% Mizar problem: t8_lfuzzy_0,lfuzzy_0,406,5 
fof(t8_lfuzzy_0, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_lfuzzy_0(A) & l1_orders_2(A)) )  =>  (! [B] : r1_yellow_0(A, B)) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc10_waybel_1, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v11_waybel_1(A))  =>  ( ~ (v2_struct_0(A))  & v9_waybel_1(A)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc1_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v1_lattice3(A) =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_lfuzzy_0(A) =>  ( ~ (v2_struct_0(A))  & v1_lfuzzy_0(A)) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_orders_2(A) => v2_orders_2(A)) ) ) ).
fof(cc1_orders_4, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_struct_0(A) =>  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_waybel_2, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v16_waybel_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ).
fof(cc1_waybel_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v16_waybel_0(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_waybel_0(B, A) & v2_waybel_0(B, A)) ) ) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc2_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_lattice3(A) =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_struct_0(A) => v1_lfuzzy_0(A)) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v6_orders_2(B, A)) ) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_waybel_2, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) &  (v2_waybel_1(A) & v10_waybel_1(A)) ) ) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_lfuzzy_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_lfuzzy_0(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v1_xreal_0(B)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_waybel_2, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) & v1_waybel_2(A)) ) ) ) ) ).
fof(cc3_waybel_3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) & v2_waybel_3(A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v1_lfuzzy_0(A) =>  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v1_lfuzzy_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v16_waybel_0(A) & v1_lfuzzy_0(A)) ) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_waybel_1, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v9_waybel_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ) ) ) ).
fof(cc6_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v1_lfuzzy_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_lattice3(A) &  (v2_lattice3(A) & v1_lfuzzy_0(A)) ) ) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_waybel_1, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v9_waybel_1(A))  =>  ( ~ (v2_struct_0(A))  & v2_waybel_1(A)) ) ) ) ).
fof(cc7_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v2_lfuzzy_0(A))  =>  ( ~ (v2_struct_0(A))  & v3_yellow_0(A)) ) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_waybel_1, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v9_waybel_1(A))  =>  ( ~ (v2_struct_0(A))  & v2_yellow_0(A)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_waybel_1, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v11_waybel_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v3_yellow_0(A) &  (v2_waybel_1(A) & v10_waybel_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(cc9_waybel_1, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v3_yellow_0(A) &  (v2_waybel_1(A) & v10_waybel_1(A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v11_waybel_1(A)) ) ) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d1_seq_4, axiom,  (! [A] :  (v3_membered(A) =>  (v4_xxreal_2(A) =>  (v1_xboole_0(A) |  (! [B] :  (v1_xreal_0(B) =>  (B=k2_seq_4(A) <=>  ( (! [C] :  (v1_xreal_0(C) =>  (r2_hidden(C, A) => r1_xxreal_0(C, B)) ) )  &  (! [C] :  (v1_xreal_0(C) =>  ~ ( ( ~ (r1_xxreal_0(C, k5_numbers))  &  (! [D] :  (v1_xreal_0(D) =>  ~ ( (r2_hidden(D, A) &  ~ (r1_xxreal_0(D, k6_xcmplx_0(B, C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_lfuzzy_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_lfuzzy_0(A) <=>  (v1_lfuzzy_0(A) &  (? [B] :  (v1_xreal_0(B) &  (? [C] :  (v1_xreal_0(C) &  (r1_xxreal_0(B, C) & u1_struct_0(A)=k1_rcomp_1(B, C)) ) ) ) ) ) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d7_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (r1_yellow_0(A, B) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (r2_lattice3(A, B, C) &  ( (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_lattice3(A, B, D) => r1_orders_2(A, C, D)) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r2_lattice3(A, B, D) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_lattice3(A, B, E) => r1_orders_2(A, D, E)) ) ) )  => D=C) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (r2_yellow_0(A, B) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (r1_lattice3(A, B, C) &  ( (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_lattice3(A, B, D) => r1_orders_2(A, D, C)) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r1_lattice3(A, B, D) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r1_lattice3(A, B, E) => r1_orders_2(A, E, D)) ) ) )  => D=C) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_lattice3(A, B, C) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, B) => r1_orders_2(A, D, C)) ) ) ) ) ) ) ) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_rcomp_1, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => m1_subset_1(k1_rcomp_1(A, B), k1_zfmisc_1(k1_numbers))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xxreal_1, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_seq_4, axiom,  (! [A] :  (v3_membered(A) => v1_xreal_0(k2_seq_4(A))) ) ).
