% Mizar problem: t75_scmpds_6,scmpds_6,3397,35 
fof(t75_scmpds_6, conjecture,  (! [A] :  ( (v1_ami_2(A) & m1_subset_1(A, u1_struct_0(k1_scmpds_2)))  =>  (! [B] :  (v1_int_1(B) =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(C) &  (v1_finset_1(C) & v1_afinsq_1(C)) ) ) ) ) )  => k4_card_1(k7_scmpds_6(A, B, C))=k1_nat_1(k4_card_1(C), 1)) ) ) ) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_card_3, axiom, $true).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(cc2_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(cc3_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(fc10_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(C, B)) &  (v4_relat_1(k1_funct_4(C, B), A) &  (v1_funct_1(k1_funct_4(C, B)) & v1_partfun1(k1_funct_4(C, B), A)) ) ) ) ) ).
fof(fc12_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v9_ordinal1(A))  & v1_relat_1(B))  =>  (v1_relat_1(k3_relat_1(B, A)) & v9_ordinal1(k3_relat_1(B, A))) ) ) ).
fof(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1)))) )  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, B)))) ) ) )  =>  (v1_relat_1(k3_relat_1(A, C)) &  (v4_relat_1(k3_relat_1(A, C), k4_ordinal1) &  (v5_relat_1(k3_relat_1(A, C), B) & v1_funct_1(k3_relat_1(A, C))) ) ) ) ) ).
fof(fc9_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v4_relat_1(k1_funct_4(B, C), A) &  (v1_funct_1(k1_funct_4(B, C)) & v1_partfun1(k1_funct_4(B, C), A)) ) ) ) ) ).
fof(fc9_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1)))) )  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, B)))) ) ) )  =>  (v1_relat_1(k3_relat_1(A, C)) & v1_partfun1(k3_relat_1(A, C), k4_ordinal1)) ) ) ).
fof(fc9_scmpds_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_afinsq_1(A) & v3_scmpds_4(A)) ) ) ) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_afinsq_1(B) & v3_scmpds_4(B)) ) ) ) ) ) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v4_relat_1(k1_ordinal4(A, B), k4_ordinal1) &  (v5_relat_1(k1_ordinal4(A, B), u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(k1_ordinal4(A, B)))  &  (v1_funct_1(k1_ordinal4(A, B)) &  (v1_finset_1(k1_ordinal4(A, B)) &  (v1_afinsq_1(k1_ordinal4(A, B)) & v3_scmpds_4(k1_ordinal4(A, B))) ) ) ) ) ) ) ) ) ).
fof(rc2_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v3_card_1(B, 1) & v1_afinsq_1(B)) ) ) ) ) ) ) ) ).
fof(rc4_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) ) ) ) ).
fof(free_g1_extpro_1, axiom,  (! [A, B, C, D, E, F, G] :  ( (m1_subset_1(C, B) &  ( (v1_compos_0(D) &  (v2_compos_0(D) &  (v3_compos_0(D) & v5_compos_0(D)) ) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, B, A) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) )  &  ( (v1_relat_1(F) &  (v4_relat_1(F, A) &  (v1_funct_1(F) & v1_partfun1(F, A)) ) )  &  (v1_funct_1(G) &  (v1_funct_2(G, D, k1_funct_2(k4_card_3(k3_relat_1(E, F)), k4_card_3(k3_relat_1(E, F)))) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(D, k1_funct_2(k4_card_3(k3_relat_1(E, F)), k4_card_3(k3_relat_1(E, F))))))) ) ) ) ) )  =>  (! [H, I, J, K, L, M, N] :  (g1_extpro_1(A, B, C, D, E, F, G)=g1_extpro_1(H, I, J, K, L, M, N) =>  (A=H &  (B=I &  (C=J &  (D=K &  (E=L &  (F=M & G=N) ) ) ) ) ) ) ) ) ) ).
