% Mizar problem: t27_gr_free0,gr_free0,780,5 
fof(t27_gr_free0, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v1_group_7(C) & v2_group_7(C, A)) ) ) ) )  =>  (! [D] :  (m2_finseq_1(D, k1_gr_free0(C)) =>  (! [E] :  (m2_finseq_1(E, k1_gr_free0(C)) => r2_hidden(k4_tarski(k7_finseq_1(k7_finseq_1(D, k9_finseq_1(k4_tarski(B, k1_group_1(k1_group_7(A, C, B))))), E), k1_monoid_0(k1_gr_free0(C), D, E)), k2_gr_free0(A, C))) ) ) ) ) ) ) ) ) ) ).
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(abstractness_v22_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (v22_algstr_0(A) => A=g4_algstr_0(u1_struct_0(A), u2_algstr_0(A), u3_struct_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_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v13_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & v16_monoid_0(A)) ) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_rewrite1(A))  =>  (v1_relat_1(A) & v4_rewrite1(A)) ) ) ).
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_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (! [B] :  (m1_monoid_0(B, A) =>  ~ (v2_struct_0(B)) ) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_rewrite1(A) & v4_rewrite1(A)) )  =>  (v1_relat_1(A) & v8_rewrite1(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_monoid_0, axiom,  (! [A] :  ( (v1_monoid_0(A) & l3_algstr_0(A))  =>  (! [B] :  (m1_monoid_0(B, A) => v1_monoid_0(B)) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_rewrite1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v6_rewrite1(A)) ) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_monoid_0, axiom,  (! [A] :  ( (v2_monoid_0(A) & l3_algstr_0(A))  =>  (! [B] :  (m1_monoid_0(B, A) => v2_monoid_0(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_rewrite1(A) & v9_rewrite1(A)) )  =>  (v1_relat_1(A) & v7_rewrite1(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_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_monoid_0(B, A) => v1_group_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v10_rewrite1(A))  =>  (v1_relat_1(A) &  (v3_rewrite1(A) & v7_rewrite1(A)) ) ) ) ).
fof(cc15_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_monoid_0(B, A) => v3_group_1(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_rewrite1(A) & v7_rewrite1(A)) )  =>  (v1_relat_1(A) & v10_rewrite1(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_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_monoid_0(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_monoid_0(B, A) => v13_monoid_0(B)) ) ) ) ).
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_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v16_monoid_0(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_monoid_0(B, A) => v16_monoid_0(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v17_monoid_0(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_monoid_0(B, A) => v17_monoid_0(B)) ) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_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_algstr_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) =>  ( (v1_partfun1(B, u1_struct_0(A)) &  (v3_relat_2(B) & v8_relat_2(B)) )  =>  (v1_partfun1(B, u1_struct_0(A)) &  (v3_relat_2(B) &  (v8_relat_2(B) & v1_algstr_4(B, 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_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v2_group_1(A) => v1_group_1(A)) ) ) ).
fof(cc1_group_7, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_group_7(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_pralg_1(A)) ) ) ) ).
fof(cc1_monoid_0, axiom,  (! [A] :  ( (v1_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
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(cc1_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc1_pre_poly, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k3_finseq_2(A)) => v1_finseq_1(B)) ) ) ).
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_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_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(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_facirc_2, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v1_xtuple_0(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_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v2_struct_0(A) => v3_group_1(A)) ) ) ).
fof(cc2_monoid_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_monoid_0(A) => v1_monoid_0(A)) ) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v2_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, 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_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_rewrite1(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) & v1_rewrite1(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_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_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(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_facirc_2, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_facirc_1(A)) ) ) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_monoid_0, axiom,  (! [A] :  ( (v2_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v1_finseq_1(B)) ) ) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_pre_poly, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, k3_finseq_2(A)) => v1_pre_poly(B)) ) ) ).
