% Mizar problem: t28_random_1,random_1,1809,5 
fof(t28_random_1, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, A, k1_numbers) &  (v1_mesfunc6(E, A, B, k4_prob_1(A, B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  =>  ( (r1_random_1(A, B, D, C) & r1_random_1(A, B, E, C))  => k8_random_1(A, B, C, k4_random_1(A, B, D, E))=k6_xcmplx_0(k8_random_1(A, B, C, D), k8_random_1(A, B, C, E))) ) ) ) ) ) ) ) ) ) ) ).
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_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(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_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(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_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v3_valued_0(A) & v7_valued_0(A)) ) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) & v3_valued_0(A)) ) ) ) ) ).
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_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_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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
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_jordan5a, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) =>  (v1_finset_1(A) => v1_rcomp_1(A)) ) ) ).
fof(cc1_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( (v1_finsub_1(B) & v1_prob_1(B, A))  => v2_finsub_1(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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc1_xxreal_0, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => v1_xxreal_0(A)) ) ).
fof(cc1_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v3_xxreal_0(A))  &  ~ (v1_xreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_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_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_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
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_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( (v2_finsub_1(B) & v1_prob_1(B, A))  => v1_finsub_1(B)) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc2_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v1_xreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_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_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [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_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
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_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( (v2_finsub_1(B) & v1_prob_1(B, A))  => v3_finsub_1(B)) ) ) ) ).
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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k2_numbers) => v1_xcmplx_0(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(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
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_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( (v1_prob_1(B, A) & v4_prob_1(B, A))  => v3_measure1(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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(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(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(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_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_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
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_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( (v1_prob_1(B, A) & v3_measure1(B, A))  => v4_prob_1(B, 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_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_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(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_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_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) & v4_prob_1(B, A)) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) & v4_prob_1(B, 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_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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_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_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_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_measure1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) & v3_measure1(B, A)) )  =>  ( ~ (v1_xboole_0(B))  & v1_finsub_1(B)) ) ) ) ) ).
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_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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_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_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_measure1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) & v4_measure1(C, A, B)) ) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) & v2_measure1(C, A, B)) ) ) ) ) ) ) ) ) ).
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_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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(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_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k1_xxreal_3(A, B)=k1_xxreal_3(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_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) )  => k3_random_1(A, B, C, D)=k3_random_1(A, B, D, C)) ) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(commutativity_k4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k4_xxreal_3(A, B)=k4_xxreal_3(B, A)) ) ).
fof(d16_mesfunc5, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  => k7_mesfunc5(A, B, C, D)=k10_xxreal_3(k6_mesfunc5(A, B, C, k1_mesfunc2(A, D)), k6_mesfunc5(A, B, C, k2_mesfunc2(A, D)))) ) ) ) ) ) ) ) ).
fof(d1_prob_4, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) => k2_prob_4(A, B, C)=C) ) ) ) ) ) ).
fof(d2_random_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  =>  (! [D] :  (m2_prob_1(D, A, B) =>  (r1_random_1(A, B, C, D) <=> r2_mesfunc6(A, B, k2_prob_4(A, B, D), C)) ) ) ) ) ) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_mesfunc6, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers))))  => k1_mesfunc6(A, B, C, D)=k7_mesfunc5(A, B, C, k1_mesfunc5(A, D))) ) ) ) ) ) ) ) ).
fof(d4_mesfunc6, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers))))  =>  (r2_mesfunc6(A, B, C, D) <=> r1_mesfunc5(A, B, C, k1_mesfunc5(A, D))) ) ) ) ) ) ) ) ) ).
fof(d4_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) => k3_xxreal_3(A, B)=k1_xxreal_3(A, k2_xxreal_3(B))) ) ) ) ).
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(d7_mesfunc5, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers))))  => k1_mesfunc5(A, B)=B) ) ) ) ).
fof(d7_prob_1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  => k4_prob_1(A, B)=A) ) ) ).
