% Mizar problem: t70_group_5,group_5,1494,5 
fof(t70_group_5, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  ( (v15_algstr_0(B) &  (v1_group_3(B, A) & m1_group_2(B, A)) )  =>  (! [C] :  ( (v15_algstr_0(C) &  (v1_group_3(C, A) & m1_group_2(C, A)) )  =>  (! [D] :  ( (v15_algstr_0(D) &  (v1_group_3(D, A) & m1_group_2(D, A)) )  => r1_group_2(A, k8_group_5(A, k8_group_4(A, B, C), D), k8_group_4(A, k8_group_5(A, B, D), k8_group_5(A, C, D)))) ) ) ) ) ) ) ) ).
fof(abstractness_v15_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v15_algstr_0(A) => A=g3_algstr_0(u1_struct_0(A), u2_algstr_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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(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(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_numbers) => v5_valued_0(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_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v2_group_1(A) => v1_group_1(A)) ) ) ).
fof(cc1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) => v3_group_1(B)) ) ) ) ).
fof(cc1_int_1, axiom,  (! [A] :  (m1_subset_1(A, k4_numbers) => v1_int_1(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(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_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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v2_struct_0(A) => v3_group_1(A)) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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_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_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_group_2(B, A) => v8_struct_0(B)) ) ) ) ).
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_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(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_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_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
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(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
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(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, 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(commutativity_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
fof(d13_group_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (v1_group_3(B, A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k6_group_3(A, B, C)=g3_algstr_0(u1_struct_0(B), u2_algstr_0(B))) ) ) ) ) ) ) ).
fof(d2_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => k2_group_2(A, B, C)=a_3_0_group_2(A, B, C)) ) ) ) ) ) ).
fof(d2_group_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_group_3(A, B, C)=k6_algstr_0(A, k6_algstr_0(A, k2_group_1(A, C), B), C)) ) ) ) ) ) ).
fof(d2_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (! [B] :  (m2_finseq_1(B, u1_struct_0(A)) => k3_group_4(A, B)=k1_finsop_1(u1_struct_0(A), B, u2_algstr_0(A))) ) ) ) ).
fof(d2_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_group_5(A, B, C)=k6_algstr_0(A, k6_algstr_0(A, k6_algstr_0(A, k2_group_1(A, B), k2_group_1(A, C)), 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_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => k4_group_5(A, B, C)=a_3_0_group_5(A, B, C)) ) ) ) ) ) ).
fof(d5_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) => k5_group_5(A, B, C)=k4_group_5(A, k8_group_2(A, B), k8_group_2(A, C))) ) ) ) ) ) ).
fof(d7_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) => k7_group_5(A, B, C)=k5_group_4(A, k4_group_5(A, B, C))) ) ) ) ) ) ).
fof(d8_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) => k7_group_4(A, B, C)=k2_group_2(A, k8_group_2(A, B), k8_group_2(A, C))) ) ) ) ) ) ).
fof(d8_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) => k8_group_5(A, B, C)=k7_group_5(A, k8_group_2(A, B), k8_group_2(A, C))) ) ) ) ) ) ).
fof(d9_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) => k8_group_2(A, B)=u1_struct_0(B)) ) ) ) ).
fof(d9_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) => k8_group_4(A, B, C)=k5_group_4(A, k4_subset_1(u1_struct_0(A), k8_group_2(A, B), k8_group_2(A, C)))) ) ) ) ) ) ).
fof(dt_g3_algstr_0, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  =>  (v15_algstr_0(g3_algstr_0(A, B)) & l3_algstr_0(g3_algstr_0(A, B))) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_finsop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) ) ) )  => m1_subset_1(k1_finsop_1(A, B, C), 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_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_group_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k2_group_1(A, B), u1_struct_0(A))) ) ).
fof(dt_k2_group_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  => m1_subset_1(k2_group_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_group_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_group_3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_group_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_group_5(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_group_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  & m1_finseq_1(B, u1_struct_0(A)))  => m1_subset_1(k3_group_4(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_group_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_finseq_1(B, k4_numbers) & m1_finseq_1(C, u1_struct_0(A))) )  => m2_finseq_1(k4_group_4(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k4_group_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  => m1_subset_1(k4_group_5(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k5_group_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  =>  (v15_algstr_0(k5_group_4(A, B)) & m1_group_2(k5_group_4(A, B), A)) ) ) ).