fof(idempotence_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(A, A)=A) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(existence_l1_memstr_0, axiom,  (! [A] :  (? [B] : l1_memstr_0(B, A)) ) ).
fof(dt_g1_extpro_1, axiom,  (! [A, B, C, D, E, F, G] :  ( (m1_subset_1(C, B) &  ( (v1_compos_0(D) &  (v2_compos_0(D) &  (v3_compos_0(D) & v5_compos_0(D)) ) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, B, A) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, A)))) )  &  ( (v1_relat_1(F) &  (v4_relat_1(F, A) &  (v1_funct_1(F) & v1_partfun1(F, A)) ) )  &  (v1_funct_1(G) &  (v1_funct_2(G, D, k1_funct_2(k4_card_3(k3_relat_1(E, F)), k4_card_3(k3_relat_1(E, F)))) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(D, k1_funct_2(k4_card_3(k3_relat_1(E, F)), k4_card_3(k3_relat_1(E, F))))))) ) ) ) ) )  =>  (v1_extpro_1(g1_extpro_1(A, B, C, D, E, F, G), A) & l1_extpro_1(g1_extpro_1(A, B, C, D, E, F, G), A)) ) ) ).
fof(dt_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ).
fof(dt_k1_ordinal4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  &  (v1_relat_1(B) &  (v5_ordinal1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v5_ordinal1(k1_ordinal4(A, B)) & v1_funct_1(k1_ordinal4(A, B))) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k3_afinsq_1, axiom, $true).
fof(dt_k61_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  & v7_ordinal1(B))  =>  (v1_relat_1(k61_valued_1(A, B)) & v1_funct_1(k61_valued_1(A, B))) ) ) ).
fof(dt_k6_ordinal1, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_memstr_0, axiom,  (! [A] :  (! [B] :  (l1_memstr_0(B, A) => l2_struct_0(B)) ) ) ).
fof(dt_u1_extpro_1, axiom,  (! [A, B] :  (l1_extpro_1(B, A) =>  (v1_funct_1(u1_extpro_1(A, B)) &  (v1_funct_2(u1_extpro_1(A, B), u1_compos_1(B), k1_funct_2(k4_card_3(k3_relat_1(u1_memstr_0(A, B), u2_memstr_0(A, B))), k4_card_3(k3_relat_1(u1_memstr_0(A, B), u2_memstr_0(A, B))))) & m1_subset_1(u1_extpro_1(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_compos_1(B), k1_funct_2(k4_card_3(k3_relat_1(u1_memstr_0(A, B), u2_memstr_0(A, B))), k4_card_3(k3_relat_1(u1_memstr_0(A, B), u2_memstr_0(A, B)))))))) ) ) ) ).
fof(dt_u1_memstr_0, axiom,  (! [A, B] :  (l1_memstr_0(B, A) =>  (v1_funct_1(u1_memstr_0(A, B)) &  (v1_funct_2(u1_memstr_0(A, B), u1_struct_0(B), A) & m1_subset_1(u1_memstr_0(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), A)))) ) ) ) ).
fof(dt_u2_memstr_0, axiom,  (! [A, B] :  (l1_memstr_0(B, A) =>  (v1_relat_1(u2_memstr_0(A, B)) &  (v4_relat_1(u2_memstr_0(A, B), A) &  (v1_funct_1(u2_memstr_0(A, B)) & v1_partfun1(u2_memstr_0(A, B), A)) ) ) ) ) ).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_memstr_0, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_zfmisc_1(B) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v1_finset_1(B) & v4_compos_1(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v1_finset_1(B) & v2_compos_1(B, A)) ) ) ) ) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v1_finset_1(B) & v4_compos_1(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(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_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(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(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc11_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v5_relat_1(k1_funct_4(B, C), A) & v1_funct_1(k1_funct_4(B, C))) ) ) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k6_ordinal1(A))) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_afinsq_1, axiom,  (! [A] : v3_card_1(k3_afinsq_1(A), 1)) ).