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(de_c1__random_1, axiom, c1__random_1=1).
fof(dt_c1__random_1, axiom, v1_xreal_0(c1__random_1)).
fof(dt_k10_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => m1_subset_1(k10_xxreal_3(A, B), k6_numbers)) ) ).
fof(dt_k1_mesfunc2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  =>  (v1_funct_1(k1_mesfunc2(A, B)) & m1_subset_1(k1_mesfunc2(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ).
fof(dt_k1_mesfunc5, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) )  =>  (v1_funct_1(k1_mesfunc5(A, B)) & m1_subset_1(k1_mesfunc5(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ).
fof(dt_k1_mesfunc6, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) )  => m1_subset_1(k1_mesfunc6(A, B, C, D), k6_numbers)) ) ).
fof(dt_k1_numbers, axiom, $true).
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_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k1_xxreal_3(A, B))) ) ).
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_k26_valued_1, axiom,  (! [A, B, C, D] :  ( (v3_membered(B) &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  & v1_xreal_0(D)) )  =>  (v1_funct_1(k26_valued_1(A, B, C, D)) & m1_subset_1(k26_valued_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ).
fof(dt_k2_mesfunc2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  =>  (v1_funct_1(k2_mesfunc2(A, B)) & m1_subset_1(k2_mesfunc2(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_prob_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  & m2_prob_1(C, A, B)) )  =>  (v1_funct_1(k2_prob_4(A, B, C)) &  (v1_funct_2(k2_prob_4(A, B, C), B, k6_numbers) &  (v12_valued_0(k2_prob_4(A, B, C)) &  (v6_supinf_2(k2_prob_4(A, B, C)) &  (v4_measure1(k2_prob_4(A, B, C), A, B) & m1_subset_1(k2_prob_4(A, B, C), k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) ) ) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => v1_xxreal_0(k2_xxreal_3(A))) ) ).
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_k3_numbers, axiom, $true).
fof(dt_k3_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) )  =>  (v1_funct_1(k3_random_1(A, B, C, D)) &  (v1_funct_2(k3_random_1(A, B, C, D), A, k1_numbers) &  (v1_mesfunc6(k3_random_1(A, B, C, D), A, B, k4_prob_1(A, B)) & m1_subset_1(k3_random_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) ).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k3_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k3_xxreal_3(A, B))) ) ).
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_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  => m1_prob_1(k4_prob_1(A, B), A, B)) ) ).
fof(dt_k4_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) )  =>  (v1_funct_1(k4_random_1(A, B, C, D)) &  (v1_funct_2(k4_random_1(A, B, C, D), A, k1_numbers) &  (v1_mesfunc6(k4_random_1(A, B, C, D), A, B, k4_prob_1(A, B)) & m1_subset_1(k4_random_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) ).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k4_xxreal_3(A, B))) ) ).
fof(dt_k5_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  & v1_xreal_0(D)) ) )  =>  (v1_funct_1(k5_random_1(A, B, C, D)) &  (v1_funct_2(k5_random_1(A, B, C, D), A, k1_numbers) &  (v1_mesfunc6(k5_random_1(A, B, C, D), A, B, k4_prob_1(A, B)) & m1_subset_1(k5_random_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) ).
fof(dt_k6_mesfunc5, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) )  => m1_subset_1(k6_mesfunc5(A, B, C, D), k6_numbers)) ) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_mesfunc5, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) )  => m1_subset_1(k7_mesfunc5(A, B, C, D), k6_numbers)) ) ).
fof(dt_k8_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  (m2_prob_1(C, A, B) &  (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) )  => v1_xreal_0(k8_random_1(A, B, C, D))) ) ).
fof(dt_m1_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m1_prob_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(A))) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) =>  (v1_funct_1(C) &  (v1_funct_2(C, B, k1_numbers) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k1_numbers)))) ) ) ) ) ) ).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(existence_m1_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (? [C] : m1_prob_1(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  (? [C] : m2_prob_1(C, 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_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(fc10_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v2_xxreal_0(k1_xxreal_3(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_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(fc11_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(B, A)) & v2_xxreal_0(k1_xxreal_3(B, A))) ) ) ).
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_valued_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(k1_valued_1(A, B)) &  (v1_funct_1(k1_valued_1(A, B)) & v1_finseq_1(k1_valued_1(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(fc12_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v3_xxreal_0(k1_xxreal_3(A, B))) ) ) ).