fof(dt_k5_group_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_group_2(B, A) & m1_group_2(C, A)) )  => m1_subset_1(k5_group_5(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_algstr_0, axiom,  (! [A, B, C] :  ( (l3_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k6_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k6_group_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_group_2(B, A) & m1_subset_1(C, u1_struct_0(A))) )  =>  (v15_algstr_0(k6_group_3(A, B, C)) & m1_group_2(k6_group_3(A, B, C), A)) ) ) ).
fof(dt_k7_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ).
fof(dt_k7_group_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_group_2(B, A) & m1_group_2(C, A)) )  => m1_subset_1(k7_group_4(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k7_group_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (v15_algstr_0(k7_group_5(A, B, C)) & m1_group_2(k7_group_5(A, B, C), A)) ) ) ).
fof(dt_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => m2_finseq_1(k8_finseq_1(A, B, C), A)) ) ).
fof(dt_k8_group_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  & m1_group_2(B, A))  => m1_subset_1(k8_group_2(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k8_group_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_group_2(B, A) & m1_group_2(C, A)) )  =>  (v15_algstr_0(k8_group_4(A, B, C)) & m1_group_2(k8_group_4(A, B, C), A)) ) ) ).
fof(dt_k8_group_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_group_2(B, A) & m1_group_2(C, A)) )  =>  (v15_algstr_0(k8_group_5(A, B, C)) & m1_group_2(k8_group_5(A, B, C), A)) ) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_group_2(B, A) =>  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) & l3_algstr_0(B)) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & l3_algstr_0(A)) )  =>  (? [B] : m1_group_2(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(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(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(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc19_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  ( ~ (v2_struct_0(g3_algstr_0(u1_struct_0(A), u2_algstr_0(A))))  & v15_algstr_0(g3_algstr_0(u1_struct_0(A), u2_algstr_0(A)))) ) ) ).
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_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
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(fc24_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  ( ~ (v1_xboole_0(k7_finseq_1(A, B)))  & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc25_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, A)) &  (v1_funct_1(k7_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k7_finseq_1(B, A)))  & v1_finseq_1(k7_finseq_1(B, A))) ) ) ) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & l3_algstr_0(A)) )  =>  (v15_algstr_0(g3_algstr_0(u1_struct_0(A), u2_algstr_0(A))) & v3_group_1(g3_algstr_0(u1_struct_0(A), u2_algstr_0(A)))) ) ) ).
fof(fc2_group_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (v8_struct_0(C) & m1_group_2(C, A)) ) )  =>  (v8_struct_0(k6_group_3(A, C, B)) & v15_algstr_0(k6_group_3(A, C, B))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc38_finseq_1, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ( (v1_relat_1(C) &  (v1_funct_1(C) &  (v3_card_1(C, A) & v1_finseq_1(C)) ) )  &  (v1_relat_1(D) &  (v1_funct_1(D) &  (v3_card_1(D, B) & v1_finseq_1(D)) ) ) ) ) )  =>  (v1_relat_1(k7_finseq_1(C, D)) &  (v1_funct_1(k7_finseq_1(C, D)) &  (v3_card_1(k7_finseq_1(C, D), k2_xcmplx_0(A, B)) & v1_finseq_1(k7_finseq_1(C, D))) ) ) ) ) ).
fof(fc3_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (v15_algstr_0(g3_algstr_0(u1_struct_0(A), u2_algstr_0(A))) & v2_group_1(g3_algstr_0(u1_struct_0(A), u2_algstr_0(A)))) ) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & l3_algstr_0(A)) )  =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_algstr_0(A), u1_struct_0(A))) ) ) ) ).
fof(fc4_group_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  & m1_group_2(B, A))  =>  ~ (v1_xboole_0(k8_group_2(A, B))) ) ) ).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc54_finseq_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, C)) &  (v5_relat_1(k7_finseq_1(B, C), A) &  (v1_funct_1(k7_finseq_1(B, C)) & v1_finseq_1(k7_finseq_1(B, C))) ) ) ) ) ).