fof(fc14_ordinal1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k6_ordinal1(A))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_compos_1, axiom,  (! [A, B, C] :  ( (l1_compos_1(A) &  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) & v1_funct_1(B)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, u1_compos_1(A)) &  (v1_funct_1(C) &  ~ (v2_compos_1(C, A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v1_funct_1(k1_funct_4(B, C)) &  ~ (v2_compos_1(k1_funct_4(B, C), A)) ) ) ) ) ).
fof(fc18_afinsq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => v5_relat_1(k3_afinsq_1(B), A)) ) ).
fof(fc18_scmpds_4, axiom,  (! [A, B, C] :  ( (v1_int_1(A) &  ( (v1_ami_2(B) & m1_subset_1(B, u1_struct_0(k1_scmpds_2)))  & v7_ordinal1(C)) )  =>  (v1_relat_1(k3_afinsq_1(k8_scmpds_2(B, A, C))) &  (v4_relat_1(k3_afinsq_1(k8_scmpds_2(B, A, C)), k4_ordinal1) &  (v5_relat_1(k3_afinsq_1(k8_scmpds_2(B, A, C)), u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(k3_afinsq_1(k8_scmpds_2(B, A, C))))  &  (v1_funct_1(k3_afinsq_1(k8_scmpds_2(B, A, C))) &  (v1_finset_1(k3_afinsq_1(k8_scmpds_2(B, A, C))) &  (v1_afinsq_1(k3_afinsq_1(k8_scmpds_2(B, A, C))) & v3_scmpds_4(k3_afinsq_1(k8_scmpds_2(B, A, C)))) ) ) ) ) ) ) ) ) ).
fof(fc1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  => v7_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc1_ami_3, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ~ (v1_setfam_1(k6_ordinal1(A))) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc24_scmpds_5, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_afinsq_1(A) & v2_compos_1(A, k1_scmpds_2)) ) ) ) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_afinsq_1(B) & v2_compos_1(B, k1_scmpds_2)) ) ) ) ) ) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v5_ordinal1(k1_ordinal4(A, B)) &  (v1_funct_1(k1_ordinal4(A, B)) & v2_compos_1(k1_ordinal4(A, B), k1_scmpds_2)) ) ) ) ) ).
fof(fc25_scmpds_5, axiom,  (! [A] :  ( (v6_compos_0(A, u1_compos_1(k1_scmpds_2)) & m1_subset_1(A, u1_compos_1(k1_scmpds_2)))  => v2_compos_1(k3_afinsq_1(A), k1_scmpds_2)) ) ).
fof(fc26_scmpds_5, axiom,  (! [A, B] :  ( ( (v6_compos_0(A, u1_compos_1(k1_scmpds_2)) & m1_subset_1(A, u1_compos_1(k1_scmpds_2)))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_afinsq_1(B) & v2_compos_1(B, k1_scmpds_2)) ) ) ) ) ) ) )  =>  (v1_relat_1(k2_scmpds_4(A, B)) &  (v4_relat_1(k2_scmpds_4(A, B), k4_ordinal1) &  (v5_relat_1(k2_scmpds_4(A, B), u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(k2_scmpds_4(A, B)))  &  (v1_funct_1(k2_scmpds_4(A, B)) &  (v1_finset_1(k2_scmpds_4(A, B)) &  (v1_afinsq_1(k2_scmpds_4(A, B)) & v2_compos_1(k2_scmpds_4(A, B), k1_scmpds_2)) ) ) ) ) ) ) ) ) ).
fof(fc4_afinsq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k3_afinsq_1(A))) ) ).
fof(fc4_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ~ (v1_xboole_0(B)) ) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) &  ~ (v1_xboole_0(k1_funct_4(A, B))) ) ) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc5_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ~ (v1_xboole_0(B)) ) ) )  =>  (v1_relat_1(k1_funct_4(B, A)) &  (v1_funct_1(k1_funct_4(B, A)) &  ~ (v1_xboole_0(k1_funct_4(B, A))) ) ) ) ) ).