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_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(fc13_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(B, A)) & v3_xxreal_0(k1_xxreal_3(B, A))) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(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(fc14_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  =>  (v1_xxreal_0(k2_xxreal_3(A)) &  ~ (v3_xxreal_0(k2_xxreal_3(A))) ) ) ) ).
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(fc15_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  =>  (v1_xxreal_0(k2_xxreal_3(A)) &  ~ (v2_xxreal_0(k2_xxreal_3(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(fc16_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  (v1_xxreal_0(k2_xxreal_3(A)) & v3_xxreal_0(k2_xxreal_3(A))) ) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
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(fc17_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  (v1_xxreal_0(k2_xxreal_3(A)) & v2_xxreal_0(k2_xxreal_3(A))) ) ) ).
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(fc18_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k3_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k3_xxreal_3(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(fc19_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k3_xxreal_3(B, A)) &  ~ (v2_xxreal_0(k3_xxreal_3(B, A))) ) ) ) ).
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_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xxreal_3, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xxreal_0(k2_xxreal_3(A)) & v1_xreal_0(k2_xxreal_3(A))) ) ) ).
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(fc20_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k3_xxreal_3(A, B)) & v2_xxreal_0(k3_xxreal_3(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(fc21_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k3_xxreal_3(B, A)) & v3_xxreal_0(k3_xxreal_3(B, A))) ) ) ).
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(fc22_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k3_xxreal_3(A, B)) & v3_xxreal_0(k3_xxreal_3(A, B))) ) ) ).
fof(fc23_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc23_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k3_xxreal_3(B, A)) & v2_xxreal_0(k3_xxreal_3(B, A))) ) ) ).
fof(fc24_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(B, A))) ) ) ).
fof(fc24_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) & v3_xxreal_0(B)) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v3_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc25_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc25_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) & v3_xxreal_0(B)) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v2_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) & v2_xxreal_0(B)) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v2_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc27_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) &  ~ (v2_xxreal_0(k4_xxreal_3(A, B))) ) ) ) ).
fof(fc28_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k4_xxreal_3(A, B))) ) ) ) ).
fof(fc29_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k4_xxreal_3(A, B))) ) ) ) ).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
fof(fc2_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
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(fc2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(fc2_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v1_xreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc36_xxreal_3, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xxreal_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xxreal_0(B)) )  =>  ( ~ (v8_ordinal1(k4_xxreal_3(A, B)))  & v1_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc37_xxreal_3, axiom,  (! [A, B] :  ( ( (v8_ordinal1(A) & v1_xxreal_0(A))  & v1_xxreal_0(B))  =>  (v8_ordinal1(k4_xxreal_3(A, B)) & v1_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc39_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v1_xreal_0(k4_xxreal_3(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_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_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k3_xcmplx_0(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(fc3_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k3_xxreal_3(A, B)) & v1_xreal_0(k3_xxreal_3(A, B))) ) ) ).
fof(fc43_xxreal_3, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v7_ordinal1(k1_xxreal_3(A, B)) & v1_xxreal_0(k1_xxreal_3(A, B))) ) ) ).
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(fc44_xxreal_3, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v7_ordinal1(k4_xxreal_3(A, B)) & v1_xxreal_0(k4_xxreal_3(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(fc45_xxreal_3, axiom,  (v1_xxreal_0(k2_xxreal_3(1)) & v2_int_1(k2_xxreal_3(1))) ).
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(fc46_xxreal_3, axiom,  (! [A] :  (v2_int_1(A) =>  (v7_ordinal1(k1_xxreal_3(A, 1)) & v1_xxreal_0(k1_xxreal_3(A, 1))) ) ) ).
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_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(fc4_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k6_xcmplx_0(A, B))) ) ).
fof(fc4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) &  (v1_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) )  =>  ~ (v1_xreal_0(k1_xxreal_3(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(fc54_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  & v1_xcmplx_0(B))  =>  (v1_relat_1(k24_valued_1(A, B)) &  (v1_funct_1(k24_valued_1(A, B)) & v1_finseq_1(k24_valued_1(A, B))) ) ) ) ).
