1662)) = relation_dom(U_1663)
| ~ subset(relation_rng(U_1663),relation_dom(U_1662))
| ~ relation(U_1662) )
| ~ relation(U_1663) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( relation_dom(relation_composition(U_1663,U_1662)) = relation_dom(U_1663)
| ~ subset(relation_rng(U_1663),relation_dom(U_1662))
| ~ relation(U_1662)
| ~ relation(U_1663) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_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_415_2,plain,
! [U_1665,U_1664] :
( complements_of_subsets(U_1665,U_1664) != empty_set
| U_1664 = empty_set
| ~ element(U_1664,powerset(powerset(U_1665))) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( complements_of_subsets(U_1665,U_1664) != empty_set
| U_1664 = empty_set
| ~ element(U_1664,powerset(powerset(U_1665))) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_416_2,plain,
! [U_1667,U_1666] :
( set_union2(singleton(U_1667),U_1666) = U_1666
| ~ in(U_1667,U_1666) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( set_union2(singleton(U_1667),U_1666) = U_1666
| ~ in(U_1667,U_1666) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_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_417_2,plain,
! [U_1669] :
( ! [U_1668] :
( relation_rng(relation_composition(U_1668,U_1669)) = relation_rng(U_1669)
| ~ subset(relation_dom(U_1669),relation_rng(U_1668))
| ~ relation(U_1668) )
| ~ relation(U_1669) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( relation_rng(relation_composition(U_1668,U_1669)) = relation_rng(U_1669)
| ~ subset(relation_dom(U_1669),relation_rng(U_1668))
| ~ relation(U_1668)
| ~ relation(U_1669) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_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_418_2,plain,
! [U_1671,U_1670] :
( subset_difference(U_1671,cast_to_subset(U_1671),union_of_subsets(U_1671,U_1670)) = meet_of_subsets(U_1671,complements_of_subsets(U_1671,U_1670))
| U_1670 = empty_set
| ~ element(U_1670,powerset(powerset(U_1671))) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( subset_difference(U_1671,cast_to_subset(U_1671),union_of_subsets(U_1671,U_1670)) = meet_of_subsets(U_1671,complements_of_subsets(U_1671,U_1670))
| U_1670 = empty_set
| ~ element(U_1670,powerset(powerset(U_1671))) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_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_419_2,plain,
! [U_1673,U_1672] :
( union_of_subsets(U_1673,complements_of_subsets(U_1673,U_1672)) = subset_difference(U_1673,cast_to_subset(U_1673),meet_of_subsets(U_1673,U_1672))
| U_1672 = empty_set
| ~ element(U_1672,powerset(powerset(U_1673))) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( union_of_subsets(U_1673,complements_of_subsets(U_1673,U_1672)) = subset_difference(U_1673,cast_to_subset(U_1673),meet_of_subsets(U_1673,U_1672))
| U_1672 = empty_set
| ~ element(U_1672,powerset(powerset(U_1673))) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_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_420_2,plain,
! [U_1675,U_1674] : set_difference(U_1675,set_difference(U_1675,U_1674)) = set_intersection2(U_1675,U_1674),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
set_difference(U_1675,set_difference(U_1675,U_1674)) = set_intersection2(U_1675,U_1674),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_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_421_2,plain,
! [U_1678] :
( ! [U_1677] :
( ! [U_1676] :
( relation_isomorphism(U_1677,U_1678,function_inverse(U_1676))
| ~ relation_isomorphism(U_1678,U_1677,U_1676)
| ~ function(U_1676)
| ~ relation(U_1676) )
| ~ relation(U_1677) )
| ~ relation(U_1678) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( relation_isomorphism(U_1677,U_1678,function_inverse(U_1676))
| ~ relation_isomorphism(U_1678,U_1677,U_1676)
| ~ function(U_1676)
| ~ relation(U_1676)
| ~ relation(U_1677)
| ~ relation(U_1678) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_422_2,plain,
! [U_1679] : set_difference(empty_set,U_1679) = empty_set,
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
set_difference(empty_set,U_1679) = empty_set,
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_423_2,plain,
! [U_1682,U_1681,U_1680] :
( element(U_1682,U_1680)
| ~ element(U_1681,powerset(U_1680))
| ~ in(U_1682,U_1681) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
( element(U_1682,U_1680)
| ~ element(U_1681,powerset(U_1680))
| ~ in(U_1682,U_1681) ),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_1,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t4_wellord2]) ).
fof(f_424_2,plain,
! [U_1683] :
( connected(inclusion_relation(U_1683))
| ~ ordinal(U_1683) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
( connected(inclusion_relation(U_1683))
| ~ ordinal(U_1683) ),
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_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_425_2,plain,
! [U_1687,U_1686] :
( ( ~ disjoint(U_1687,U_1686)
| ! [U_1685] : ~ in(U_1685,set_intersection2(U_1687,U_1686)) )
& ( ? [U_1684] : in(U_1684,set_intersection2(U_1687,U_1686))
| disjoint(U_1687,U_1686) ) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
( ! [U_1691,U_1689] :
( ~ disjoint(U_1691,U_1689)
| ! [U_1685] : ~ in(U_1685,set_intersection2(U_1691,U_1689)) )
& ! [U_1690,U_1688] :
( ? [U_1684] : in(U_1684,set_intersection2(U_1690,U_1688))
| disjoint(U_1690,U_1688) ) ),
inference(miniscope,[status(thm)],[f_425_2]) ).
fof(f_425_4,plain,
( ! [U_1691,U_1689] :
( ~ disjoint(U_1691,U_1689)
| ! [U_1685] : ~ in(U_1685,set_intersection2(U_1691,U_1689)) )
& ! [U_1690,U_1688] :
( in(sK345(U_1690,U_1688),set_intersection2(U_1690,U_1688))
| disjoint(U_1690,U_1688) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_1684,sK345(U_1690,U_1688))],[f_425_3]) ).
cnf(f_425_5,plain,
( in(sK345(U_1690,U_1688),set_intersection2(U_1690,U_1688))
| disjoint(U_1690,U_1688) ),
inference(clausify,[status(thm)],[f_425_4]) ).
cnf(f_425_6,plain,
( ~ disjoint(U_1691,U_1689)
| ~ in(U_1685,set_intersection2(U_1691,U_1689)) ),
inference(clausify,[status(thm)],[f_425_4]) ).
fof(f_426_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_426_2,plain,
! [U_1694] :
( ! [U_1693] :
( ! [U_1692] :
( in(U_1692,subset_complement(U_1694,U_1693))
| in(U_1692,U_1693)
| ~ element(U_1692,U_1694) )
| ~ element(U_1693,powerset(U_1694)) )
| U_1694 = empty_set ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
( in(U_1692,subset_complement(U_1694,U_1693))
| in(U_1692,U_1693)
| ~ element(U_1692,U_1694)
| ~ element(U_1693,powerset(U_1694))
| U_1694 = empty_set ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_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_427_2,plain,
! [U_1697] :
( ! [U_1696] :
( ! [U_1695] :
( ( ( well_founded_relation(U_1696)
| ~ well_founded_relation(U_1697) )
& ( antisymmetric(U_1696)
| ~ antisymmetric(U_1697) )
& ( connected(U_1696)
| ~ connected(U_1697) )
& ( transitive(U_1696)
| ~ transitive(U_1697) )
& ( reflexive(U_1696)
| ~ reflexive(U_1697) ) )
| ~ relation_isomorphism(U_1697,U_1696,U_1695)
| ~ function(U_1695)
| ~ relation(U_1695) )
| ~ relation(U_1696) )
| ~ relation(U_1697) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( reflexive(U_1696)
| ~ reflexive(U_1697)
| ~ relation_isomorphism(U_1697,U_1696,U_1695)
| ~ function(U_1695)
| ~ relation(U_1695)
| ~ relation(U_1696)
| ~ relation(U_1697) ),
inference(clausify,[status(thm)],[f_427_2]) ).
cnf(f_427_4,plain,
( transitive(U_1696)
| ~ transitive(U_1697)
| ~ relation_isomorphism(U_1697,U_1696,U_1695)
| ~ function(U_1695)
| ~ relation(U_1695)
| ~ relation(U_1696)
| ~ relation(U_1697) ),
inference(clausify,[status(thm)],[f_427_2]) ).
cnf(f_427_5,plain,
( connected(U_1696)
| ~ connected(U_1697)
| ~ relation_isomorphism(U_1697,U_1696,U_1695)
| ~ function(U_1695)
| ~ relation(U_1695)
| ~ relation(U_1696)
| ~ relation(U_1697) ),
inference(clausify,[status(thm)],[f_427_2]) ).
cnf(f_427_6,plain,
( antisymmetric(U_1696)
| ~ antisymmetric(U_1697)
| ~ relation_isomorphism(U_1697,U_1696,U_1695)
| ~ function(U_1695)
| ~ relation(U_1695)
| ~ relation(U_1696)
| ~ relation(U_1697) ),
inference(clausify,[status(thm)],[f_427_2]) ).
