% Mizar problem: t46_limfunc2,limfunc2,2765,5 
fof(t46_limfunc2, conjecture,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  =>  ( (r1_limfunc2(B, A) &  (r1_limfunc2(C, A) &  (! [D] :  (v1_xreal_0(D) =>  ~ ( ( ~ (r1_xxreal_0(A, D))  &  (! [E] :  (v1_xreal_0(E) =>  ~ ( ( ~ (r1_xxreal_0(E, D))  &  ( ~ (r1_xxreal_0(A, E))  & r2_hidden(E, k1_relset_1(k1_numbers, k47_valued_1(k1_numbers, k1_numbers, k1_numbers, B, C)))) ) ) ) ) ) ) ) ) ) )  =>  (r1_limfunc2(k47_valued_1(k1_numbers, k1_numbers, k1_numbers, B, C), A) & k1_limfunc2(k47_valued_1(k1_numbers, k1_numbers, k1_numbers, B, C), A)=k6_xcmplx_0(k1_limfunc2(B, A), k1_limfunc2(C, 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_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_0(B)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_0(B)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_0(B)) ) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_0(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_0(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_0(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc16_valued_0, axiom,  (! [A, B] :  (v1_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_valued_0(C)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_valued_0, axiom,  (! [A, B] :  (v2_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v2_valued_0(C)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc18_valued_0, axiom,  (! [A, B] :  (v3_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v3_valued_0(C)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc19_valued_0, axiom,  (! [A, B] :  (v4_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v4_valued_0(C)) ) ) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(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_seq_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_comseq_2(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) &  (v1_seq_2(A) & v2_seq_2(A)) ) ) ) ) ) ).
fof(cc1_seq_4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers))) =>  ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) &  (v9_valued_0(A) & v1_seq_2(A)) ) )  =>  (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) & v2_comseq_2(A)) ) ) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc20_valued_0, axiom,  (! [A, B] :  (v5_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v5_valued_0(C)) ) ) ) ).
fof(cc21_valued_0, axiom,  (! [A, B] :  (v6_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v6_valued_0(C)) ) ) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_zfmisc_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v7_valued_0(A) & v8_valued_0(A)) ) ) ) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) ) ) ) ).
fof(cc28_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k2_numbers))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc29_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k2_numbers)) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(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_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_seq_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) &  (v1_seq_2(A) & v2_seq_2(A)) ) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_comseq_2(A)) ) ) ) ) ).
fof(cc2_seq_4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers))) =>  ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) &  (v10_valued_0(A) & v2_seq_2(A)) ) )  =>  (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) & v2_comseq_2(A)) ) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k6_numbers))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k6_numbers)) ) ) ).
fof(cc32_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc33_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k1_numbers)) ) ) ).
fof(cc34_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc35_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc36_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc37_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc38_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc39_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1)) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
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_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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc40_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k2_numbers)) ) ) ) ) ).
fof(cc41_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v1_valued_0(B)) ) ) ) ) ).
fof(cc42_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k6_numbers)) ) ) ) ) ).
fof(cc43_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v2_valued_0(B)) ) ) ) ) ).
fof(cc44_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k1_numbers)) ) ) ) ) ).
fof(cc45_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v3_valued_0(B)) ) ) ) ) ).
fof(cc46_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k3_numbers)) ) ) ) ) ).
fof(cc47_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v4_valued_0(B)) ) ) ) ) ).
fof(cc48_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_numbers)) ) ) ) ) ).
fof(cc49_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_valued_0(B)) ) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(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_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_seq_2, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers))) =>  ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) & v2_comseq_2(A)) )  =>  (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) & v1_comseq_2(A)) ) ) ) ) ).
fof(cc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc50_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_ordinal1)) ) ) ) ) ).
fof(cc51_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v6_valued_0(B)) ) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(commutativity_k1_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  => k1_valued_1(A, B)=k1_valued_1(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_k3_valued_1, axiom,  (! [A, B, C, D, E] :  ( (v3_membered(B) &  (v3_membered(C) &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) )  => k3_valued_1(A, B, C, D, E)=k3_valued_1(A, B, C, E, D)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d10_prob_1, axiom,  (! [A] :  (v1_xxreal_0(A) => k10_prob_1(A)=k4_xxreal_1(k2_xxreal_0, A)) ) ).
