% Mizar problem: t37_pcs_0,pcs_0,3232,5 
fof(t37_pcs_0, conjecture,  (! [A] :  (l2_pcs_0(A) =>  (! [B] :  (l2_pcs_0(B) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k23_pcs_0(A, B))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k23_pcs_0(A, B))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(B)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(B)) =>  ~ ( (C=k4_tarski(E, G) &  (D=k4_tarski(F, H) &  (r1_pcs_0(k23_pcs_0(A, B), C, D) &  ( ~ (r1_pcs_0(A, E, F))  &  ~ (r1_pcs_0(B, G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v12_pcs_0, axiom,  (! [A] :  (l2_pcs_0(A) =>  (v12_pcs_0(A) => A=g2_pcs_0(u1_struct_0(A), u1_orders_2(A), u1_pcs_0(A))) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, A)) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relat_2, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) &  (v1_relat_2(A) &  (v2_relat_2(A) &  (v3_relat_2(A) &  (v4_relat_2(A) &  (v5_relat_2(A) &  (v6_relat_2(A) &  (v7_relat_2(A) & v8_relat_2(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(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_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_partfun1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ~ (v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(A)) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
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(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_partfun1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(A)) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v5_relat_2(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
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(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_2(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) & v4_relat_2(A)) ) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
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(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_pcs_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) &  (v9_pcs_0(A) &  (v10_pcs_0(A) & v11_pcs_0(A)) ) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v7_relat_2(A))  =>  (v1_relat_1(A) &  (v1_relat_2(A) & v6_relat_2(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(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(d2_pcs_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (! [F] :  (m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))) =>  (! [G] :  (m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, C), k2_zfmisc_1(B, D)))) =>  (G=k4_pcs_0(A, B, C, D, E, F) <=>  (! [H] :  (! [I] :  (r2_hidden(k4_tarski(H, I), G) <=>  (? [J] :  (? [K] :  (? [L] :  (? [M] :  (H=k4_tarski(J, K) &  (I=k4_tarski(L, M) &  (r2_tarski(J, A) &  (r2_tarski(K, C) &  (r2_tarski(L, B) &  (r2_tarski(M, D) &  (r2_hidden(k4_tarski(J, L), E) | r2_hidden(k4_tarski(K, M), F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d42_pcs_0, axiom,  (! [A] :  (l2_pcs_0(A) =>  (! [B] :  (l2_pcs_0(B) => k23_pcs_0(A, B)=g2_pcs_0(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), k2_yellow_3(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_orders_2(A), u1_orders_2(B)), k4_pcs_0(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), u1_struct_0(B), u1_pcs_0(A), u1_pcs_0(B)))) ) ) ) ).
fof(d7_pcs_0, axiom,  (! [A] :  (l1_pcs_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_pcs_0(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_pcs_0(A))) ) ) ) ) ) ) ).
fof(dt_g2_pcs_0, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))))  =>  (v12_pcs_0(g2_pcs_0(A, B, C)) & l2_pcs_0(g2_pcs_0(A, B, C))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_yellow_3, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k1_yellow_3(A, B))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k23_pcs_0, axiom,  (! [A, B] :  ( (l2_pcs_0(A) & l2_pcs_0(B))  => l2_pcs_0(k23_pcs_0(A, B))) ) ).
fof(dt_k2_yellow_3, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => m1_subset_1(k2_yellow_3(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, C), k2_zfmisc_1(B, D))))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k4_pcs_0, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => m1_subset_1(k4_pcs_0(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, C), k2_zfmisc_1(B, D))))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_l1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => l1_struct_0(A)) ) ).
fof(dt_l1_pcs_0, axiom,  (! [A] :  (l1_pcs_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_pcs_0, axiom,  (! [A] :  (l2_pcs_0(A) =>  (l1_orders_2(A) & l1_pcs_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => m1_subset_1(u1_orders_2(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ).
fof(dt_u1_pcs_0, axiom,  (! [A] :  (l1_pcs_0(A) => m1_subset_1(u1_pcs_0(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_orders_2, axiom,  (? [A] : l1_orders_2(A)) ).
fof(existence_l1_pcs_0, axiom,  (? [A] : l1_pcs_0(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_pcs_0, axiom,  (? [A] : l2_pcs_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc4_pcs_0, axiom,  (! [A, B, C, D] :  ( ( (v1_partfun1(C, A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))))  &  (v1_partfun1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  => v1_partfun1(k4_pcs_0(A, A, B, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(fc5_pcs_0, axiom,  (! [A, B, C, D] :  ( ( (v1_relat_2(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))))  &  (v1_relat_2(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  => v1_relat_2(k4_pcs_0(A, A, B, B, C, D))) ) ).
fof(fc66_pcs_0, axiom,  (! [A, B] :  ( (l2_pcs_0(A) & l2_pcs_0(B))  => v12_pcs_0(k23_pcs_0(A, B))) ) ).
fof(fc6_pcs_0, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (v1_partfun1(D, B) &  (v1_relat_2(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, B)))) ) )  => v1_relat_2(k4_pcs_0(A, A, B, B, C, D))) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc7_pcs_0, axiom,  (! [A, B, C, D] :  ( ( (v1_partfun1(C, A) &  (v1_relat_2(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A)))) )  & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, B))))  => v1_relat_2(k4_pcs_0(A, A, B, B, C, D))) ) ).
fof(fc8_pcs_0, axiom,  (! [A, B, C, D] :  ( ( (v3_relat_2(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))))  &  (v3_relat_2(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  => v3_relat_2(k4_pcs_0(A, A, B, B, C, D))) ) ).
fof(free_g2_pcs_0, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))))  =>  (! [D, E, F] :  (g2_pcs_0(A, B, C)=g2_pcs_0(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc10_pcs_0, axiom,  (? [A] :  (l2_pcs_0(A) & v12_pcs_0(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_partfun1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, A) &  (v1_relat_2(B) &  (v3_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
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(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k2_yellow_3, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => k2_yellow_3(A, B, C, D, E, F)=k1_yellow_3(E, F)) ) ).
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(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (k4_tarski(A, B)=k4_tarski(C, D) =>  (A=C & B=D) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
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(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(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