cnf(f_427_7,plain,
( well_founded_relation(U_1696)
| ~ well_founded_relation(U_1697)
| ~ relation_isomorphism(U_1697,U_1696,U_1695)
| ~ function(U_1695)
| ~ relation(U_1695)
| ~ relation(U_1696)
| ~ relation(U_1697) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_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_428_2,plain,
! [U_1703] :
( ! [U_1702] :
( ( ( U_1702 = function_inverse(U_1703)
| ? [U_1701,U_1700] :
( ( ( U_1700 != apply(U_1702,U_1701)
| ~ in(U_1701,relation_rng(U_1703)) )
& U_1701 = apply(U_1703,U_1700)
& in(U_1700,relation_dom(U_1703)) )
| ( ( U_1701 != apply(U_1703,U_1700)
| ~ in(U_1700,relation_dom(U_1703)) )
& U_1700 = apply(U_1702,U_1701)
& in(U_1701,relation_rng(U_1703)) ) )
| relation_dom(U_1702) != relation_rng(U_1703) )
& ( ( ! [U_1699,U_1698] :
( ( ( U_1698 = apply(U_1702,U_1699)
& in(U_1699,relation_rng(U_1703)) )
| U_1699 != apply(U_1703,U_1698)
| ~ in(U_1698,relation_dom(U_1703)) )
& ( ( U_1699 = apply(U_1703,U_1698)
& in(U_1698,relation_dom(U_1703)) )
| U_1698 != apply(U_1702,U_1699)
| ~ in(U_1699,relation_rng(U_1703)) ) )
& relation_dom(U_1702) = relation_rng(U_1703) )
| U_1702 != function_inverse(U_1703) ) )
| ~ function(U_1702)
| ~ relation(U_1702) )
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_1703] :
( ! [U_1702] :
( ( ( U_1702 = function_inverse(U_1703)
| ? [U_1711,U_1709] :
( ( U_1709 != apply(U_1702,U_1711)
| ~ in(U_1711,relation_rng(U_1703)) )
& U_1711 = apply(U_1703,U_1709)
& in(U_1709,relation_dom(U_1703)) )
| ? [U_1710,U_1708] :
( ( U_1710 != apply(U_1703,U_1708)
| ~ in(U_1708,relation_dom(U_1703)) )
& U_1708 = apply(U_1702,U_1710)
& in(U_1710,relation_rng(U_1703)) )
| relation_dom(U_1702) != relation_rng(U_1703) )
& ( ( ! [U_1707,U_1705] :
( ( U_1705 = apply(U_1702,U_1707)
& in(U_1707,relation_rng(U_1703)) )
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703)) )
& ! [U_1706,U_1704] :
( ( U_1706 = apply(U_1703,U_1704)
& in(U_1704,relation_dom(U_1703)) )
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703)) )
& relation_dom(U_1702) = relation_rng(U_1703) )
| U_1702 != function_inverse(U_1703) ) )
| ~ function(U_1702)
| ~ relation(U_1702) )
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(miniscope,[status(thm)],[f_428_2]) ).
fof(f_428_4,plain,
! [U_1703] :
( ! [U_1702] :
( ( ( U_1702 = function_inverse(U_1703)
| ? [U_1711,U_1709] :
( ( U_1709 != apply(U_1702,U_1711)
| ~ in(U_1711,relation_rng(U_1703)) )
& U_1711 = apply(U_1703,U_1709)
& in(U_1709,relation_dom(U_1703)) )
| ? [U_1708] :
( ( sK346(U_1703,U_1702) != apply(U_1703,U_1708)
| ~ in(U_1708,relation_dom(U_1703)) )
& U_1708 = apply(U_1702,sK346(U_1703,U_1702))
& in(sK346(U_1703,U_1702),relation_rng(U_1703)) )
| relation_dom(U_1702) != relation_rng(U_1703) )
& ( ( ! [U_1707,U_1705] :
( ( U_1705 = apply(U_1702,U_1707)
& in(U_1707,relation_rng(U_1703)) )
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703)) )
& ! [U_1706,U_1704] :
( ( U_1706 = apply(U_1703,U_1704)
& in(U_1704,relation_dom(U_1703)) )
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703)) )
& relation_dom(U_1702) = relation_rng(U_1703) )
| U_1702 != function_inverse(U_1703) ) )
| ~ function(U_1702)
| ~ relation(U_1702) )
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_1710,sK346(U_1703,U_1702))],[f_428_3]) ).
fof(f_428_5,plain,
! [U_1703] :
( ! [U_1702] :
( ( ( U_1702 = function_inverse(U_1703)
| ? [U_1711,U_1709] :
( ( U_1709 != apply(U_1702,U_1711)
| ~ in(U_1711,relation_rng(U_1703)) )
& U_1711 = apply(U_1703,U_1709)
& in(U_1709,relation_dom(U_1703)) )
| ( ( sK346(U_1703,U_1702) != apply(U_1703,sK347(U_1703,U_1702))
| ~ in(sK347(U_1703,U_1702),relation_dom(U_1703)) )
& sK347(U_1703,U_1702) = apply(U_1702,sK346(U_1703,U_1702))
& in(sK346(U_1703,U_1702),relation_rng(U_1703)) )
| relation_dom(U_1702) != relation_rng(U_1703) )
& ( ( ! [U_1707,U_1705] :
( ( U_1705 = apply(U_1702,U_1707)
& in(U_1707,relation_rng(U_1703)) )
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703)) )
& ! [U_1706,U_1704] :
( ( U_1706 = apply(U_1703,U_1704)
& in(U_1704,relation_dom(U_1703)) )
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703)) )
& relation_dom(U_1702) = relation_rng(U_1703) )
| U_1702 != function_inverse(U_1703) ) )
| ~ function(U_1702)
| ~ relation(U_1702) )
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_1708,sK347(U_1703,U_1702))],[f_428_4]) ).
fof(f_428_6,plain,
! [U_1703] :
( ! [U_1702] :
( ( ( U_1702 = function_inverse(U_1703)
| ? [U_1709] :
( ( U_1709 != apply(U_1702,sK348(U_1703,U_1702))
| ~ in(sK348(U_1703,U_1702),relation_rng(U_1703)) )
& sK348(U_1703,U_1702) = apply(U_1703,U_1709)
& in(U_1709,relation_dom(U_1703)) )
| ( ( sK346(U_1703,U_1702) != apply(U_1703,sK347(U_1703,U_1702))
| ~ in(sK347(U_1703,U_1702),relation_dom(U_1703)) )
& sK347(U_1703,U_1702) = apply(U_1702,sK346(U_1703,U_1702))
& in(sK346(U_1703,U_1702),relation_rng(U_1703)) )
| relation_dom(U_1702) != relation_rng(U_1703) )
& ( ( ! [U_1707,U_1705] :
( ( U_1705 = apply(U_1702,U_1707)
& in(U_1707,relation_rng(U_1703)) )
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703)) )
& ! [U_1706,U_1704] :
( ( U_1706 = apply(U_1703,U_1704)
& in(U_1704,relation_dom(U_1703)) )
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703)) )
& relation_dom(U_1702) = relation_rng(U_1703) )
| U_1702 != function_inverse(U_1703) ) )
| ~ function(U_1702)
| ~ relation(U_1702) )
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_1711,sK348(U_1703,U_1702))],[f_428_5]) ).
fof(f_428_7,plain,
! [U_1703] :
( ! [U_1702] :
( ( ( U_1702 = function_inverse(U_1703)
| ( ( sK349(U_1703,U_1702) != apply(U_1702,sK348(U_1703,U_1702))
| ~ in(sK348(U_1703,U_1702),relation_rng(U_1703)) )
& sK348(U_1703,U_1702) = apply(U_1703,sK349(U_1703,U_1702))
& in(sK349(U_1703,U_1702),relation_dom(U_1703)) )
| ( ( sK346(U_1703,U_1702) != apply(U_1703,sK347(U_1703,U_1702))
| ~ in(sK347(U_1703,U_1702),relation_dom(U_1703)) )
& sK347(U_1703,U_1702) = apply(U_1702,sK346(U_1703,U_1702))
& in(sK346(U_1703,U_1702),relation_rng(U_1703)) )
| relation_dom(U_1702) != relation_rng(U_1703) )
& ( ( ! [U_1707,U_1705] :
( ( U_1705 = apply(U_1702,U_1707)
& in(U_1707,relation_rng(U_1703)) )
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703)) )
& ! [U_1706,U_1704] :
( ( U_1706 = apply(U_1703,U_1704)
& in(U_1704,relation_dom(U_1703)) )
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703)) )
& relation_dom(U_1702) = relation_rng(U_1703) )
| U_1702 != function_inverse(U_1703) ) )
| ~ function(U_1702)
| ~ relation(U_1702) )
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_1709,sK349(U_1703,U_1702))],[f_428_6]) ).