fof(d1_limfunc2, axiom,  (! [A] :  ( (v1_funct_1(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  =>  (! [B] :  (v1_xreal_0(B) =>  (r1_limfunc2(A, B) <=>  ( (! [C] :  (v1_xreal_0(C) =>  ~ ( ( ~ (r1_xxreal_0(B, C))  &  (! [D] :  (v1_xreal_0(D) =>  ~ ( ( ~ (r1_xxreal_0(D, C))  &  ( ~ (r1_xxreal_0(B, D))  & r2_hidden(D, k1_relset_1(k1_numbers, A))) ) ) ) ) ) ) ) )  &  (? [C] :  (v1_xreal_0(C) &  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k1_numbers) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) )  =>  ( (v2_comseq_2(D) &  (k1_seq_2(D)=B & r1_tarski(k2_relset_1(k1_numbers, D), k9_subset_1(k1_numbers, k1_relset_1(k1_numbers, A), k10_prob_1(B)))) )  =>  (v2_comseq_2(k8_funct_2(k4_ordinal1, k1_numbers, k1_numbers, D, A)) & k1_seq_2(k8_funct_2(k4_ordinal1, k1_numbers, k1_numbers, D, A))=C) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => k30_valued_1(A)=k24_valued_1(A, k4_xcmplx_0(1))) ) ).
fof(d9_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) )  => k45_valued_1(A, B)=k1_valued_1(A, k30_valued_1(B))) ) ) ) ).
fof(dt_k10_prob_1, axiom,  (! [A] :  (v1_xxreal_0(A) => m1_subset_1(k10_prob_1(A), k1_zfmisc_1(k1_numbers))) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_limfunc2, axiom,  (! [A, B] :  ( ( (v1_funct_1(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  & v1_xreal_0(B))  => v1_xreal_0(k1_limfunc2(A, B))) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_seq_2, axiom,  (! [A] :  ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) )  => v1_xreal_0(k1_seq_2(A))) ) ).
fof(dt_k1_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) & v1_funct_1(k1_valued_1(A, B))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k24_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  & v1_xcmplx_0(B))  =>  (v1_relat_1(k24_valued_1(A, B)) & v1_funct_1(k24_valued_1(A, B))) ) ) ).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xxreal_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k30_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v1_funct_1(k30_valued_1(A)) & v1_valued_0(k30_valued_1(A))) ) ) ) ).
fof(dt_k32_valued_1, axiom,  (! [A, B, C] :  ( (v3_membered(B) &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (v1_funct_1(k32_valued_1(A, B, C)) & m1_subset_1(k32_valued_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_valued_1, axiom,  (! [A, B, C, D, E] :  ( (v3_membered(B) &  (v3_membered(C) &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) )  =>  (v1_funct_1(k3_valued_1(A, B, C, D, E)) & m1_subset_1(k3_valued_1(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k45_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  =>  (v1_relat_1(k45_valued_1(A, B)) & v1_funct_1(k45_valued_1(A, B))) ) ) ).
fof(dt_k47_valued_1, axiom,  (! [A, B, C, D, E] :  ( (v3_membered(B) &  (v3_membered(C) &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) )  =>  (v1_funct_1(k47_valued_1(A, B, C, D, E)) & m1_subset_1(k47_valued_1(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k4_xxreal_1, axiom, $true).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k8_funct_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  &  (v1_relat_1(E) &  (v5_relat_1(E, B) & v1_funct_1(E)) ) ) )  =>  (v1_funct_1(k8_funct_2(A, B, C, D, E)) &  (v1_funct_2(k8_funct_2(A, B, C, D, E), A, B) & m1_subset_1(k8_funct_2(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc108_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_relat_1(A, k4_ordinal1))  => v6_membered(k9_xtuple_0(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v5_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v5_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k1_valued_1(D, E)) & v1_partfun1(k1_valued_1(D, E), A)) ) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc111_valued_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  =>  (v1_relat_1(k30_valued_1(B)) &  (v4_relat_1(k30_valued_1(B), A) &  (v1_funct_1(k30_valued_1(B)) & v1_valued_0(k30_valued_1(B))) ) ) ) ) ).