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_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_2(A) & v1_rewrite1(A)) )  =>  (v1_relat_1(A) & v3_rewrite1(A)) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
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_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_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & v3_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v13_monoid_0(A)) ) ) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc4_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(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_rewrite1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) &  (v2_rewrite1(A) & v3_rewrite1(A)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(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_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_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_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v13_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v2_group_1(A)) ) ) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc5_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(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_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_rewrite1(A))  =>  (v1_relat_1(A) & v2_rewrite1(A)) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(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_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(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_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v13_monoid_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v11_monoid_0(A) & v12_monoid_0(A)) ) ) ) ) ).
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(cc6_pre_poly, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v1_card_3(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_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_rewrite1(A))  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(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_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(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_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v11_monoid_0(A) & v12_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v13_monoid_0(A)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_pre_poly(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(cc7_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v7_rewrite1(A))  =>  (v1_relat_1(A) &  (v8_rewrite1(A) & v9_rewrite1(A)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_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_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(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_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_group_7, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_group_7(B)) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_partfun1(B, A) & v1_group_7(B)) ) ) ) ) ) ) ) ) ).
fof(cc8_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v16_monoid_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v14_monoid_0(A) & v15_monoid_0(A)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_pre_poly, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_pre_poly(B)) ) ) ) ) ) ) ) ).
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(cc8_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_rewrite1(A))  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
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(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_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_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v14_monoid_0(A) & v15_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v16_monoid_0(A)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_rewrite1(A))  =>  (v1_relat_1(A) & v5_rewrite1(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(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(d18_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k6_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u2_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d1_gr_free0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_group_7(A)) )  => k1_gr_free0(A)=k5_waybel26(k13_pralg_1(A))) ) ).
fof(d3_gr_free0, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_group_7(B) & v2_group_7(B, A)) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k10_monoid_0(k1_gr_free0(B))), u1_struct_0(k10_monoid_0(k1_gr_free0(B)))))) =>  (C=k2_gr_free0(A, B) <=>  (! [D] :  (m2_finseq_1(D, k1_gr_free0(B)) =>  (! [E] :  (m2_finseq_1(E, k1_gr_free0(B)) =>  (r2_hidden(k4_tarski(D, E), C) <=>  ~ ( ( (! [F] :  (m2_finseq_1(F, k1_gr_free0(B)) =>  (! [G] :  (m2_finseq_1(G, k1_gr_free0(B)) =>  (! [H] :  (m1_subset_1(H, A) =>  ~ ( (D=k7_finseq_1(k7_finseq_1(F, k9_finseq_1(k4_tarski(H, k1_group_1(k1_group_7(A, B, H))))), G) & E=k1_monoid_0(k1_gr_free0(B), F, G)) ) ) ) ) ) ) )  &  (! [F] :  (m2_finseq_1(F, k1_gr_free0(B)) =>  (! [G] :  (m2_finseq_1(G, k1_gr_free0(B)) =>  (! [H] :  (m1_subset_1(H, A) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k1_group_7(A, B, H))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k1_group_7(A, B, H))) =>  ~ ( (D=k7_finseq_1(k7_finseq_1(F, k10_finseq_1(k4_tarski(H, I), k4_tarski(H, J))), G) & E=k7_finseq_1(k7_finseq_1(F, k9_finseq_1(k4_tarski(H, k6_algstr_0(k1_group_7(A, B, H), I, J)))), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_waybel26, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => k5_waybel26(A)=k2_relat_1(k3_card_3(k2_card_3(A)))) ) ).