cnf(f_428_8,plain,
( relation_dom(U_1702) = relation_rng(U_1703)
| U_1702 != function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_9,plain,
( in(U_1704,relation_dom(U_1703))
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703))
| U_1702 != function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_10,plain,
( U_1706 = apply(U_1703,U_1704)
| U_1704 != apply(U_1702,U_1706)
| ~ in(U_1706,relation_rng(U_1703))
| U_1702 != function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_11,plain,
( in(U_1707,relation_rng(U_1703))
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703))
| U_1702 != function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_12,plain,
( U_1705 = apply(U_1702,U_1707)
| U_1707 != apply(U_1703,U_1705)
| ~ in(U_1705,relation_dom(U_1703))
| U_1702 != function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_13,plain,
( in(sK349(U_1703,U_1702),relation_dom(U_1703))
| in(sK346(U_1703,U_1702),relation_rng(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_14,plain,
( sK348(U_1703,U_1702) = apply(U_1703,sK349(U_1703,U_1702))
| in(sK346(U_1703,U_1702),relation_rng(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_15,plain,
( in(sK349(U_1703,U_1702),relation_dom(U_1703))
| sK347(U_1703,U_1702) = apply(U_1702,sK346(U_1703,U_1702))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_16,plain,
( sK348(U_1703,U_1702) = apply(U_1703,sK349(U_1703,U_1702))
| sK347(U_1703,U_1702) = apply(U_1702,sK346(U_1703,U_1702))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_17,plain,
( in(sK346(U_1703,U_1702),relation_rng(U_1703))
| sK349(U_1703,U_1702) != apply(U_1702,sK348(U_1703,U_1702))
| ~ in(sK348(U_1703,U_1702),relation_rng(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_18,plain,
( sK347(U_1703,U_1702) = apply(U_1702,sK346(U_1703,U_1702))
| sK349(U_1703,U_1702) != apply(U_1702,sK348(U_1703,U_1702))
| ~ in(sK348(U_1703,U_1702),relation_rng(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_19,plain,
( in(sK349(U_1703,U_1702),relation_dom(U_1703))
| sK346(U_1703,U_1702) != apply(U_1703,sK347(U_1703,U_1702))
| ~ in(sK347(U_1703,U_1702),relation_dom(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_20,plain,
( sK348(U_1703,U_1702) = apply(U_1703,sK349(U_1703,U_1702))
| sK346(U_1703,U_1702) != apply(U_1703,sK347(U_1703,U_1702))
| ~ in(sK347(U_1703,U_1702),relation_dom(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
cnf(f_428_21,plain,
( sK349(U_1703,U_1702) != apply(U_1702,sK348(U_1703,U_1702))
| ~ in(sK348(U_1703,U_1702),relation_rng(U_1703))
| sK346(U_1703,U_1702) != apply(U_1703,sK347(U_1703,U_1702))
| ~ in(sK347(U_1703,U_1702),relation_dom(U_1703))
| relation_dom(U_1702) != relation_rng(U_1703)
| U_1702 = function_inverse(U_1703)
| ~ function(U_1702)
| ~ relation(U_1702)
| ~ one_to_one(U_1703)
| ~ function(U_1703)
| ~ relation(U_1703) ),
inference(clausify,[status(thm)],[f_428_7]) ).
fof(f_429_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_429_2,plain,
! [U_1714,U_1713,U_1712] :
( ~ in(U_1713,U_1712)
| ~ in(U_1713,subset_complement(U_1714,U_1712))
| ~ element(U_1712,powerset(U_1714)) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( ~ in(U_1713,U_1712)
| ~ in(U_1713,subset_complement(U_1714,U_1712))
| ~ element(U_1712,powerset(U_1714)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_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_430_2,plain,
! [U_1717] :
( ! [U_1716] :
( ! [U_1715] :
( well_ordering(U_1716)
| ~ relation_isomorphism(U_1717,U_1716,U_1715)
| ~ well_ordering(U_1717)
| ~ function(U_1715)
| ~ relation(U_1715) )
| ~ relation(U_1716) )
| ~ relation(U_1717) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( well_ordering(U_1716)
| ~ relation_isomorphism(U_1717,U_1716,U_1715)
| ~ well_ordering(U_1717)
| ~ function(U_1715)
| ~ relation(U_1715)
| ~ relation(U_1716)
| ~ relation(U_1717) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_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_431_2,plain,
! [U_1718] :
( ( relation_dom(U_1718) = relation_rng(function_inverse(U_1718))
& relation_rng(U_1718) = relation_dom(function_inverse(U_1718)) )
| ~ one_to_one(U_1718)
| ~ function(U_1718)
| ~ relation(U_1718) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
( relation_rng(U_1718) = relation_dom(function_inverse(U_1718))
| ~ one_to_one(U_1718)
| ~ function(U_1718)
| ~ relation(U_1718) ),
inference(clausify,[status(thm)],[f_431_2]) ).
cnf(f_431_4,plain,
( relation_dom(U_1718) = relation_rng(function_inverse(U_1718))
| ~ one_to_one(U_1718)
| ~ function(U_1718)
| ~ relation(U_1718) ),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_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_432_2,plain,
! [U_1721] :
( U_1721 = empty_set
| ? [U_1720,U_1719] : in(ordered_pair(U_1720,U_1719),U_1721)
| ~ relation(U_1721) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1721] :
( U_1721 = empty_set
| ? [U_1719] : in(ordered_pair(sK350(U_1721),U_1719),U_1721)
| ~ relation(U_1721) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_1720,sK350(U_1721))],[f_432_2]) ).
fof(f_432_4,plain,
! [U_1721] :
( U_1721 = empty_set
| in(ordered_pair(sK350(U_1721),sK351(U_1721)),U_1721)
| ~ relation(U_1721) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_1719,sK351(U_1721))],[f_432_3]) ).
cnf(f_432_5,plain,
( U_1721 = empty_set
| in(ordered_pair(sK350(U_1721),sK351(U_1721)),U_1721)
| ~ relation(U_1721) ),
inference(clausify,[status(thm)],[f_432_4]) ).
fof(f_433_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_433_2,plain,
! [U_1723,U_1722] :
( ( U_1723 = apply(relation_composition(function_inverse(U_1722),U_1722),U_1723)
& U_1723 = apply(U_1722,apply(function_inverse(U_1722),U_1723)) )
| ~ in(U_1723,relation_rng(U_1722))
| ~ one_to_one(U_1722)
| ~ function(U_1722)
| ~ relation(U_1722) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( U_1723 = apply(U_1722,apply(function_inverse(U_1722),U_1723))
| ~ in(U_1723,relation_rng(U_1722))
| ~ one_to_one(U_1722)
| ~ function(U_1722)
| ~ relation(U_1722) ),
inference(clausify,[status(thm)],[f_433_2]) ).
cnf(f_433_4,plain,
( U_1723 = apply(relation_composition(function_inverse(U_1722),U_1722),U_1723)
| ~ in(U_1723,relation_rng(U_1722))
| ~ one_to_one(U_1722)
| ~ function(U_1722)
| ~ relation(U_1722) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_434_2,plain,
! [U_1726,U_1725,U_1724] :
( ~ empty(U_1724)
| ~ element(U_1725,powerset(U_1724))
| ~ in(U_1726,U_1725) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1726,U_1725] :
( ! [U_1724] :
( ~ empty(U_1724)
| ~ element(U_1725,powerset(U_1724)) )
| ~ in(U_1726,U_1725) ),
inference(miniscope,[status(thm)],[f_434_2]) ).
cnf(f_434_4,plain,
( ~ empty(U_1724)
| ~ element(U_1725,powerset(U_1724))
| ~ in(U_1726,U_1725) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_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_435_2,plain,
! [U_1727] :
( ( ( well_founded_relation(U_1727)
| ~ is_well_founded_in(U_1727,relation_field(U_1727)) )
& ( is_well_founded_in(U_1727,relation_field(U_1727))
| ~ well_founded_relation(U_1727) ) )
| ~ relation(U_1727) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
( is_well_founded_in(U_1727,relation_field(U_1727))
| ~ well_founded_relation(U_1727)
| ~ relation(U_1727) ),
inference(clausify,[status(thm)],[f_435_2]) ).
cnf(f_435_4,plain,
( well_founded_relation(U_1727)
| ~ is_well_founded_in(U_1727,relation_field(U_1727))
| ~ relation(U_1727) ),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_1,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t5_wellord2]) ).
fof(f_436_2,plain,
! [U_1728] : antisymmetric(inclusion_relation(U_1728)),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
antisymmetric(inclusion_relation(U_1728)),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_437_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_437_1]) ).
fof(f_438_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_438_2,plain,
! [U_1730,U_1729] :
( ~ proper_subset(U_1729,U_1730)
| ~ subset(U_1730,U_1729) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( ~ proper_subset(U_1729,U_1730)
| ~ subset(U_1730,U_1729) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_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_439_2,plain,
! [U_1731] :
( one_to_one(function_inverse(U_1731))
| ~ one_to_one(U_1731)
| ~ function(U_1731)
| ~ relation(U_1731) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( one_to_one(function_inverse(U_1731))
| ~ one_to_one(U_1731)
| ~ function(U_1731)
| ~ relation(U_1731) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_440_2,plain,
! [U_1734,U_1733,U_1732] :
( disjoint(U_1734,U_1732)
| ~ disjoint(U_1733,U_1732)
| ~ subset(U_1734,U_1733) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
( disjoint(U_1734,U_1732)
| ~ disjoint(U_1733,U_1732)
| ~ subset(U_1734,U_1733) ),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_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_441_2,plain,
! [U_1735] :
( U_1735 = empty_set
| ( relation_rng(U_1735) != empty_set
& relation_dom(U_1735) != empty_set )
| ~ relation(U_1735) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
( relation_dom(U_1735) != empty_set
| U_1735 = empty_set
| ~ relation(U_1735) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( relation_rng(U_1735) != empty_set
| U_1735 = empty_set
| ~ relation(U_1735) ),
inference(clausify,[status(thm)],[f_441_2]) ).
fof(f_442_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_442_2,plain,
! [U_1736] :
( ( ( relation_dom(U_1736) = empty_set
| relation_rng(U_1736) != empty_set )
& ( relation_rng(U_1736) = empty_set
| relation_dom(U_1736) != empty_set ) )
| ~ relation(U_1736) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
( relation_rng(U_1736) = empty_set
| relation_dom(U_1736) != empty_set
| ~ relation(U_1736) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_4,plain,
( relation_dom(U_1736) = empty_set
| relation_rng(U_1736) != empty_set
| ~ relation(U_1736) ),
inference(clausify,[status(thm)],[f_442_2]) ).
fof(f_443_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_443_2,plain,
! [U_1738,U_1737] :
( ( set_difference(U_1738,singleton(U_1737)) = U_1738
| in(U_1737,U_1738) )
& ( ~ in(U_1737,U_1738)
| set_difference(U_1738,singleton(U_1737)) != U_1738 ) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
( ! [U_1742,U_1740] :
( set_difference(U_1742,singleton(U_1740)) = U_1742
| in(U_1740,U_1742) )
& ! [U_1741,U_1739] :
( ~ in(U_1739,U_1741)
| set_difference(U_1741,singleton(U_1739)) != U_1741 ) ),
inference(miniscope,[status(thm)],[f_443_2]) ).