fof(fc115_valued_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_valued_0(B)) ) ) )  =>  (v1_relat_1(k30_valued_1(B)) &  (v1_funct_1(k30_valued_1(B)) &  (v1_partfun1(k30_valued_1(B), A) & v1_valued_0(k30_valued_1(B))) ) ) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v6_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v6_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k1_valued_1(D, E)) & v1_partfun1(k1_valued_1(D, E), 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(fc121_valued_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  & v1_xcmplx_0(C))  =>  (v1_relat_1(k24_valued_1(B, C)) &  (v4_relat_1(k24_valued_1(B, C), A) & v1_funct_1(k24_valued_1(B, C))) ) ) ) ).
fof(fc124_valued_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_valued_0(B)) ) ) )  & v1_xcmplx_0(C))  =>  (v1_relat_1(k24_valued_1(B, C)) &  (v1_funct_1(k24_valued_1(B, C)) & v1_partfun1(k24_valued_1(B, C), A)) ) ) ) ).
fof(fc125_valued_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_valued_0(C)) ) ) )  =>  (v1_relat_1(k1_valued_1(B, C)) &  (v4_relat_1(k1_valued_1(B, C), A) & v1_funct_1(k1_valued_1(B, C))) ) ) ) ).
fof(fc126_valued_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_valued_0(C)) ) ) )  =>  (v1_relat_1(k45_valued_1(B, C)) &  (v4_relat_1(k45_valued_1(B, C), A) & v1_funct_1(k45_valued_1(B, C))) ) ) ) ).
fof(fc129_valued_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_valued_0(B)) ) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) & v1_valued_0(C)) ) ) ) )  =>  (v1_relat_1(k1_valued_1(B, C)) &  (v1_funct_1(k1_valued_1(B, C)) & v1_partfun1(k1_valued_1(B, C), A)) ) ) ) ).
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(fc130_valued_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_valued_0(B)) ) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) & v1_valued_0(C)) ) ) ) )  =>  (v1_relat_1(k45_valued_1(B, C)) &  (v1_funct_1(k45_valued_1(B, C)) & v1_partfun1(k45_valued_1(B, C), A)) ) ) ) ).
fof(fc13_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  & v1_relat_1(B))  => v1_valued_0(k3_xboole_0(A, B))) ) ).
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_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_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  & v1_relat_1(B))  => v2_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc17_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  & v1_relat_1(B))  => v3_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc17_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(A, B))) ) ) ).
fof(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, A))) ) ) ).
fof(fc19_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  & v1_relat_1(B))  => v4_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc19_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_seq_2, axiom,  (! [A, B] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) &  (v2_comseq_2(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) ) )  &  (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k1_numbers) &  (v2_comseq_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) ) ) )  =>  (v1_funct_1(k1_valued_1(A, B)) &  (v1_funct_2(k1_valued_1(A, B), k4_ordinal1, k1_numbers) & v2_comseq_2(k1_valued_1(A, B))) ) ) ) ).
fof(fc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  => v1_membered(k10_xtuple_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xreal_0, axiom,  ~ (v1_xreal_0(k2_xxreal_0)) ).
fof(fc20_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  & v1_relat_1(B))  => v5_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc23_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  & v1_relat_1(B))  => v6_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
fof(fc2_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_seq_2, axiom,  (! [A, B] :  ( (v1_xreal_0(A) &  (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k1_numbers) &  (v2_comseq_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) ) ) )  =>  (v1_funct_1(k24_valued_1(B, A)) &  (v1_funct_2(k24_valued_1(B, A), k4_ordinal1, k1_numbers) & v2_comseq_2(k24_valued_1(B, A))) ) ) ) ).
fof(fc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  => v2_membered(k10_xtuple_0(A))) ) ).
fof(fc2_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) &  (v1_funct_1(k1_valued_1(A, B)) & v1_valued_0(k1_valued_1(A, B))) ) ) ) ).