fof(fc6_afinsq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  &  (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v5_ordinal1(k1_ordinal4(A, B)) &  (v1_funct_1(k1_ordinal4(A, B)) & v1_finset_1(k1_ordinal4(A, B))) ) ) ) ) ).
fof(fc6_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  &  (v1_relat_1(B) &  (v2_relat_1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v2_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ) ).
fof(fc7_afinsq_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v5_ordinal1(C) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) )  =>  (v1_relat_1(k1_ordinal4(B, C)) &  (v5_relat_1(k1_ordinal4(B, C), A) &  (v5_ordinal1(k1_ordinal4(B, C)) & v1_funct_1(k1_ordinal4(B, C))) ) ) ) ) ).
fof(fc7_int_1, axiom,  (! [A] :  (v2_int_1(A) => v7_ordinal1(k2_xcmplx_0(A, 1))) ) ).
fof(fc8_afinsq_1, axiom,  (! [A] :  (v1_relat_1(k3_afinsq_1(A)) & v1_funct_1(k3_afinsq_1(A))) ) ).
fof(fc8_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v4_relat_1(k1_funct_4(B, C), A) & v1_funct_1(k1_funct_4(B, C))) ) ) ) ).
fof(fc8_int_1, axiom,  (! [A, B] :  ( (v2_int_1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc9_afinsq_1, axiom,  (! [A] :  (v5_ordinal1(k3_afinsq_1(A)) & v1_finset_1(k3_afinsq_1(A))) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (? [B] :  ( ~ (v1_xboole_0(B))  &  (v1_zfmisc_1(B) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_memstr_0, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  =>  (? [B] :  (l1_memstr_0(B, A) & v2_memstr_0(B, A)) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_afinsq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v6_valued_0(A)) ) ) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_compos_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) &  (v1_compos_0(A) &  (v2_compos_0(A) &  (v3_compos_0(A) & v5_compos_0(A)) ) ) ) ) ) ) ).
fof(rc6_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (? [B] :  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v5_ordinal1(B) &  (v1_finset_1(B) &  (v1_afinsq_1(B) &  ~ (v2_compos_1(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc7_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (? [B] :  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v5_ordinal1(B) &  (v1_finset_1(B) &  (v1_afinsq_1(B) &  ~ (v2_compos_1(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(ie2_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  => k9_xtuple_0(A)=k1_card_1(A)) ) ).
fof(rd1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_xboole_0(B)) ) )  => k1_funct_4(B, A)=A) ) ).
fof(rd2_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_xboole_0(B)) ) )  => k1_funct_4(A, B)=A) ) ).
fof(rd4_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(k1_funct_4(A, B), B)=k1_funct_4(A, B)) ) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
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(d17_ordinal1, axiom,  (! [A] : k6_ordinal1(A)=A) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(abstractness_v1_extpro_1, axiom,  (! [A, B] :  (l1_extpro_1(B, A) =>  (v1_extpro_1(B, A) => B=g1_extpro_1(A, u1_struct_0(B), u2_struct_0(B), u1_compos_1(B), u1_memstr_0(A, B), u2_memstr_0(A, B), u1_extpro_1(A, B))) ) ) ).
fof(existence_l1_compos_1, axiom,  (? [A] : l1_compos_1(A)) ).
fof(existence_l1_extpro_1, axiom,  (! [A] :  (? [B] : l1_extpro_1(B, A)) ) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(redefinition_k1_scmpds_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) ) )  => k1_scmpds_4(A, B)=k1_ordinal4(A, B)) ) ).
fof(redefinition_k5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => k5_card_1(A)=k6_ordinal1(A)) ) ).