cnf(f_443_4,plain,
( ~ in(U_1739,U_1741)
| set_difference(U_1741,singleton(U_1739)) != U_1741 ),
inference(clausify,[status(thm)],[f_443_3]) ).
cnf(f_443_5,plain,
( set_difference(U_1742,singleton(U_1740)) = U_1742
| in(U_1740,U_1742) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_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_444_2,plain,
! [U_1747,U_1746] :
( ! [U_1745] :
( ( ( U_1746 = relation_dom_restriction(U_1745,U_1747)
| ? [U_1744] :
( apply(U_1746,U_1744) != apply(U_1745,U_1744)
& in(U_1744,relation_dom(U_1746)) )
| relation_dom(U_1746) != set_intersection2(relation_dom(U_1745),U_1747) )
& ( ( ! [U_1743] :
( apply(U_1746,U_1743) = apply(U_1745,U_1743)
| ~ in(U_1743,relation_dom(U_1746)) )
& relation_dom(U_1746) = set_intersection2(relation_dom(U_1745),U_1747) )
| U_1746 != relation_dom_restriction(U_1745,U_1747) ) )
| ~ function(U_1745)
| ~ relation(U_1745) )
| ~ function(U_1746)
| ~ relation(U_1746) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_1747,U_1746] :
( ! [U_1745] :
( ( ( U_1746 = relation_dom_restriction(U_1745,U_1747)
| ( apply(U_1746,sK352(U_1747,U_1746,U_1745)) != apply(U_1745,sK352(U_1747,U_1746,U_1745))
& in(sK352(U_1747,U_1746,U_1745),relation_dom(U_1746)) )
| relation_dom(U_1746) != set_intersection2(relation_dom(U_1745),U_1747) )
& ( ( ! [U_1743] :
( apply(U_1746,U_1743) = apply(U_1745,U_1743)
| ~ in(U_1743,relation_dom(U_1746)) )
& relation_dom(U_1746) = set_intersection2(relation_dom(U_1745),U_1747) )
| U_1746 != relation_dom_restriction(U_1745,U_1747) ) )
| ~ function(U_1745)
| ~ relation(U_1745) )
| ~ function(U_1746)
| ~ relation(U_1746) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_1744,sK352(U_1747,U_1746,U_1745))],[f_444_2]) ).
cnf(f_444_4,plain,
( relation_dom(U_1746) = set_intersection2(relation_dom(U_1745),U_1747)
| U_1746 != relation_dom_restriction(U_1745,U_1747)
| ~ function(U_1745)
| ~ relation(U_1745)
| ~ function(U_1746)
| ~ relation(U_1746) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_5,plain,
( apply(U_1746,U_1743) = apply(U_1745,U_1743)
| ~ in(U_1743,relation_dom(U_1746))
| U_1746 != relation_dom_restriction(U_1745,U_1747)
| ~ function(U_1745)
| ~ relation(U_1745)
| ~ function(U_1746)
| ~ relation(U_1746) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_6,plain,
( in(sK352(U_1747,U_1746,U_1745),relation_dom(U_1746))
| relation_dom(U_1746) != set_intersection2(relation_dom(U_1745),U_1747)
| U_1746 = relation_dom_restriction(U_1745,U_1747)
| ~ function(U_1745)
| ~ relation(U_1745)
| ~ function(U_1746)
| ~ relation(U_1746) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_7,plain,
( apply(U_1746,sK352(U_1747,U_1746,U_1745)) != apply(U_1745,sK352(U_1747,U_1746,U_1745))
| relation_dom(U_1746) != set_intersection2(relation_dom(U_1745),U_1747)
| U_1746 = relation_dom_restriction(U_1745,U_1747)
| ~ function(U_1745)
| ~ relation(U_1745)
| ~ function(U_1746)
| ~ relation(U_1746) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_445_2,plain,
! [U_1748] : unordered_pair(U_1748,U_1748) = singleton(U_1748),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
unordered_pair(U_1748,U_1748) = singleton(U_1748),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_446_2,plain,
! [U_1749] :
( U_1749 = empty_set
| ~ empty(U_1749) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( U_1749 = empty_set
| ~ empty(U_1749) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_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_447_2,plain,
! [U_1753,U_1752,U_1751,U_1750] :
( in(apply(U_1750,U_1751),relation_rng(U_1750))
| U_1752 = empty_set
| ~ in(U_1751,U_1753)
| ~ relation_of2_as_subset(U_1750,U_1753,U_1752)
| ~ quasi_total(U_1750,U_1753,U_1752)
| ~ function(U_1750) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( in(apply(U_1750,U_1751),relation_rng(U_1750))
| U_1752 = empty_set
| ~ in(U_1751,U_1753)
| ~ relation_of2_as_subset(U_1750,U_1753,U_1752)
| ~ quasi_total(U_1750,U_1753,U_1752)
| ~ function(U_1750) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t6_wellord2]) ).
fof(f_448_2,plain,
! [U_1754] :
( well_founded_relation(inclusion_relation(U_1754))
| ~ ordinal(U_1754) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
( well_founded_relation(inclusion_relation(U_1754))
| ~ ordinal(U_1754) ),
inference(clausify,[status(thm)],[f_448_2]) ).
fof(f_449_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_449_2,plain,
! [U_1756,U_1755] :
( U_1756 = U_1755
| ~ subset(singleton(U_1756),singleton(U_1755)) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
cnf(f_449_3,plain,
( U_1756 = U_1755
| ~ subset(singleton(U_1756),singleton(U_1755)) ),
inference(clausify,[status(thm)],[f_449_2]) ).
fof(f_450_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_450_2,plain,
! [U_1759,U_1758,U_1757] :
( apply(relation_dom_restriction(U_1757,U_1759),U_1758) = apply(U_1757,U_1758)
| ~ in(U_1758,relation_dom(relation_dom_restriction(U_1757,U_1759)))
| ~ function(U_1757)
| ~ relation(U_1757) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
( apply(relation_dom_restriction(U_1757,U_1759),U_1758) = apply(U_1757,U_1758)
| ~ in(U_1758,relation_dom(relation_dom_restriction(U_1757,U_1759)))
| ~ function(U_1757)
| ~ relation(U_1757) ),
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_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_451_2,plain,
! [U_1760] :
( relation_rng(identity_relation(U_1760)) = U_1760
& relation_dom(identity_relation(U_1760)) = U_1760 ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
( ! [U_1762] : relation_rng(identity_relation(U_1762)) = U_1762
& ! [U_1761] : relation_dom(identity_relation(U_1761)) = U_1761 ),
inference(miniscope,[status(thm)],[f_451_2]) ).
cnf(f_451_4,plain,
relation_dom(identity_relation(U_1761)) = U_1761,
inference(clausify,[status(thm)],[f_451_3]) ).
cnf(f_451_5,plain,
relation_rng(identity_relation(U_1762)) = U_1762,
inference(clausify,[status(thm)],[f_451_3]) ).
fof(f_452_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_452_2,plain,
! [U_1765,U_1764,U_1763] :
( apply(relation_dom_restriction(U_1763,U_1765),U_1764) = apply(U_1763,U_1764)
| ~ in(U_1764,U_1765)
| ~ function(U_1763)
| ~ relation(U_1763) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
( apply(relation_dom_restriction(U_1763,U_1765),U_1764) = apply(U_1763,U_1764)
| ~ in(U_1764,U_1765)
| ~ function(U_1763)
| ~ relation(U_1763) ),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_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_453_2,plain,
! [U_1769,U_1768,U_1767,U_1766] :
( ( ( in(ordered_pair(U_1769,U_1768),relation_composition(identity_relation(U_1767),U_1766))
| ~ in(ordered_pair(U_1769,U_1768),U_1766)
| ~ in(U_1769,U_1767) )
& ( ( in(ordered_pair(U_1769,U_1768),U_1766)
& in(U_1769,U_1767) )
| ~ in(ordered_pair(U_1769,U_1768),relation_composition(identity_relation(U_1767),U_1766)) ) )
| ~ relation(U_1766) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
( in(U_1769,U_1767)
| ~ in(ordered_pair(U_1769,U_1768),relation_composition(identity_relation(U_1767),U_1766))
| ~ relation(U_1766) ),
inference(clausify,[status(thm)],[f_453_2]) ).
cnf(f_453_4,plain,
( in(ordered_pair(U_1769,U_1768),U_1766)
| ~ in(ordered_pair(U_1769,U_1768),relation_composition(identity_relation(U_1767),U_1766))
| ~ relation(U_1766) ),
inference(clausify,[status(thm)],[f_453_2]) ).
cnf(f_453_5,plain,
( in(ordered_pair(U_1769,U_1768),relation_composition(identity_relation(U_1767),U_1766))
| ~ in(ordered_pair(U_1769,U_1768),U_1766)
| ~ in(U_1769,U_1767)
| ~ relation(U_1766) ),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_454_2,plain,
! [U_1771,U_1770] :
( ~ empty(U_1770)
| ~ in(U_1771,U_1770) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
( ~ empty(U_1770)
| ~ in(U_1771,U_1770) ),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_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_455_2,plain,
! [U_1773,U_1772] :
( pair_second(ordered_pair(U_1773,U_1772)) = U_1772
& pair_first(ordered_pair(U_1773,U_1772)) = U_1773 ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_1777,U_1775] : pair_second(ordered_pair(U_1777,U_1775)) = U_1775
& ! [U_1776,U_1774] : pair_first(ordered_pair(U_1776,U_1774)) = U_1776 ),
inference(miniscope,[status(thm)],[f_455_2]) ).