fof(dt_k3_seq_4, axiom,  (! [A] :  (v3_membered(A) => v1_xreal_0(k3_seq_4(A))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_l1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_o_1_4_lfuzzy_0, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) => m1_subset_1(o_1_4_lfuzzy_0(A), A)) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_orders_2, axiom,  (? [A] : l1_orders_2(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc17_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(A, B))) ) ) ).
fof(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, A))) ) ) ).
fof(fc19_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc20_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc31_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(A, B))) ) ).
fof(fc32_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(B, A))) ) ).
fof(fc33_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(A, B))) ) ).
fof(fc34_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(B, A))) ) ).
fof(fc35_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(A, B))) ) ).
fof(fc36_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(B, A))) ) ).
fof(fc37_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(A, B))) ) ).
fof(fc38_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(B, A))) ) ).
fof(fc39_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(A, B))) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc40_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(B, A))) ) ).
fof(fc41_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(A, B))) ) ).
fof(fc42_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(B, A))) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v6_orders_2(B, A)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(redefinition_k1_rcomp_1, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => k1_rcomp_1(A, B)=k1_xxreal_1(A, B)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t144_seq_4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(A, k1_zfmisc_1(k1_numbers)))  =>  (! [B] :  (v1_xreal_0(B) =>  ( (! [C] :  (v1_xreal_0(C) =>  (r2_hidden(C, A) => r1_xxreal_0(C, B)) ) )  => r1_xxreal_0(k2_seq_4(A), B)) ) ) ) ) ).
fof(t14_measure5, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) =>  ( ( ~ (v1_xboole_0(A))  & v2_measure5(A))  <=>  (? [B] :  (v1_xreal_0(B) &  (? [C] :  (v1_xreal_0(C) &  (r1_xxreal_0(B, C) & A=k1_rcomp_1(B, C)) ) ) ) ) ) ) ) ).
fof(t15_yellow_0, axiom,  (! [A] :  ( (v5_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (r1_yellow_0(A, B) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (r2_lattice3(A, B, C) &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_lattice3(A, B, D) => r1_orders_2(A, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(t17_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(k3_xboole_0(A, B), A)) ) ).
fof(t19_jordan5a, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (k3_seq_4(k1_rcomp_1(A, B))=A & k2_seq_4(k1_rcomp_1(A, B))=B) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_xxreal_1, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  (r2_hidden(C, k1_xxreal_1(A, B)) <=>  (r1_xxreal_0(A, C) & r1_xxreal_0(C, B)) ) ) ) ) ) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(B, C))  => r1_xxreal_0(A, C)) ) ) ) ) ) ) ).
fof(t3_integra1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v2_measure5(A) & m1_subset_1(A, k1_zfmisc_1(k1_numbers))) )  =>  (v3_xxreal_2(A) & v4_xxreal_2(A)) ) ) ).
fof(t3_lfuzzy_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_lfuzzy_0(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_xxreal_0(B, C) <=> r1_orders_2(A, B, C)) ) ) ) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t43_xxreal_2, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (v2_membered(B) =>  ( (r1_tarski(A, B) & v4_xxreal_2(B))  => v4_xxreal_2(A)) ) ) ) ) ).
fof(t48_seq_4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_membered(A))  =>  (! [B] :  (v3_membered(B) =>  ( (r1_tarski(A, B) & v4_xxreal_2(B))  => r1_xxreal_0(k2_seq_4(A), k2_seq_4(B))) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t50_yellow_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_orders_2(A))  =>  (! [B] :  ( (r1_yellow_0(A, B) => r1_yellow_0(A, k3_xboole_0(B, u1_struct_0(A))))  &  ( (r1_yellow_0(A, k3_xboole_0(B, u1_struct_0(A))) => r1_yellow_0(A, B))  &  ( (r2_yellow_0(A, B) => r2_yellow_0(A, k3_xboole_0(B, u1_struct_0(A))))  &  (r2_yellow_0(A, k3_xboole_0(B, u1_struct_0(A))) => r2_yellow_0(A, B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