fof(redefinition_k9_compos_1, axiom,  (! [A, B] :  ( (l1_compos_1(A) & m1_subset_1(B, u1_compos_1(A)))  => k9_compos_1(A, B)=k3_afinsq_1(B)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_scmpds_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) ) )  =>  (v1_relat_1(k1_scmpds_4(A, B)) &  (v4_relat_1(k1_scmpds_4(A, B), k4_ordinal1) &  (v5_relat_1(k1_scmpds_4(A, B), u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(k1_scmpds_4(A, B)))  &  (v1_funct_1(k1_scmpds_4(A, B)) &  (v1_finset_1(k1_scmpds_4(A, B)) & v1_afinsq_1(k1_scmpds_4(A, B))) ) ) ) ) ) ) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k5_card_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k8_scmpds_2, axiom,  (! [A, B, C] :  ( ( (v1_ami_2(A) & m1_subset_1(A, u1_struct_0(k1_scmpds_2)))  &  (v1_int_1(B) & v1_int_1(C)) )  => m1_subset_1(k8_scmpds_2(A, B, C), u1_compos_1(k1_scmpds_2))) ) ).
fof(dt_k9_compos_1, axiom,  (! [A, B] :  ( (l1_compos_1(A) & m1_subset_1(B, u1_compos_1(A)))  =>  (v1_relat_1(k9_compos_1(A, B)) &  (v4_relat_1(k9_compos_1(A, B), k4_ordinal1) &  (v5_relat_1(k9_compos_1(A, B), u1_compos_1(A)) &  (v1_funct_1(k9_compos_1(A, B)) & v1_finset_1(k9_compos_1(A, B))) ) ) ) ) ) ).
fof(dt_l1_compos_1, axiom, $true).
fof(dt_l1_extpro_1, axiom,  (! [A] :  (! [B] :  (l1_extpro_1(B, A) =>  (l1_memstr_0(B, A) & l1_compos_1(B)) ) ) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(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(cc1_compos_0, axiom,  (! [A] :  (v1_compos_0(A) => v1_relat_1(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc2_compos_0, axiom,  (! [A] :  (v5_compos_0(A) =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (! [B] :  ( (v1_xboole_0(B) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v1_finset_1(B) & v2_compos_1(B, A)) ) ) ) ) ) ) ) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v6_valued_0(A)) ) ) ) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc7_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) ) ) ) ).
fof(cc8_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc5_scmpds_5, axiom,  (! [A, B, C] :  ( ( (v1_ami_2(A) & m1_subset_1(A, u1_struct_0(k1_scmpds_2)))  &  (v1_int_1(B) & v1_int_1(C)) )  => v6_compos_0(k8_scmpds_2(A, B, C), u1_compos_1(k1_scmpds_2))) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(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_afinsq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ).
fof(rc1_compos_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_compos_0(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_afinsq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_xboole_0(B) & v1_finset_1(B)) ) ) ) ) ) ) ).
fof(rc2_compos_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_compos_0(A) &  (v2_compos_0(A) & v3_compos_0(A)) ) ) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_afinsq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_compos_0, axiom,  (? [A] :  (v1_compos_0(A) & v5_compos_0(A)) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_compos_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_compos_0(A) &  (v2_compos_0(A) &  (v3_compos_0(A) & v5_compos_0(A)) ) ) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc5_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (? [B] :  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (? [B] :  (v1_xboole_0(B) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(A)) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(ie1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  => k1_card_1(A)=k9_xtuple_0(A)) ) ).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(d1_scmpds_4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) ) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) )  => k1_scmpds_4(A, B)=k1_funct_4(A, k61_valued_1(B, k4_card_1(A)))) ) ) ) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(commutativity_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k1_nat_1(B, A)) ) ).
fof(projectivity_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => k4_card_1(k4_card_1(A))=k4_card_1(A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(redefinition_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k2_xcmplx_0(A, B)) ) ).
fof(redefinition_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => k4_card_1(A)=k1_card_1(A)) ) ).
fof(dt_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k1_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_scmpds_2, axiom,  (v1_extpro_1(k1_scmpds_2, k5_card_1(2)) & l1_extpro_1(k1_scmpds_2, k5_card_1(2))) ).