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_g4_algstr_0, axiom,  (! [A, B, C] :  ( ( (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)))) )  & m1_subset_1(C, A))  =>  (v22_algstr_0(g4_algstr_0(A, B, C)) & l4_algstr_0(g4_algstr_0(A, B, C))) ) ) ).
fof(dt_k10_finseq_1, axiom, $true).
fof(dt_k10_monoid_0, axiom,  (! [A] :  ( ~ (v2_struct_0(k10_monoid_0(A)))  &  (v22_algstr_0(k10_monoid_0(A)) &  (v4_vectsp_1(k10_monoid_0(A)) & m1_monoid_0(k10_monoid_0(A), k9_monoid_0(A))) ) ) ) ).
fof(dt_k12_finseq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m2_finseq_1(k12_finseq_1(A, B), A)) ) ).
fof(dt_k13_finseq_1, axiom, $true).
fof(dt_k13_pralg_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_pralg_1(A)) )  =>  (v1_relat_1(k13_pralg_1(A)) & v1_funct_1(k13_pralg_1(A))) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_gr_free0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_group_7(A)) )  => v1_relat_1(k1_gr_free0(A))) ) ).
fof(dt_k1_group_1, axiom,  (! [A] :  (l3_algstr_0(A) => m1_subset_1(k1_group_1(A), u1_struct_0(A))) ) ).
fof(dt_k1_group_7, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_group_7(B)) ) ) )  & m1_subset_1(C, A)) )  =>  ( ~ (v2_struct_0(k1_group_7(A, B, C)))  & l3_algstr_0(k1_group_7(A, B, C))) ) ) ).
fof(dt_k1_monoid_0, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => m2_finseq_2(k1_monoid_0(A, B, C), A, k3_finseq_2(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A))) ) ) ).
fof(dt_k2_gr_free0, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_group_7(B) & v2_group_7(B, A)) ) ) ) )  => m1_subset_1(k2_gr_free0(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k10_monoid_0(k1_gr_free0(B))), u1_struct_0(k10_monoid_0(k1_gr_free0(B))))))) ) ).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(A))) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_finseq_2, axiom,  (! [A] : m1_finseq_2(k3_finseq_2(A), A)) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (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)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_finseq_1, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k5_waybel26, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v1_relat_1(k5_waybel26(A))) ) ).
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_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_k9_finseq_1, axiom,  (! [A] :  (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A))) ) ).
fof(dt_k9_monoid_0, axiom,  (! [A] :  ( ~ (v2_struct_0(k9_monoid_0(A)))  &  (v15_algstr_0(k9_monoid_0(A)) &  (v1_group_1(k9_monoid_0(A)) &  (v3_group_1(k9_monoid_0(A)) &  (v2_monoid_0(k9_monoid_0(A)) &  (v16_monoid_0(k9_monoid_0(A)) &  (v17_monoid_0(k9_monoid_0(A)) & l3_algstr_0(k9_monoid_0(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_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_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_finseq_2, axiom, $true).
fof(dt_m1_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (! [B] :  (m1_monoid_0(B, A) => l4_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_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) => m2_finseq_1(C, A)) ) ) ) ).
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(dt_u3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(u3_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_l3_struct_0, axiom,  (? [A] : l3_struct_0(A)) ).
fof(existence_l4_algstr_0, axiom,  (? [A] : l4_algstr_0(A)) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, A)) ) ).
fof(existence_m1_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (? [B] : m1_monoid_0(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(existence_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (? [C] : m2_finseq_2(C, A, B)) ) ) ).
fof(fc10_finseq_1, axiom,  (! [A, B] : v1_finseq_1(k10_finseq_1(A, B))) ).
fof(fc10_group_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & l3_algstr_0(A)) )  => v2_group_7(k5_finseq_1(A), k1_tarski(1))) ) ).
fof(fc10_pre_poly, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_card_3(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_card_3(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v1_card_3(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
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_group_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & l3_algstr_0(A)) )  => v3_group_7(k5_finseq_1(A), k1_tarski(1))) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
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_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k13_finseq_1(A))) ) ).
fof(fc12_nat_1, axiom,  (! [A, B] :  ( ( ~ (v8_ordinal1(A))  &  ~ (v8_ordinal1(B)) )  => v1_setfam_1(k2_tarski(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_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_group_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l3_algstr_0(B)) )  => v4_relat_1(k10_finseq_1(A, B), k2_tarski(1, 2))) ) ).