fof(fc31_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(A, B))) ) ).
fof(fc32_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(B, A))) ) ).
fof(fc33_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(A, B))) ) ).
fof(fc34_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(B, A))) ) ).
fof(fc35_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(A, B))) ) ).
fof(fc36_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(B, A))) ) ).
fof(fc37_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(A, B))) ) ).
fof(fc38_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(B, A))) ) ).
fof(fc39_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(A, B))) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_seq_2, axiom,  (! [A] :  ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) &  (v2_comseq_2(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) ) )  =>  (v1_funct_1(k30_valued_1(A)) &  (v1_funct_2(k30_valued_1(A), k4_ordinal1, k1_numbers) & v2_comseq_2(k30_valued_1(A))) ) ) ) ).
fof(fc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  => v3_membered(k10_xtuple_0(A))) ) ).
fof(fc3_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) &  (v1_funct_1(k1_valued_1(A, B)) & v3_valued_0(k1_valued_1(A, B))) ) ) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc40_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(B, A))) ) ).
fof(fc41_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(A, B))) ) ).
fof(fc42_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(B, A))) ) ).
fof(fc44_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  & v1_xcmplx_0(B))  =>  (v1_relat_1(k24_valued_1(A, B)) &  (v1_funct_1(k24_valued_1(A, B)) & v1_valued_0(k24_valued_1(A, B))) ) ) ) ).
fof(fc45_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  & v1_xreal_0(B))  =>  (v1_relat_1(k24_valued_1(A, B)) &  (v1_funct_1(k24_valued_1(A, B)) & v3_valued_0(k24_valued_1(A, B))) ) ) ) ).
fof(fc46_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  & v1_rat_1(B))  =>  (v1_relat_1(k24_valued_1(A, B)) &  (v5_relat_1(k24_valued_1(A, B), k3_numbers) & v1_funct_1(k24_valued_1(A, B))) ) ) ) ).
fof(fc47_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  & v1_int_1(B))  =>  (v1_relat_1(k24_valued_1(A, B)) &  (v5_relat_1(k24_valued_1(A, B), k4_numbers) & v1_funct_1(k24_valued_1(A, B))) ) ) ) ).
fof(fc48_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  & v7_ordinal1(B))  =>  (v1_relat_1(k24_valued_1(A, B)) &  (v1_funct_1(k24_valued_1(A, B)) & v6_valued_0(k24_valued_1(A, B))) ) ) ) ).
fof(fc49_valued_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  & v1_membered(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & v1_xcmplx_0(D)) )  =>  (v1_funct_1(k24_valued_1(C, D)) & v1_partfun1(k24_valued_1(C, D), A)) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_seq_2, axiom,  (! [A, B] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k1_numbers) &  (v2_comseq_2(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) ) )  &  (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k1_numbers) &  (v2_comseq_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers)))) ) ) )  =>  (v1_funct_1(k45_valued_1(A, B)) &  (v1_funct_2(k45_valued_1(A, B), k4_ordinal1, k1_numbers) & v2_comseq_2(k45_valued_1(A, B))) ) ) ) ).
fof(fc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  => v4_membered(k10_xtuple_0(A))) ) ).
fof(fc4_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v4_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) &  (v5_relat_1(k1_valued_1(A, B), k3_numbers) & v1_funct_1(k1_valued_1(A, B))) ) ) ) ).
fof(fc50_valued_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  & v3_membered(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & v1_xreal_0(D)) )  =>  (v1_funct_1(k24_valued_1(C, D)) & v1_partfun1(k24_valued_1(C, D), A)) ) ) ).
fof(fc51_valued_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  & v4_membered(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & v1_rat_1(D)) )  =>  (v1_funct_1(k24_valued_1(C, D)) & v1_partfun1(k24_valued_1(C, D), A)) ) ) ).
fof(fc52_valued_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  & v5_membered(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & v1_int_1(D)) )  =>  (v1_funct_1(k24_valued_1(C, D)) & v1_partfun1(k24_valued_1(C, D), A)) ) ) ).