fof(fc55_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v6_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v6_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc56_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v5_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v5_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v5_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc5_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l3_algstr_0(A)) )  =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v1_setwiseo(u2_algstr_0(A), u1_struct_0(A))) ) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v1_finseqop(u2_algstr_0(A), u1_struct_0(A))) ) ) ) ).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(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_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_int_1, axiom,  (! [A] :  (v2_int_1(A) => v7_ordinal1(k2_xcmplx_0(A, 1))) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
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_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_3_0_group_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l3_algstr_0(B))  &  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) )  =>  (r2_hidden(A, a_3_0_group_2(B, C, D)) <=>  (? [E, F] :  ( (m1_subset_1(E, u1_struct_0(B)) & m1_subset_1(F, u1_struct_0(B)))  &  (A=k6_algstr_0(B, E, F) &  (r2_tarski(E, C) & r2_tarski(F, D)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_group_5, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  &  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) )  =>  (r2_hidden(A, a_3_0_group_5(B, C, D)) <=>  (? [E, F] :  ( (m1_subset_1(E, u1_struct_0(B)) & m1_subset_1(F, u1_struct_0(B)))  &  (A=k2_group_5(B, E, F) &  (r2_tarski(E, C) & r2_tarski(F, D)) ) ) ) ) ) ) ).
fof(free_g3_algstr_0, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  =>  (! [C, D] :  (g3_algstr_0(A, B)=g3_algstr_0(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
fof(involutiveness_k2_group_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k2_group_1(A, k2_group_1(A, B))=B) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
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(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_group_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v15_algstr_0(A) &  (v2_group_1(A) & v3_group_1(A)) ) ) ) ) ).
fof(rc1_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (? [B] :  (m1_group_2(B, A) &  ( ~ (v2_struct_0(B))  &  (v15_algstr_0(B) &  (v1_group_1(B) &  (v2_group_1(B) & v3_group_1(B)) ) ) ) ) ) ) ) ).
fof(rc1_group_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (? [B] :  (m1_group_2(B, A) &  ( ~ (v2_struct_0(B))  &  (v15_algstr_0(B) &  (v1_group_1(B) &  (v2_group_1(B) &  (v3_group_1(B) & v1_group_3(B, A)) ) ) ) ) ) ) ) ) ).
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_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_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(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (? [B] :  (m1_group_2(B, A) &  ( ~ (v2_struct_0(B))  &  (v8_struct_0(B) &  (v15_algstr_0(B) &  (v1_group_1(B) &  (v2_group_1(B) & v3_group_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(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_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_group_2, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v15_algstr_0(A) &  (v1_group_1(A) &  (v2_group_1(A) & v3_group_1(A)) ) ) ) ) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(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_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
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(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(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(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=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_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => k8_finseq_1(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_r1_group_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( (v15_algstr_0(B) & m1_group_2(B, A))  &  (v15_algstr_0(C) & m1_group_2(C, A)) ) )  =>  (r1_group_2(A, B, C) <=> B=C) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_group_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( (v15_algstr_0(B) & m1_group_2(B, A))  &  (v15_algstr_0(C) & m1_group_2(C, A)) ) )  => r1_group_2(A, B, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(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(symmetry_r1_group_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  &  ( (v15_algstr_0(B) & m1_group_2(B, A))  &  (v15_algstr_0(C) & m1_group_2(C, A)) ) )  =>  (r1_group_2(A, B, C) => r1_group_2(A, C, B)) ) ) ).
fof(t13_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (r1_tarski(A, B) & r1_tarski(C, D))  => r1_tarski(k2_xboole_0(A, C), k2_xboole_0(B, D))) ) ) ) ) ).
fof(t19_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m2_finseq_1(B, u1_struct_0(A)) =>  (! [C] :  (m2_finseq_1(C, u1_struct_0(A)) =>  (! [D] :  (m2_finseq_1(D, k4_numbers) =>  (! [E] :  (m2_finseq_1(E, k4_numbers) =>  ( (k3_finseq_1(B)=k3_finseq_1(D) & k3_finseq_1(C)=k3_finseq_1(E))  => k4_group_4(A, k8_finseq_1(k4_numbers, D, E), k8_finseq_1(u1_struct_0(A), B, C))=k8_finseq_1(u1_struct_0(A), k4_group_4(A, D, B), k4_group_4(A, E, C))) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t22_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  => k3_finseq_1(k7_finseq_1(A, B))=k1_nat_1(k3_finseq_1(A), k3_finseq_1(B))) ) ) ) ).
fof(t25_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k2_group_5(A, k6_algstr_0(A, B, C), D)=k6_algstr_0(A, k2_group_3(A, k2_group_5(A, B, D), C), k2_group_5(A, C, D))) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t31_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  => k10_xtuple_0(k7_finseq_1(A, B))=k2_xboole_0(k10_xtuple_0(A), k10_xtuple_0(B))) ) ) ) ).