cnf(f_455_4,plain,
pair_first(ordered_pair(U_1776,U_1774)) = U_1776,
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_5,plain,
pair_second(ordered_pair(U_1777,U_1775)) = U_1775,
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_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_456_2,plain,
! [U_1781,U_1780] :
( ? [U_1779] :
( ! [U_1778] :
( ~ in(U_1778,U_1779)
| ~ in(U_1778,U_1780) )
& in(U_1779,U_1780) )
| ~ in(U_1781,U_1780) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
! [U_1781,U_1780] :
( ( ! [U_1778] :
( ~ in(U_1778,sK353(U_1781,U_1780))
| ~ in(U_1778,U_1780) )
& in(sK353(U_1781,U_1780),U_1780) )
| ~ in(U_1781,U_1780) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_1779,sK353(U_1781,U_1780))],[f_456_2]) ).
cnf(f_456_4,plain,
( in(sK353(U_1781,U_1780),U_1780)
| ~ in(U_1781,U_1780) ),
inference(clausify,[status(thm)],[f_456_3]) ).
cnf(f_456_5,plain,
( ~ in(U_1778,sK353(U_1781,U_1780))
| ~ in(U_1778,U_1780)
| ~ in(U_1781,U_1780) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_1,plain,
! [A] :
( well_ordering(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t7_wellord2]) ).
fof(f_457_2,plain,
! [U_1782] :
( well_ordering(inclusion_relation(U_1782))
| ~ ordinal(U_1782) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
( well_ordering(inclusion_relation(U_1782))
| ~ ordinal(U_1782) ),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_458_2,plain,
! [U_1784,U_1783] : subset(U_1784,set_union2(U_1784,U_1783)),
inference(variable_rename,[status(thm)],[f_458_1]) ).
cnf(f_458_3,plain,
subset(U_1784,set_union2(U_1784,U_1783)),
inference(clausify,[status(thm)],[f_458_2]) ).
fof(f_459_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_459_2,plain,
! [U_1786,U_1785] :
( ( disjoint(U_1786,U_1785)
| set_difference(U_1786,U_1785) != U_1786 )
& ( set_difference(U_1786,U_1785) = U_1786
| ~ disjoint(U_1786,U_1785) ) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
( ! [U_1790,U_1788] :
( disjoint(U_1790,U_1788)
| set_difference(U_1790,U_1788) != U_1790 )
& ! [U_1789,U_1787] :
( set_difference(U_1789,U_1787) = U_1789
| ~ disjoint(U_1789,U_1787) ) ),
inference(miniscope,[status(thm)],[f_459_2]) ).
cnf(f_459_4,plain,
( set_difference(U_1789,U_1787) = U_1789
| ~ disjoint(U_1789,U_1787) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_5,plain,
( disjoint(U_1790,U_1788)
| set_difference(U_1790,U_1788) != U_1790 ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_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_460_2,plain,
! [U_1793,U_1792,U_1791] :
( ( ( in(U_1793,relation_dom(relation_dom_restriction(U_1791,U_1792)))
| ~ in(U_1793,relation_dom(U_1791))
| ~ in(U_1793,U_1792) )
& ( ( in(U_1793,relation_dom(U_1791))
& in(U_1793,U_1792) )
| ~ in(U_1793,relation_dom(relation_dom_restriction(U_1791,U_1792))) ) )
| ~ relation(U_1791) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( in(U_1793,U_1792)
| ~ in(U_1793,relation_dom(relation_dom_restriction(U_1791,U_1792)))
| ~ relation(U_1791) ),
inference(clausify,[status(thm)],[f_460_2]) ).
cnf(f_460_4,plain,
( in(U_1793,relation_dom(U_1791))
| ~ in(U_1793,relation_dom(relation_dom_restriction(U_1791,U_1792)))
| ~ relation(U_1791) ),
inference(clausify,[status(thm)],[f_460_2]) ).
cnf(f_460_5,plain,
( in(U_1793,relation_dom(relation_dom_restriction(U_1791,U_1792)))
| ~ in(U_1793,relation_dom(U_1791))
| ~ in(U_1793,U_1792)
| ~ relation(U_1791) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_461_2,plain,
! [U_1795,U_1794] :
( subset(relation_dom_restriction(U_1794,U_1795),U_1794)
| ~ relation(U_1794) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( subset(relation_dom_restriction(U_1794,U_1795),U_1794)
| ~ relation(U_1794) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_462_2,plain,
! [U_1797,U_1796] :
( ~ empty(U_1796)
| U_1797 = U_1796
| ~ empty(U_1797) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1797] :
( ! [U_1796] :
( ~ empty(U_1796)
| U_1797 = U_1796 )
| ~ empty(U_1797) ),
inference(miniscope,[status(thm)],[f_462_2]) ).
cnf(f_462_4,plain,
( ~ empty(U_1796)
| U_1797 = U_1796
| ~ empty(U_1797) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_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_463_2,plain,
! [U_1800,U_1799,U_1798] :
( ( ( in(ordered_pair(U_1800,U_1799),U_1798)
| U_1799 != apply(U_1798,U_1800)
| ~ in(U_1800,relation_dom(U_1798)) )
& ( ( U_1799 = apply(U_1798,U_1800)
& in(U_1800,relation_dom(U_1798)) )
| ~ in(ordered_pair(U_1800,U_1799),U_1798) ) )
| ~ function(U_1798)
| ~ relation(U_1798) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( in(U_1800,relation_dom(U_1798))
| ~ in(ordered_pair(U_1800,U_1799),U_1798)
| ~ function(U_1798)
| ~ relation(U_1798) ),
inference(clausify,[status(thm)],[f_463_2]) ).
cnf(f_463_4,plain,
( U_1799 = apply(U_1798,U_1800)
| ~ in(ordered_pair(U_1800,U_1799),U_1798)
| ~ function(U_1798)
| ~ relation(U_1798) ),
inference(clausify,[status(thm)],[f_463_2]) ).
cnf(f_463_5,plain,
( in(ordered_pair(U_1800,U_1799),U_1798)
| U_1799 != apply(U_1798,U_1800)
| ~ in(U_1800,relation_dom(U_1798))
| ~ function(U_1798)
| ~ relation(U_1798) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_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_464_2,plain,
! [U_1801] :
( ( ( well_orders(U_1801,relation_field(U_1801))
| ~ well_ordering(U_1801) )
& ( well_ordering(U_1801)
| ~ well_orders(U_1801,relation_field(U_1801)) ) )
| ~ relation(U_1801) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( well_ordering(U_1801)
| ~ well_orders(U_1801,relation_field(U_1801))
| ~ relation(U_1801) ),
inference(clausify,[status(thm)],[f_464_2]) ).
cnf(f_464_4,plain,
( well_orders(U_1801,relation_field(U_1801))
| ~ well_ordering(U_1801)
| ~ relation(U_1801) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_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_465_2,plain,
! [U_1804,U_1803,U_1802] :
( subset(set_union2(U_1804,U_1802),U_1803)
| ~ subset(U_1802,U_1803)
| ~ subset(U_1804,U_1803) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
( subset(set_union2(U_1804,U_1802),U_1803)
| ~ subset(U_1802,U_1803)
| ~ subset(U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_466_2,plain,
! [U_1807,U_1806,U_1805] :
( U_1807 = U_1806
| singleton(U_1807) != unordered_pair(U_1806,U_1805) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
! [U_1807,U_1806] :
( ! [U_1805] : singleton(U_1807) != unordered_pair(U_1806,U_1805)
| U_1807 = U_1806 ),
inference(miniscope,[status(thm)],[f_466_2]) ).
cnf(f_466_4,plain,
( singleton(U_1807) != unordered_pair(U_1806,U_1805)
| U_1807 = U_1806 ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_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_467_2,plain,
! [U_1809,U_1808] :
( relation_dom(relation_dom_restriction(U_1808,U_1809)) = set_intersection2(relation_dom(U_1808),U_1809)
| ~ relation(U_1808) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( relation_dom(relation_dom_restriction(U_1808,U_1809)) = set_intersection2(relation_dom(U_1808),U_1809)
| ~ relation(U_1808) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_468_2,plain,
! [U_1811,U_1810] :
( subset(U_1811,union(U_1810))
| ~ in(U_1811,U_1810) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( subset(U_1811,union(U_1810))
| ~ in(U_1811,U_1810) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_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_469_2,plain,
! [U_1813,U_1812] :
( relation_dom_restriction(U_1812,U_1813) = relation_composition(identity_relation(U_1813),U_1812)
| ~ relation(U_1812) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( relation_dom_restriction(U_1812,U_1813) = relation_composition(identity_relation(U_1813),U_1812)
| ~ relation(U_1812) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_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_470_2,plain,
! [U_1815,U_1814] :
( subset(relation_rng(relation_dom_restriction(U_1814,U_1815)),relation_rng(U_1814))
| ~ relation(U_1814) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
( subset(relation_rng(relation_dom_restriction(U_1814,U_1815)),relation_rng(U_1814))
| ~ relation(U_1814) ),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_471_2,plain,
! [U_1816] : union(powerset(U_1816)) = U_1816,
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
union(powerset(U_1816)) = U_1816,
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_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_472_2,plain,
! [U_1820,U_1819,U_1818,U_1817] :
( ( relation_of2_as_subset(U_1817,U_1820,U_1818)
& quasi_total(U_1817,U_1820,U_1818)
& function(U_1817) )
| ( U_1820 != empty_set
& U_1819 = empty_set )
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
( function(U_1817)
| U_1819 = empty_set
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(clausify,[status(thm)],[f_472_2]) ).