fof(fc53_valued_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  & v6_membered(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & v7_ordinal1(D)) )  =>  (v1_funct_1(k24_valued_1(C, D)) & v1_partfun1(k24_valued_1(C, D), A)) ) ) ).
fof(fc55_membered, axiom, v7_membered(k2_numbers)).
fof(fc55_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v1_funct_1(k30_valued_1(A)) & v1_valued_0(k30_valued_1(A))) ) ) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc56_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v1_funct_1(k30_valued_1(A)) &  (v1_valued_0(k30_valued_1(A)) & v3_valued_0(k30_valued_1(A))) ) ) ) ) ).
fof(fc57_membered, axiom, v7_membered(k3_numbers)).
fof(fc57_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v5_relat_1(k30_valued_1(A), k3_numbers) &  (v1_funct_1(k30_valued_1(A)) & v1_valued_0(k30_valued_1(A))) ) ) ) ) ).
fof(fc58_membered, axiom, v7_membered(k4_numbers)).
fof(fc58_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v5_relat_1(k30_valued_1(A), k4_numbers) &  (v1_funct_1(k30_valued_1(A)) & v1_valued_0(k30_valued_1(A))) ) ) ) ) ).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc59_valued_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(B))  & v1_membered(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k30_valued_1(C)) & v1_partfun1(k30_valued_1(C), A)) ) ) ).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc5_numbers, axiom,  ~ (v1_xboole_0(k6_numbers)) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  => v5_membered(k10_xtuple_0(A))) ) ).
fof(fc5_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v5_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) &  (v5_relat_1(k1_valued_1(A, B), k4_numbers) & v1_funct_1(k1_valued_1(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_valued_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(B))  & v3_membered(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k30_valued_1(C)) & v1_partfun1(k30_valued_1(C), A)) ) ) ).
fof(fc61_valued_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(B))  & v4_membered(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k30_valued_1(C)) & v1_partfun1(k30_valued_1(C), A)) ) ) ).
fof(fc62_valued_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(B))  & v5_membered(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k30_valued_1(C)) & v1_partfun1(k30_valued_1(C), A)) ) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  => v6_membered(k10_xtuple_0(A))) ) ).
fof(fc6_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v6_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) &  (v1_funct_1(k1_valued_1(A, B)) & v6_valued_0(k1_valued_1(A, B))) ) ) ) ).
fof(fc7_numbers, axiom,  ~ (v1_finset_1(k3_numbers)) ).
fof(fc7_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v1_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v1_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k1_valued_1(D, E)) & v1_partfun1(k1_valued_1(D, E), A)) ) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc81_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  =>  (v1_relat_1(k45_valued_1(A, B)) &  (v1_funct_1(k45_valued_1(A, B)) & v1_valued_0(k45_valued_1(A, B))) ) ) ) ).
fof(fc82_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_valued_0(B)) ) )  =>  (v1_relat_1(k45_valued_1(A, B)) &  (v1_funct_1(k45_valued_1(A, B)) & v3_valued_0(k45_valued_1(A, B))) ) ) ) ).
fof(fc83_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v4_valued_0(B)) ) )  =>  (v1_relat_1(k45_valued_1(A, B)) &  (v5_relat_1(k45_valued_1(A, B), k3_numbers) & v1_funct_1(k45_valued_1(A, B))) ) ) ) ).
fof(fc84_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v5_valued_0(B)) ) )  =>  (v1_relat_1(k45_valued_1(A, B)) &  (v5_relat_1(k45_valued_1(A, B), k4_numbers) & v1_funct_1(k45_valued_1(A, B))) ) ) ) ).
fof(fc85_valued_0, axiom,  (! [A, B] :  (v1_membered(B) => v1_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc85_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v1_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v1_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k45_valued_1(D, E)) & v1_partfun1(k45_valued_1(D, E), A)) ) ) ).
fof(fc86_valued_0, axiom,  (! [A, B] :  (v2_membered(B) => v2_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc86_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v3_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v3_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k45_valued_1(D, E)) & v1_partfun1(k45_valued_1(D, E), A)) ) ) ).
fof(fc87_valued_0, axiom,  (! [A, B] :  (v3_membered(B) => v3_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc87_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v4_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v4_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k45_valued_1(D, E)) & v1_partfun1(k45_valued_1(D, E), A)) ) ) ).