fof(t32_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (r1_tarski(B, C) => m1_group_2(k5_group_4(A, B), k5_group_4(A, C))) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_group_5, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  (! [C] :  (m1_group_2(C, B) =>  (! [D] :  (m1_group_2(D, B) =>  (r2_tarski(A, k7_group_4(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (? [F] :  (m1_subset_1(F, u1_struct_0(B)) &  (A=k6_algstr_0(B, E, F) &  (r1_struct_0(C, E) & r1_struct_0(D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) => r1_group_2(A, k8_group_4(A, B, C), k5_group_4(A, k7_group_4(A, B, C)))) ) ) ) ) ) ).
fof(t52_group_5, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  (! [C] :  (m1_group_2(C, B) =>  (! [D] :  (m1_group_2(D, B) =>  (r2_tarski(A, k5_group_5(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (? [F] :  (m1_subset_1(F, u1_struct_0(B)) &  (A=k2_group_5(B, E, F) &  (r1_struct_0(C, E) & r1_struct_0(D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t54_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  => m1_group_2(A, A)) ) ).
fof(t55_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  ( (m1_group_2(A, B) & m1_group_2(B, A))  => g3_algstr_0(u1_struct_0(A), u2_algstr_0(A))=g3_algstr_0(u1_struct_0(B), u2_algstr_0(B))) ) ) ) ) ).
fof(t56_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) =>  (! [D] :  (m1_group_2(D, A) =>  (! [E] :  (m1_group_2(E, A) =>  ( (m1_group_2(B, C) & m1_group_2(D, E))  => r1_tarski(k5_group_5(A, B, D), k5_group_5(A, C, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t58_group_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) =>  ( (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_struct_0(B, D) => r1_struct_0(C, D)) ) )  => m1_group_2(B, C)) ) ) ) ) ) ) ).
fof(t58_group_3, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_group_2(D, B) =>  (r1_struct_0(k6_group_3(B, D, C), A) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=k2_group_3(B, E, C) & r1_struct_0(D, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m2_finseq_1(B, u1_struct_0(A)) =>  (! [C] :  (m2_finseq_1(C, u1_struct_0(A)) => k3_group_4(A, k8_finseq_1(u1_struct_0(A), B, C))=k6_algstr_0(A, k3_group_4(A, B), k3_group_4(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(t60_group_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_group_2(B, A) =>  (! [C] :  (m1_group_2(C, A) =>  (m1_group_2(B, k8_group_4(A, B, C)) & m1_group_2(C, k8_group_4(A, B, C))) ) ) ) ) ) ) ).
fof(t61_group_5, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) =>  (r1_struct_0(k7_group_5(B, C, D), A) <=>  (? [E] :  (m2_finseq_1(E, u1_struct_0(B)) &  (? [F] :  (m2_finseq_1(F, k4_numbers) &  (k3_finseq_1(E)=k3_finseq_1(F) &  (r1_tarski(k10_xtuple_0(E), k4_group_5(B, C, D)) & A=k3_group_4(B, k4_group_4(B, F, E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t65_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_group_2(D, A) =>  (! [E] :  (m1_group_2(E, A) =>  ( (r1_struct_0(D, B) & r1_struct_0(E, C))  => r1_struct_0(k8_group_5(A, D, E), k2_group_5(A, B, C))) ) ) ) ) ) ) ) ) ) ) ).
fof(t68_group_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  ( (v15_algstr_0(B) &  (v1_group_3(B, A) & m1_group_2(B, A)) )  =>  (! [C] :  ( (v15_algstr_0(C) &  (v1_group_3(C, A) & m1_group_2(C, A)) )  =>  (v1_group_3(k8_group_5(A, B, C), A) & m1_group_2(k8_group_5(A, B, C), A)) ) ) ) ) ) ) ).
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_group_5, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_group_1(B) &  (v3_group_1(B) & l3_algstr_0(B)) ) )  =>  (! [C] :  ( (v15_algstr_0(C) &  (v1_group_3(C, B) & m1_group_2(C, B)) )  =>  (! [D] :  ( (v15_algstr_0(D) &  (v1_group_3(D, B) & m1_group_2(D, B)) )  =>  (r1_struct_0(k8_group_4(B, C, D), A) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (? [F] :  (m1_subset_1(F, u1_struct_0(B)) &  (A=k6_algstr_0(B, E, F) &  (r1_struct_0(C, E) & r1_struct_0(D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, C) & r1_tarski(B, C))  => r1_tarski(k2_xboole_0(A, B), C)) ) ) ) ).