cnf(f_472_4,plain,
( quasi_total(U_1817,U_1820,U_1818)
| U_1819 = empty_set
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(clausify,[status(thm)],[f_472_2]) ).
cnf(f_472_5,plain,
( relation_of2_as_subset(U_1817,U_1820,U_1818)
| U_1819 = empty_set
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(clausify,[status(thm)],[f_472_2]) ).
cnf(f_472_6,plain,
( function(U_1817)
| U_1820 != empty_set
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(clausify,[status(thm)],[f_472_2]) ).
cnf(f_472_7,plain,
( quasi_total(U_1817,U_1820,U_1818)
| U_1820 != empty_set
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(clausify,[status(thm)],[f_472_2]) ).
cnf(f_472_8,plain,
( relation_of2_as_subset(U_1817,U_1820,U_1818)
| U_1820 != empty_set
| ~ subset(U_1819,U_1818)
| ~ relation_of2_as_subset(U_1817,U_1820,U_1819)
| ~ quasi_total(U_1817,U_1820,U_1819)
| ~ function(U_1817) ),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_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_473_2,plain,
! [U_1828] :
? [U_1827] :
( ! [U_1826] :
( in(U_1826,U_1827)
| are_equipotent(U_1826,U_1827)
| ~ subset(U_1826,U_1827) )
& ! [U_1825] :
( ? [U_1824] :
( ! [U_1823] :
( in(U_1823,U_1824)
| ~ subset(U_1823,U_1825) )
& in(U_1824,U_1827) )
| ~ in(U_1825,U_1827) )
& ! [U_1822,U_1821] :
( in(U_1821,U_1827)
| ~ subset(U_1821,U_1822)
| ~ in(U_1822,U_1827) )
& in(U_1828,U_1827) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_1828] :
( ! [U_1826] :
( in(U_1826,sK354(U_1828))
| are_equipotent(U_1826,sK354(U_1828))
| ~ subset(U_1826,sK354(U_1828)) )
& ! [U_1825] :
( ? [U_1824] :
( ! [U_1823] :
( in(U_1823,U_1824)
| ~ subset(U_1823,U_1825) )
& in(U_1824,sK354(U_1828)) )
| ~ in(U_1825,sK354(U_1828)) )
& ! [U_1822,U_1821] :
( in(U_1821,sK354(U_1828))
| ~ subset(U_1821,U_1822)
| ~ in(U_1822,sK354(U_1828)) )
& in(U_1828,sK354(U_1828)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_1827,sK354(U_1828))],[f_473_2]) ).
fof(f_473_4,plain,
! [U_1828] :
( ! [U_1826] :
( in(U_1826,sK354(U_1828))
| are_equipotent(U_1826,sK354(U_1828))
| ~ subset(U_1826,sK354(U_1828)) )
& ! [U_1825] :
( ( ! [U_1823] :
( in(U_1823,sK355(U_1828,U_1825))
| ~ subset(U_1823,U_1825) )
& in(sK355(U_1828,U_1825),sK354(U_1828)) )
| ~ in(U_1825,sK354(U_1828)) )
& ! [U_1822,U_1821] :
( in(U_1821,sK354(U_1828))
| ~ subset(U_1821,U_1822)
| ~ in(U_1822,sK354(U_1828)) )
& in(U_1828,sK354(U_1828)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_1824,sK355(U_1828,U_1825))],[f_473_3]) ).
cnf(f_473_5,plain,
in(U_1828,sK354(U_1828)),
inference(clausify,[status(thm)],[f_473_4]) ).
cnf(f_473_6,plain,
( in(U_1821,sK354(U_1828))
| ~ subset(U_1821,U_1822)
| ~ in(U_1822,sK354(U_1828)) ),
inference(clausify,[status(thm)],[f_473_4]) ).
cnf(f_473_7,plain,
( in(sK355(U_1828,U_1825),sK354(U_1828))
| ~ in(U_1825,sK354(U_1828)) ),
inference(clausify,[status(thm)],[f_473_4]) ).
cnf(f_473_8,plain,
( in(U_1823,sK355(U_1828,U_1825))
| ~ subset(U_1823,U_1825)
| ~ in(U_1825,sK354(U_1828)) ),
inference(clausify,[status(thm)],[f_473_4]) ).
cnf(f_473_9,plain,
( in(U_1826,sK354(U_1828))
| are_equipotent(U_1826,sK354(U_1828))
| ~ subset(U_1826,sK354(U_1828)) ),
inference(clausify,[status(thm)],[f_473_4]) ).
fof(f_474_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_474_2,plain,
! [U_1831,U_1830,U_1829] :
( U_1830 = U_1829
| singleton(U_1831) != unordered_pair(U_1830,U_1829) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( U_1830 = U_1829
| singleton(U_1831) != unordered_pair(U_1830,U_1829) ),
inference(clausify,[status(thm)],[f_474_2]) ).
cnf(f_22_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_5]) ).
cnf(f_25_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_3]) ).
cnf(f_25_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_4]) ).
cnf(f_62_11_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_62_11]) ).
cnf(f_62_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_62_12]) ).
cnf(f_107_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_8]) ).
cnf(f_107_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_9]) ).
cnf(f_111_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_111_2]) ).
cnf(f_112_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_112_2]) ).
cnf(f_113_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_113_2]) ).
cnf(f_114_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_114_2]) ).
cnf(f_116_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_116_2]) ).
cnf(f_117_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_117_2]) ).
cnf(f_118_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_118_2]) ).
cnf(f_119_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_119_2]) ).
cnf(f_120_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_120_2]) ).
cnf(f_121_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_121_2]) ).
cnf(f_123_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_123_2]) ).
cnf(f_124_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_124_2]) ).
cnf(f_128_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_128_2]) ).
cnf(f_130_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_130_2]) ).
cnf(f_132_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_132_2]) ).
cnf(f_134_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_134_2]) ).
cnf(f_135_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_135_2]) ).
cnf(f_137_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_137_2]) ).
cnf(f_139_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_139_2]) ).
cnf(f_140_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_140_2]) ).
cnf(f_144_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_144_2]) ).
cnf(f_145_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_145_2]) ).
cnf(f_146_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_146_2]) ).
cnf(f_156_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_156_2]) ).
cnf(f_158_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_158_2]) ).
cnf(f_161_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_161_2]) ).
cnf(f_162_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_162_2]) ).
cnf(f_165_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_165_2]) ).
cnf(f_279_33_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_33]) ).
cnf(f_279_34_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_34]) ).
cnf(f_279_50_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_50]) ).
cnf(f_279_51_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK171(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_51]) ).
cnf(f_279_52_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_52]) ).
cnf(f_279_53_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK169(U_1005,U_1004),sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_53]) ).
cnf(f_279_54_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_54]) ).
cnf(f_279_55_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK169(U_1005,U_1004),U_990),U_1004)
| ~ in(U_990,sK171(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_55]) ).
cnf(f_279_61_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_61]) ).
cnf(f_279_62_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK168(U_1005,U_1004),U_1005)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_62]) ).
cnf(f_279_78_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_78]) ).
cnf(f_279_79_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK168(U_1005,U_1004) = sK172(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_79]) ).
cnf(f_279_80_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_80]) ).
cnf(f_279_81_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(sK170(U_1005,U_1004),sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_81]) ).
cnf(f_279_82_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_82]) ).
cnf(f_279_83_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| in(ordered_pair(sK170(U_1005,U_1004),U_992),U_1004)
| ~ in(U_992,sK172(U_1005,U_1004))
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_83]) ).
cnf(f_279_91_simplified,plain,
( in(sK175(U_1005,U_1004,U_1009,U_1007,U_1000),U_1000)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_91]) ).
cnf(f_279_92_simplified,plain,
( ~ in(ordered_pair(U_1007,sK175(U_1005,U_1004,U_1009,U_1007,U_1000)),U_1004)
| ~ in(U_1007,U_1000)
| U_1009 != U_1000
| ~ in(U_1009,U_1005)
| in(ordered_pair(U_1009,U_1007),sK173(U_1005,U_1004))
| sK169(U_1005,U_1004) != sK170(U_1005,U_1004)
| ~ relation(U_1004)
| empty(U_1005) ),
inference(simplify_clause,[status(thm)],[f_279_92]) ).
cnf(f_280_19_simplified,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| in(sK176(U_1016),U_1016) ),
inference(simplify_clause,[status(thm)],[f_280_19]) ).
cnf(f_280_23_simplified,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| sK177(U_1016) = singleton(sK176(U_1016)) ),
inference(simplify_clause,[status(thm)],[f_280_23]) ).
cnf(f_280_27_simplified,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| in(sK176(U_1016),U_1016) ),
inference(simplify_clause,[status(thm)],[f_280_27]) ).
cnf(f_280_31_simplified,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| sK178(U_1016) = singleton(sK176(U_1016)) ),
inference(simplify_clause,[status(thm)],[f_280_31]) ).
cnf(f_280_37_simplified,plain,
( in(ordered_pair(U_1020,U_1018),sK179(U_1016))
| U_1018 != singleton(U_1020)
| ~ in(U_1020,U_1016)
| sK177(U_1016) != sK178(U_1016) ),
inference(simplify_clause,[status(thm)],[f_280_37]) ).
cnf(f_284_53_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_53]) ).
cnf(f_284_54_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_54]) ).
cnf(f_284_55_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_55]) ).
cnf(f_284_56_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK196(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_56]) ).