fof(fc88_valued_0, axiom,  (! [A, B] :  (v4_membered(B) => v4_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc88_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v5_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v5_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k45_valued_1(D, E)) & v1_partfun1(k45_valued_1(D, E), A)) ) ) ).
fof(fc89_valued_0, axiom,  (! [A, B] :  (v5_membered(B) => v5_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v3_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v3_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k1_valued_1(D, E)) & v1_partfun1(k1_valued_1(D, E), A)) ) ) ).
fof(fc90_valued_0, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc9_numbers, axiom,  ~ (v1_finset_1(k2_numbers)) ).
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_valued_1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(B))  & v4_membered(B))  &  ( ( ~ (v1_xboole_0(C))  & v4_membered(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) )  =>  (v1_funct_1(k1_valued_1(D, E)) & v1_partfun1(k1_valued_1(D, E), 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(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(involutiveness_k30_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => k30_valued_1(k30_valued_1(A))=A) ) ).
fof(involutiveness_k32_valued_1, axiom,  (! [A, B, C] :  ( (v3_membered(B) &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  => k32_valued_1(A, B, k32_valued_1(A, B, C))=C) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_funct_2, axiom,  (! [A, 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_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(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_seq_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_numbers))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, k1_numbers) &  (v1_funct_1(A) &  (v9_ordinal1(A) &  (v1_valued_0(A) &  (v2_valued_0(A) & v3_valued_0(A)) ) ) ) ) ) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_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_valued_0, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_partfun1(A, k4_ordinal1) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) &  (v1_valued_0(A) &  (v2_valued_0(A) &  (v3_valued_0(A) &  (v4_valued_0(A) &  (v5_valued_0(A) &  (v6_valued_0(A) & v7_valued_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_valued_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)) ) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_valued_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_valued_0(B) &  (v2_valued_0(B) &  (v3_valued_0(B) &  (v4_valued_0(B) &  (v5_valued_0(B) & v6_valued_0(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v6_valued_0(B)) ) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k32_valued_1, axiom,  (! [A, B, C] :  ( (v3_membered(B) &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  => k32_valued_1(A, B, C)=k30_valued_1(C)) ) ).
fof(redefinition_k3_valued_1, axiom,  (! [A, B, C, D, E] :  ( (v3_membered(B) &  (v3_membered(C) &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) )  => k3_valued_1(A, B, C, D, E)=k1_valued_1(D, E)) ) ).
fof(redefinition_k47_valued_1, axiom,  (! [A, B, C, D, E] :  ( (v3_membered(B) &  (v3_membered(C) &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) )  => k47_valued_1(A, B, C, D, E)=k45_valued_1(D, E)) ) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, 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(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t44_limfunc2, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  =>  (r1_limfunc2(B, A) =>  (r1_limfunc2(k32_valued_1(k1_numbers, k1_numbers, B), A) & k1_limfunc2(k32_valued_1(k1_numbers, k1_numbers, B), A)=k4_xcmplx_0(k1_limfunc2(B, A))) ) ) ) ) ) ).
fof(t45_limfunc2, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers))))  =>  ( (r1_limfunc2(B, A) &  (r1_limfunc2(C, A) &  (! [D] :  (v1_xreal_0(D) =>  ~ ( ( ~ (r1_xxreal_0(A, D))  &  (! [E] :  (v1_xreal_0(E) =>  ~ ( ( ~ (r1_xxreal_0(E, D))  &  ( ~ (r1_xxreal_0(A, E))  & r2_hidden(E, k1_relset_1(k1_numbers, k3_valued_1(k1_numbers, k1_numbers, k1_numbers, B, C)))) ) ) ) ) ) ) ) ) ) )  =>  (r1_limfunc2(k3_valued_1(k1_numbers, k1_numbers, k1_numbers, B, C), A) & k1_limfunc2(k3_valued_1(k1_numbers, k1_numbers, k1_numbers, B, C), A)=k2_xcmplx_0(k1_limfunc2(B, A), k1_limfunc2(C, A))) ) ) ) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