fof(fc13_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_2(A))  =>  (v1_relat_1(k2_relat_1(A)) & v5_relat_2(k2_relat_1(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_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc14_group_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l3_algstr_0(B)) )  =>  (v1_partfun1(k10_finseq_1(A, B), k2_tarski(1, 2)) & v1_group_7(k10_finseq_1(A, B))) ) ) ).
fof(fc14_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v1_pre_poly(k5_finseq_1(A))) ) ).
fof(fc14_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(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_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => v4_funct_1(k2_tarski(A, B))) ) ).
fof(fc15_group_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & l3_algstr_0(A)) )  &  ( ~ (v2_struct_0(B))  &  (v2_group_1(B) & l3_algstr_0(B)) ) )  => v2_group_7(k10_finseq_1(A, B), k2_tarski(1, 2))) ) ).
fof(fc15_pre_poly, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v1_pre_poly(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_finseq_1(B) & v1_pre_poly(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)) & v1_pre_poly(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc16_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
fof(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(A))) ) ).
fof(fc16_group_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & l3_algstr_0(A)) )  &  ( ~ (v2_struct_0(B))  &  (v3_group_1(B) & l3_algstr_0(B)) ) )  => v3_group_7(k10_finseq_1(A, B), k2_tarski(1, 2))) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_relat_2(A))  =>  (v1_relat_1(k2_relat_1(A)) & v4_relat_2(k2_relat_1(A))) ) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(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_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc1_gr_cy_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(fc1_gr_free0, axiom,  ( ~ (v2_struct_0(k9_monoid_0(k1_xboole_0)))  &  (v7_struct_0(k9_monoid_0(k1_xboole_0)) &  (v15_algstr_0(k9_monoid_0(k1_xboole_0)) &  (v1_group_1(k9_monoid_0(k1_xboole_0)) &  (v3_group_1(k9_monoid_0(k1_xboole_0)) &  (v2_monoid_0(k9_monoid_0(k1_xboole_0)) &  (v16_monoid_0(k9_monoid_0(k1_xboole_0)) & v17_monoid_0(k9_monoid_0(k1_xboole_0))) ) ) ) ) ) ) ).
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_group_12, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_group_7(B) & v2_group_7(B, A)) ) ) ) )  & m1_subset_1(C, A)) )  => v2_group_1(k1_funct_1(B, C))) ) ).
fof(fc1_group_7, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_group_7(B)) ) ) )  =>  (v1_relat_1(k13_pralg_1(B)) &  (v2_relat_1(k13_pralg_1(B)) & v1_funct_1(k13_pralg_1(B))) ) ) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
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(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(fc21_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_relat_2(A))  =>  (v1_relat_1(k2_relat_1(A)) & v8_relat_2(k2_relat_1(A))) ) ) ).
fof(fc23_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k5_finseq_1(A))) ) ).
fof(fc23_group_7, axiom, v1_group_7(k1_xboole_0)).
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(fc25_funcop_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) & v1_funct_1(k1_binop_1(A, B, C))) ) ) ).
fof(fc26_finseq_1, axiom,  (! [A, B] :  ~ (v1_xboole_0(k10_finseq_1(A, B))) ) ).
fof(fc26_group_7, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v1_group_7(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_finseq_1(B) & v1_group_7(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)) & v1_group_7(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc2_facirc_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_facirc_1(A)) )  =>  ~ (v1_xtuple_0(k1_funct_1(A, B))) ) ) ).
fof(fc2_gr_free0, axiom,  ( ~ (v2_struct_0(k10_monoid_0(k1_xboole_0)))  &  (v7_struct_0(k10_monoid_0(k1_xboole_0)) &  (v22_algstr_0(k10_monoid_0(k1_xboole_0)) & v4_vectsp_1(k10_monoid_0(k1_xboole_0))) ) ) ).