cnf(f_284_57_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_57]) ).
cnf(f_284_58_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK194(U_1073,U_1072),sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_58]) ).
cnf(f_284_59_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_59]) ).
cnf(f_284_60_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK194(U_1073,U_1072),U_1057),U_1072)
| ~ in(U_1057,sK196(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_60]) ).
cnf(f_284_61_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_61]) ).
cnf(f_284_62_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK193(U_1073,U_1072),U_1073)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_62]) ).
cnf(f_284_63_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_63]) ).
cnf(f_284_64_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK193(U_1073,U_1072) = sK197(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_64]) ).
cnf(f_284_65_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_65]) ).
cnf(f_284_66_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(sK195(U_1073,U_1072),sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_66]) ).
cnf(f_284_67_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_67]) ).
cnf(f_284_68_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| in(ordered_pair(sK195(U_1073,U_1072),U_1059),U_1072)
| ~ in(U_1059,sK197(U_1073,U_1072))
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_68]) ).
cnf(f_284_74_simplified,plain,
( in(sK201(U_1073,U_1072,U_1075,U_1069,U_1068),U_1068)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_74]) ).
cnf(f_284_75_simplified,plain,
( ~ in(ordered_pair(U_1075,sK201(U_1073,U_1072,U_1075,U_1069,U_1068)),U_1072)
| ~ in(U_1075,U_1068)
| U_1069 != U_1068
| ~ in(U_1069,U_1073)
| in(U_1075,sK198(U_1073,U_1072))
| sK194(U_1073,U_1072) != sK195(U_1073,U_1072)
| ~ relation(U_1072)
| empty(U_1073) ),
inference(simplify_clause,[status(thm)],[f_284_75]) ).
cnf(f_286_21_simplified,plain,
( in(sK217(U_1111),U_1111)
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111) ),
inference(simplify_clause,[status(thm)],[f_286_21]) ).
cnf(f_286_22_simplified,plain,
( sK218(U_1111) = singleton(sK217(U_1111))
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111) ),
inference(simplify_clause,[status(thm)],[f_286_22]) ).
cnf(f_286_23_simplified,plain,
( in(sK217(U_1111),U_1111)
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111) ),
inference(simplify_clause,[status(thm)],[f_286_23]) ).
cnf(f_286_24_simplified,plain,
( sK219(U_1111) = singleton(sK217(U_1111))
| in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111) ),
inference(simplify_clause,[status(thm)],[f_286_24]) ).
cnf(f_286_28_simplified,plain,
( in(U_1113,sK220(U_1111))
| U_1113 != singleton(U_1108)
| ~ in(U_1108,U_1111)
| sK218(U_1111) != sK219(U_1111) ),
inference(simplify_clause,[status(thm)],[f_286_28]) ).
cnf(f_472_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_472_3]) ).
cnf(f_472_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_472_6]) ).
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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,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_10,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_11,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_12,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,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_15,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_16,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,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_19,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,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_25,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_26,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_27,axiom,
( pair_first(Eq_x_0) = pair_first(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,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_32,axiom,
( inclusion_relation(Eq_x_0) = inclusion_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,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_34,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_35,axiom,
( pair_second(Eq_x_0) = pair_second(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,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_37,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_38,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,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_40,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_41,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_42,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,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_44,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_45,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,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_73,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,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_76,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_77,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,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_79,axiom,
( sK29(Eq_x_0) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK32(Eq_x_0) = sK32(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,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_84,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK37(Eq_x_0) = sK37(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,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_92,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_93,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_94,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_95,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,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_99,axiom,
( sK49(Eq_x_0) = sK49(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK50(Eq_x_0,Eq_x_1) = sK50(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,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_102,axiom,
( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,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_104,axiom,
( sK54(Eq_x_0) = sK54(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,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_106,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_107,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_108,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_109,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_110,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_111,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_112,axiom,
( sK62(Eq_x_0) = sK62(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK66(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_117,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK71(Eq_x_0) = sK71(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK72(Eq_x_0) = sK72(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,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_124,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_125,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,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_127,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_128,axiom,
( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,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_131,axiom,
( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,axiom,
( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,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_137,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,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_139,axiom,
( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK91(Eq_x_0,Eq_x_1,Eq_x_2) = sK91(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK92(Eq_x_0,Eq_x_1,Eq_x_2) = sK92(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK93(Eq_x_0,Eq_x_1,Eq_x_2) = sK93(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( 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_145,axiom,
( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,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_147,axiom,
( sK97(Eq_x_0) = sK97(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,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_149,axiom,
( sK99(Eq_x_0,Eq_x_1) = sK99(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,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_151,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_152,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_153,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_154,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_155,axiom,
( sK105(Eq_x_0,Eq_x_1) = sK105(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,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_157,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_158,axiom,
( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( sK109(Eq_x_0,Eq_x_1,Eq_x_2) = sK109(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,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_161,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_162,axiom,
( sK112(Eq_x_0) = sK112(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( sK113(Eq_x_0) = sK113(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_164,axiom,
( sK114(Eq_x_0) = sK114(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( sK115(Eq_x_0) = sK115(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,axiom,
( sK116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK116(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_167,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_168,axiom,
( sK118(Eq_x_0,Eq_x_1,Eq_x_2) = sK118(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( sK119(Eq_x_0,Eq_x_1,Eq_x_2) = sK119(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_170,axiom,
( sK120(Eq_x_0,Eq_x_1,Eq_x_2) = sK120(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( sK121(Eq_x_0,Eq_x_1,Eq_x_2) = sK121(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,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_173,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_174,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_175,axiom,
( sK125(Eq_x_0,Eq_x_1,Eq_x_2) = sK125(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( sK130(Eq_x_0,Eq_x_1) = sK130(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_177,axiom,
( sK131(Eq_x_0) = sK131(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_178,axiom,
( sK132(Eq_x_0,Eq_x_1) = sK132(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,
( sK133(Eq_x_0) = sK133(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_180,axiom,
( sK134(Eq_x_0) = sK134(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_181,axiom,
( sK135(Eq_x_0) = sK135(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_182,axiom,
( sK136(Eq_x_0) = sK136(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_183,axiom,
( sK137(Eq_x_0,Eq_x_1) = sK137(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_184,axiom,
( sK138(Eq_x_0) = sK138(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_185,axiom,
( sK139(Eq_x_0) = sK139(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_186,axiom,
( sK140(Eq_x_0) = sK140(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_187,axiom,
( sK141(Eq_x_0) = sK141(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_188,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_189,axiom,
( sK146(Eq_x_0,Eq_x_1) = sK146(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_190,axiom,
( sK152(Eq_x_0) = sK152(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_191,axiom,
( sK154(Eq_x_0) = sK154(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_192,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_193,axiom,
( sK159(Eq_x_0) = sK159(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_194,axiom,
( sK161(Eq_x_0) = sK161(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_195,axiom,
( sK167(Eq_x_0) = sK167(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_196,axiom,
( sK168(Eq_x_0,Eq_x_1) = sK168(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_197,axiom,
( sK169(Eq_x_0,Eq_x_1) = sK169(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,
( sK170(Eq_x_0,Eq_x_1) = sK170(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_199,axiom,
( sK171(Eq_x_0,Eq_x_1) = sK171(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_200,axiom,
( sK172(Eq_x_0,Eq_x_1) = sK172(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_201,axiom,
( sK173(Eq_x_0,Eq_x_1) = sK173(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_202,axiom,
( sK174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK174(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_203,axiom,
( sK175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_204,axiom,
( sK176(Eq_x_0) = sK176(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_205,axiom,
( sK177(Eq_x_0) = sK177(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_206,axiom,
( sK178(Eq_x_0) = sK178(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_207,axiom,
( sK179(Eq_x_0) = sK179(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_208,axiom,
( sK180(Eq_x_0) = sK180(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_209,axiom,
( sK182(Eq_x_0) = sK182(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_210,axiom,
( sK184(Eq_x_0) = sK184(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_211,axiom,
( sK186(Eq_x_0) = sK186(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_212,axiom,
( sK188(Eq_x_0,Eq_x_1) = sK188(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_213,axiom,
( sK190(Eq_x_0) = sK190(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_214,axiom,
( sK191(Eq_x_0,Eq_x_1) = sK191(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_215,axiom,
( sK192(Eq_x_0,Eq_x_1,Eq_x_2) = sK192(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( sK193(Eq_x_0,Eq_x_1) = sK193(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_217,axiom,
( sK194(Eq_x_0,Eq_x_1) = sK194(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_218,axiom,
( sK195(Eq_x_0,Eq_x_1) = sK195(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_219,axiom,
( sK196(Eq_x_0,Eq_x_1) = sK196(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_220,axiom,
( sK197(Eq_x_0,Eq_x_1) = sK197(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,
( sK198(Eq_x_0,Eq_x_1) = sK198(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_222,axiom,
( sK199(Eq_x_0,Eq_x_1,Eq_x_2) = sK199(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_223,axiom,
( sK200(Eq_x_0,Eq_x_1,Eq_x_2) = sK200(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( sK201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK201(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_225,axiom,
( sK202(Eq_x_0,Eq_x_1) = sK202(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,
( sK203(Eq_x_0,Eq_x_1) = sK203(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,
( sK204(Eq_x_0,Eq_x_1) = sK204(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_228,axiom,
( sK205(Eq_x_0,Eq_x_1) = sK205(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,
( sK206(Eq_x_0,Eq_x_1) = sK206(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_230,axiom,
( sK207(Eq_x_0,Eq_x_1) = sK207(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,
( sK208(Eq_x_0,Eq_x_1) = sK208(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_232,axiom,
( 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_233,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_234,axiom,
( sK211(Eq_x_0,Eq_x_1,Eq_x_2) = sK211(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_235,axiom,
( sK212(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK212(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_236,axiom,