fof(dt_k2_scmpds_4, axiom,  (! [A, B] :  ( (m1_subset_1(A, u1_compos_1(k1_scmpds_2)) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) ) )  =>  (v1_relat_1(k2_scmpds_4(A, B)) &  (v4_relat_1(k2_scmpds_4(A, B), k4_ordinal1) &  (v5_relat_1(k2_scmpds_4(A, B), u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(k2_scmpds_4(A, B)))  &  (v1_funct_1(k2_scmpds_4(A, B)) &  (v1_finset_1(k2_scmpds_4(A, B)) & v1_afinsq_1(k2_scmpds_4(A, B))) ) ) ) ) ) ) ) ).
fof(dt_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => m1_subset_1(k4_card_1(A), k4_ordinal1)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k7_scmpds_6, axiom,  (! [A, B, C] :  ( ( (v1_ami_2(A) & m1_subset_1(A, u1_struct_0(k1_scmpds_2)))  &  (v1_int_1(B) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(C) &  (v1_finset_1(C) & v1_afinsq_1(C)) ) ) ) ) ) ) )  =>  (v1_relat_1(k7_scmpds_6(A, B, C)) &  (v4_relat_1(k7_scmpds_6(A, B, C), k4_ordinal1) &  (v5_relat_1(k7_scmpds_6(A, B, C), u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(k7_scmpds_6(A, B, C)))  &  (v1_funct_1(k7_scmpds_6(A, B, C)) &  (v1_finset_1(k7_scmpds_6(A, B, C)) & v1_afinsq_1(k7_scmpds_6(A, B, C))) ) ) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_compos_1, axiom,  (! [A] :  (l1_compos_1(A) =>  (v1_compos_0(u1_compos_1(A)) &  (v2_compos_0(u1_compos_1(A)) &  (v3_compos_0(u1_compos_1(A)) & v5_compos_0(u1_compos_1(A))) ) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
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(cc1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(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(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc6_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_afinsq_1(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_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(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_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(fc1_scmpds_2, axiom,  ( ~ (v2_struct_0(k1_scmpds_2))  & v1_extpro_1(k1_scmpds_2, k5_card_1(2))) ).
fof(fc2_scmpds_2, axiom,  (v2_memstr_0(k1_scmpds_2, k5_card_1(2)) &  (v3_memstr_0(k1_scmpds_2, k5_card_1(2)) & v1_extpro_1(k1_scmpds_2, k5_card_1(2))) ) ).
fof(fc4_scmpds_2, axiom,  (v1_extpro_1(k1_scmpds_2, k5_card_1(2)) & v3_extpro_1(k1_scmpds_2, k5_card_1(2))) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_scmpds_2, axiom,  (? [A] :  (m1_subset_1(A, u1_struct_0(k1_scmpds_2)) & v1_ami_2(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(d2_scmpds_4, axiom,  (! [A] :  (m1_subset_1(A, u1_compos_1(k1_scmpds_2)) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) )  => k2_scmpds_4(A, B)=k1_scmpds_4(k9_compos_1(k1_scmpds_2, A), B)) ) ) ) ).
fof(d9_scmpds_6, axiom,  (! [A] :  ( (v1_ami_2(A) & m1_subset_1(A, u1_struct_0(k1_scmpds_2)))  =>  (! [B] :  (v1_int_1(B) =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(C) &  (v1_finset_1(C) & v1_afinsq_1(C)) ) ) ) ) )  => k7_scmpds_6(A, B, C)=k2_scmpds_4(k8_scmpds_2(A, B, k1_nat_1(k4_card_1(C), 1)), C)) ) ) ) ) ) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t6_scmpds_6, axiom,  (! [A] :  (m1_subset_1(A, u1_compos_1(k1_scmpds_2)) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, u1_compos_1(k1_scmpds_2)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_afinsq_1(B)) ) ) ) ) )  => k4_card_1(k2_scmpds_4(A, B))=k1_nat_1(k4_card_1(B), 1)) ) ) ) ).