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_12, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_group_7(B) & v3_group_7(B, A)) ) ) ) )  & m1_subset_1(C, A)) )  => v3_group_1(k1_funct_1(B, C))) ) ).
fof(fc2_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  & m1_subset_1(C, A)) )  =>  ~ (v1_xboole_0(k1_funct_1(B, C))) ) ) ).
fof(fc2_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_relat_2(A))  =>  (v1_relat_1(k2_relat_1(A)) & v1_relat_2(k2_relat_1(A))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc31_finseq_1, axiom,  (! [A] : v4_funct_1(k13_finseq_1(A))) ).
fof(fc32_finseq_1, axiom,  (! [A] : v3_card_1(k5_finseq_1(A), 1)) ).
fof(fc33_finseq_1, axiom,  (! [A, B] : v3_card_1(k10_finseq_1(A, B), 2)) ).
fof(fc35_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc37_finseq_1, axiom,  (! [A] : v4_finseq_1(k13_finseq_1(A))) ).
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(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_gr_free0, axiom,  (v1_relat_1(k1_gr_free0(k1_xboole_0)) & v1_xboole_0(k1_gr_free0(k1_xboole_0))) ).
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(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc3_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_relat_2(A))  =>  (v1_relat_1(k2_relat_1(A)) & v2_relat_2(k2_relat_1(A))) ) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_gr_free0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_group_7(A)) ) )  =>  (v1_relat_1(k1_gr_free0(A)) &  ~ (v1_xboole_0(k1_gr_free0(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_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, 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(fc58_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v3_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc59_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v1_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  =>  (v1_relat_1(k2_relat_1(A)) & v1_funct_1(k2_relat_1(A))) ) ) ).
fof(fc5_gr_free0, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_group_7(B) & v2_group_7(B, A)) ) ) ) ) )  =>  (v1_relat_1(k1_gr_free0(B)) &  ~ (v1_xboole_0(k1_gr_free0(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_monoid_0, axiom,  (! [A] : v4_finseq_1(u1_struct_0(k9_monoid_0(A)))) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc60_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v2_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc61_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v6_valued_0(k5_finseq_1(A))) ) ).
fof(fc64_finseq_1, axiom,  (! [A] :  (v1_xreal_0(A) => v3_valued_0(k5_finseq_1(A))) ) ).
fof(fc65_finseq_1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_valued_0(k5_finseq_1(A))) ) ).
fof(fc66_finseq_1, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_valued_0(k5_finseq_1(A))) ) ).
fof(fc67_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(k2_card_3(A)) &  (v1_funct_1(k2_card_3(A)) & v1_finseq_1(k2_card_3(A))) ) ) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_finseq_1, axiom,  (! [A] :  (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A))) ) ).
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_monoid_0, axiom,  (! [A] : v4_finseq_1(u1_struct_0(k10_monoid_0(A)))) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
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_finseq_1, axiom,  (! [A] : v1_finseq_1(k5_finseq_1(A))) ).
fof(fc7_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  ~ (v4_group_1(k1_group_1(A), A)) ) ) ).
fof(fc7_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_finseq_1, axiom,  (! [A, B] :  (v1_relat_1(k10_finseq_1(A, B)) & v1_funct_1(k10_finseq_1(A, B))) ) ).
fof(fc8_group_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  => v4_relat_1(k5_finseq_1(A), k1_tarski(1))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_pre_poly, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(A)) )  => v1_finseq_1(k1_funct_1(A, B))) ) ).