( sK213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK213(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_237,axiom,
( sK214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK214(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_238,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_239,axiom,
( sK216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK216(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_240,axiom,
( sK217(Eq_x_0) = sK217(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_241,axiom,
( sK218(Eq_x_0) = sK218(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_242,axiom,
( sK219(Eq_x_0) = sK219(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_243,axiom,
( sK220(Eq_x_0) = sK220(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_244,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_245,axiom,
( sK222(Eq_x_0) = sK222(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_246,axiom,
( sK223(Eq_x_0) = sK223(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_247,axiom,
( sK224(Eq_x_0) = sK224(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_248,axiom,
( sK225(Eq_x_0) = sK225(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_249,axiom,
( sK226(Eq_x_0) = sK226(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_250,axiom,
( sK227(Eq_x_0) = sK227(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_251,axiom,
( sK228(Eq_x_0) = sK228(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_252,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_253,axiom,
( sK230(Eq_x_0,Eq_x_1,Eq_x_2) = sK230(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_254,axiom,
( sK231(Eq_x_0,Eq_x_1,Eq_x_2) = sK231(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_255,axiom,
( sK232(Eq_x_0,Eq_x_1,Eq_x_2) = sK232(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_256,axiom,
( sK233(Eq_x_0) = sK233(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_257,axiom,
( sK234(Eq_x_0) = sK234(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_258,axiom,
( sK235(Eq_x_0) = sK235(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_259,axiom,
( sK236(Eq_x_0) = sK236(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_260,axiom,
( sK237(Eq_x_0,Eq_x_1) = sK237(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,
( sK238(Eq_x_0) = sK238(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_262,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_263,axiom,
( sK240(Eq_x_0) = sK240(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_264,axiom,
( sK241(Eq_x_0,Eq_x_1) = sK241(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_265,axiom,
( sK242(Eq_x_0,Eq_x_1,Eq_x_2) = sK242(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_266,axiom,
( sK243(Eq_x_0,Eq_x_1) = sK243(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_267,axiom,
( sK244(Eq_x_0,Eq_x_1,Eq_x_2) = sK244(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_268,axiom,
( sK245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK245(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_269,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_270,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_271,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_272,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_273,axiom,
( sK250(Eq_x_0,Eq_x_1) = sK250(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_274,axiom,
( sK251(Eq_x_0,Eq_x_1) = sK251(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_275,axiom,
( sK252(Eq_x_0,Eq_x_1,Eq_x_2) = sK252(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_276,axiom,
( sK253(Eq_x_0,Eq_x_1,Eq_x_2) = sK253(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_277,axiom,
( sK254(Eq_x_0,Eq_x_1,Eq_x_2) = sK254(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_278,axiom,
( sK255(Eq_x_0,Eq_x_1,Eq_x_2) = sK255(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_279,axiom,
( sK256(Eq_x_0,Eq_x_1,Eq_x_2) = sK256(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_280,axiom,
( sK257(Eq_x_0,Eq_x_1,Eq_x_2) = sK257(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_281,axiom,
( sK258(Eq_x_0,Eq_x_1,Eq_x_2) = sK258(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_282,axiom,
( sK259(Eq_x_0,Eq_x_1,Eq_x_2) = sK259(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_283,axiom,
( sK260(Eq_x_0,Eq_x_1,Eq_x_2) = sK260(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_284,axiom,
( sK261(Eq_x_0,Eq_x_1,Eq_x_2) = sK261(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_285,axiom,
( sK262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK262(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_286,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_287,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_288,axiom,
( sK268(Eq_x_0) = sK268(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_289,axiom,
( sK269(Eq_x_0,Eq_x_1) = sK269(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,
( sK270(Eq_x_0,Eq_x_1,Eq_x_2) = sK270(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_291,axiom,
( sK271(Eq_x_0,Eq_x_1,Eq_x_2) = sK271(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_292,axiom,
( sK272(Eq_x_0,Eq_x_1,Eq_x_2) = sK272(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_293,axiom,
( sK273(Eq_x_0,Eq_x_1,Eq_x_2) = sK273(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_294,axiom,
( sK274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK274(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_295,axiom,
( sK275(Eq_x_0,Eq_x_1) = sK275(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_296,axiom,
( sK276(Eq_x_0,Eq_x_1) = sK276(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_297,axiom,
( sK277(Eq_x_0,Eq_x_1) = sK277(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,
( sK278(Eq_x_0,Eq_x_1) = sK278(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_299,axiom,
( sK279(Eq_x_0,Eq_x_1) = sK279(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_300,axiom,
( sK280(Eq_x_0,Eq_x_1) = sK280(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_301,axiom,
( sK281(Eq_x_0,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_302,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_303,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_304,axiom,
( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK284(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_305,axiom,
( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK285(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_306,axiom,
( sK286(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK286(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_307,axiom,
( sK287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK287(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_308,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_309,axiom,
( sK289(Eq_x_0,Eq_x_1,Eq_x_2) = sK289(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( sK290(Eq_x_0,Eq_x_1,Eq_x_2) = sK290(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_311,axiom,
( sK291(Eq_x_0) = sK291(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_312,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_313,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_314,axiom,
( sK294(Eq_x_0,Eq_x_1,Eq_x_2) = sK294(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_315,axiom,
( sK295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK295(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_316,axiom,
( sK296(Eq_x_0,Eq_x_1) = sK296(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,
( sK297(Eq_x_0,Eq_x_1,Eq_x_2) = sK297(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_318,axiom,
( sK298(Eq_x_0,Eq_x_1,Eq_x_2) = sK298(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_319,axiom,
( sK299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK299(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_320,axiom,
( sK300(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK300(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_321,axiom,
( sK301(Eq_x_0) = sK301(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_322,axiom,
( sK302(Eq_x_0,Eq_x_1,Eq_x_2) = sK302(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_323,axiom,
( sK303(Eq_x_0,Eq_x_1) = sK303(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_324,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_325,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_326,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_327,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_328,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_329,axiom,
( sK309(Eq_x_0,Eq_x_1) = sK309(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_330,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_331,axiom,
( sK311(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK311(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_332,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_333,axiom,
( sK313(Eq_x_0,Eq_x_1,Eq_x_2) = sK313(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_334,axiom,
( sK314(Eq_x_0) = sK314(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_335,axiom,
( sK315(Eq_x_0) = sK315(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_336,axiom,
( sK316(Eq_x_0) = sK316(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_337,axiom,
( sK317(Eq_x_0) = sK317(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_338,axiom,
( sK318(Eq_x_0) = sK318(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_339,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_340,axiom,
( sK322(Eq_x_0) = sK322(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_341,axiom,
( sK323(Eq_x_0,Eq_x_1) = sK323(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,
( sK324(Eq_x_0) = sK324(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_343,axiom,
( sK326(Eq_x_0) = sK326(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_344,axiom,
( sK327(Eq_x_0,Eq_x_1,Eq_x_2) = sK327(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_345,axiom,
( sK328(Eq_x_0,Eq_x_1,Eq_x_2) = sK328(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_346,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_347,axiom,
( sK330(Eq_x_0,Eq_x_1,Eq_x_2) = sK330(Eq_y_0,Eq_y_1,Eq_y_2)
| 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,
( sK331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK331(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_349,axiom,
( sK332(Eq_x_0,Eq_x_1,Eq_x_2) = sK332(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_350,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_351,axiom,
( sK334(Eq_x_0) = sK334(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_352,axiom,
( sK335(Eq_x_0) = sK335(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_353,axiom,
( sK336(Eq_x_0) = sK336(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_354,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_355,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_356,axiom,
( sK339(Eq_x_0) = sK339(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_357,axiom,
( sK340(Eq_x_0,Eq_x_1) = sK340(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,
( sK341(Eq_x_0,Eq_x_1) = sK341(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,
( 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_360,axiom,
( sK343(Eq_x_0) = sK343(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_361,axiom,
( sK344(Eq_x_0) = sK344(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_362,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_363,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_364,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_365,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_366,axiom,
( sK349(Eq_x_0,Eq_x_1) = sK349(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_367,axiom,
( sK350(Eq_x_0) = sK350(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_368,axiom,
( sK351(Eq_x_0) = sK351(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_369,axiom,
( sK352(Eq_x_0,Eq_x_1,Eq_x_2) = sK352(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_370,axiom,
( sK353(Eq_x_0,Eq_x_1) = sK353(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,
( sK354(Eq_x_0) = sK354(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_372,axiom,
( sK355(Eq_x_0,Eq_x_1) = sK355(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,
( 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_374,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_375,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_376,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_377,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_378,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_379,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_380,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_381,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_382,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_383,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_384,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_385,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_386,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_387,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_388,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_389,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_390,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_391,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_392,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_393,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_394,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_395,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_396,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_397,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_398,axiom,
( join_commutative(Eq_y_0)
| ~ join_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_399,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_400,axiom,
( meet_commutative(Eq_y_0)
| ~ meet_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_401,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_402,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_403,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_404,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_405,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_406,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_407,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_408,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_409,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_410,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_411,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_412,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_413,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_414,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_415,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_416,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_417,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_418,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_419,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_420,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_421,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_422,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_423,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_424,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_425,axiom,
( latt_str(Eq_y_0)
| ~ latt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_426,axiom,
( meet_absorbing(Eq_y_0)
| ~ meet_absorbing(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_427,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_428,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU306+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:54:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 1.98/2.25 % SZS status Theorem for theBenchmark
% 1.98/2.25 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------