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_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_group_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (v1_partfun1(k5_finseq_1(A), k1_tarski(1)) & v1_group_7(k5_finseq_1(A))) ) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_relat_2(A))  =>  (v1_relat_1(k2_relat_1(A)) & v3_relat_2(k2_relat_1(A))) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(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(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(free_g4_algstr_0, axiom,  (! [A, B, C] :  ( ( (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)))) )  & m1_subset_1(C, A))  =>  (! [D, E, F] :  (g4_algstr_0(A, B, C)=g4_algstr_0(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(ie10_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l4_algstr_0(A)) )  => k1_group_1(A)=k5_struct_0(A)) ) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=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(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(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(rc12_pre_poly, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v6_valued_0(A) & v2_pre_poly(A)) ) ) ) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc14_pre_poly, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v6_valued_0(B) & v2_pre_poly(B)) ) ) ) ) ) ) ).
fof(rc15_finseq_1, axiom,  (! [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) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
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_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_algstr_4, axiom,  (? [A] :  (l3_algstr_0(A) & v2_struct_0(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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
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_7, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_group_7(B)) ) ) ) ) ) ).
fof(rc1_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v1_monoid_0(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, 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_rewrite1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) & v10_rewrite1(A)) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_tops_5, axiom,  (! [A, B] :  (? [C] :  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v2_funct_1(C)) ) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_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_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_algstr_4, axiom,  (! [A] :  (l3_algstr_0(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v5_relat_1(B, u1_struct_0(A)) &  (v1_partfun1(B, u1_struct_0(A)) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) &  (v1_relat_2(B) &  (v3_relat_2(B) &  (v8_relat_2(B) & v1_algstr_4(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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_group_7, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_group_7(A)) ) ) ).
fof(rc2_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v2_monoid_0(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(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_tops_5, axiom,  (? [A] :  (v1_relat_1(A) &  ( ~ (v2_relat_1(A))  & v1_funct_1(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_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_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_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
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_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, 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(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_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(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_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_group_7, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finseq_1(A) & v1_group_7(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_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funcop_1(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(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_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_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (? [B] :  (m1_monoid_0(B, A) & v22_algstr_0(B)) ) ) ) ).
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_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(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_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_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_monoid_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l3_algstr_0(A)) )  =>  (? [B] :  (m1_monoid_0(B, A) &  ( ~ (v2_struct_0(B))  &  (v22_algstr_0(B) &  (v4_vectsp_1(B) & v1_group_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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_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(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_pboole, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, B)) ) ) ) ) ) ) ).
fof(rc7_pre_poly, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(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(rc8_pre_poly, axiom,  (? [A] :  (v4_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(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_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_finseq_1, axiom,  (! [A] : k1_funct_1(k9_finseq_1(A), 1)=A) ).
fof(rd2_finseq_1, axiom,  (! [A, B] : k1_funct_1(k10_finseq_1(A, B), 1)=A) ).
fof(rd3_finseq_1, axiom,  (! [A, B] : k1_funct_1(k10_finseq_1(A, B), 2)=B) ).
fof(rd7_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd8_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(A), B)=B) ) ).
fof(redefinition_k12_finseq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k12_finseq_1(A, B)=k5_finseq_1(B)) ) ).
fof(redefinition_k1_group_7, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_group_7(B)) ) ) )  & m1_subset_1(C, A)) )  => k1_group_7(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k1_monoid_0, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => k1_monoid_0(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k3_finseq_2, axiom,  (! [A] : k3_finseq_2(A)=k13_finseq_1(A)) ).
fof(redefinition_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (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)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k9_finseq_1, axiom,  (! [A] : k9_finseq_1(A)=k5_finseq_1(A)) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
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(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
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(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(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(t74_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) => m2_finseq_1(k12_finseq_1(A, B), A)) ) ) ) ).
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)) ) ) ) ) ).
fof(t8_gr_free0, axiom,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, B) =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, B) &  (v1_funct_1(D) &  (v1_partfun1(D, B) & v1_group_7(D)) ) ) )  =>  (r2_hidden(k4_tarski(C, A), k1_gr_free0(D)) <=> r2_hidden(A, u1_struct_0(k1_group_7(B, D, C)))) ) ) ) ) ) ) ) ).