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_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(fc5_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  (v2_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) )  &  (v1_xxreal_0(B) &  (v2_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v1_xreal_0(k1_xxreal_3(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(fc63_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v1_funct_1(k30_valued_1(A)) &  (v1_valued_0(k30_valued_1(A)) & v1_finseq_1(k30_valued_1(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_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
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(fc6_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k4_xcmplx_0(A)))  & v1_xcmplx_0(k4_xcmplx_0(A))) ) ) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc6_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) )  &  (v1_xxreal_0(B) &  (v3_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v1_xreal_0(k1_xxreal_3(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(fc7_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) )  &  (v1_xxreal_0(B) &  (v2_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) ) )  =>  (v8_ordinal1(k1_xxreal_3(A, B)) & v1_xxreal_0(k1_xxreal_3(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(fc89_valued_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(k45_valued_1(A, B)) &  (v1_funct_1(k45_valued_1(A, B)) & v1_finseq_1(k45_valued_1(A, B))) ) ) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
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(fc8_xcmplx_0, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xcmplx_0(B)) )  =>  ~ (v8_ordinal1(k3_xcmplx_0(A, B))) ) ) ).
fof(fc8_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k1_xxreal_3(A, B))) ) ) ) ).
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_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(fc9_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v2_xxreal_0(k1_xxreal_3(A, B))) ) ) ) ).
fof(ie1_xxreal_3, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xcmplx_0(C) & v1_xcmplx_0(D)) ) )  =>  ( (A=C & B=D)  => k1_xxreal_3(A, B)=k2_xcmplx_0(C, D)) ) ) ).
fof(ie2_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xcmplx_0(B))  =>  (A=B => k2_xxreal_3(A)=k4_xcmplx_0(B)) ) ) ).
fof(ie3_xxreal_3, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xcmplx_0(C) & v1_xcmplx_0(D)) ) )  =>  ( (A=C & B=D)  => k3_xxreal_3(A, B)=k6_xcmplx_0(C, D)) ) ) ).
fof(ie4_xxreal_3, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xcmplx_0(C) & v1_xcmplx_0(D)) ) )  =>  ( (A=C & B=D)  => k4_xxreal_3(A, B)=k3_xcmplx_0(C, D)) ) ) ).
fof(involutiveness_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k2_xxreal_3(k2_xxreal_3(A))=A) ) ).
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_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(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(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_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_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(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_measure1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v2_finsub_1(B) &  (v1_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers))) &  (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v5_relat_1(C, k6_numbers) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, B) &  (v1_funct_2(C, B, k6_numbers) &  (v2_valued_0(C) &  (v12_valued_0(C) &  (v6_supinf_2(C) & v2_measure1(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_random_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, k1_numbers) &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v1_funct_2(C, A, k1_numbers) &  (v1_valued_0(C) &  (v2_valued_0(C) &  (v3_valued_0(C) & v1_mesfunc6(C, A, B, k4_prob_1(A, B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_valued_0(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc1_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v2_xxreal_0(A) &  ~ (v1_xreal_0(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_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_measure1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  ( ~ (v1_xboole_0(B))  &  (v2_finsub_1(B) & v1_prob_1(B, 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_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_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) ) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
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_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_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_xcmplx_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xcmplx_0(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_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_measure1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) & v3_measure1(B, 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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_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_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_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_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_measure1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers))) &  (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v5_relat_1(C, k6_numbers) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, B) &  (v1_funct_2(C, B, k6_numbers) &  (v2_valued_0(C) &  (v12_valued_0(C) &  (v6_supinf_2(C) & v4_measure1(C, A, 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(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_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_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
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_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k10_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k10_xxreal_3(A, B)=k3_xxreal_3(A, B)) ) ).
fof(redefinition_k26_valued_1, axiom,  (! [A, B, C, D] :  ( (v3_membered(B) &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  & v1_xreal_0(D)) )  => k26_valued_1(A, B, C, D)=k24_valued_1(C, D)) ) ).
fof(redefinition_k3_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) )  => k3_random_1(A, B, C, D)=k1_valued_1(C, D)) ) ).
fof(redefinition_k4_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) )  => k4_random_1(A, B, C, D)=k45_valued_1(C, D)) ) ).
fof(redefinition_k5_random_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k1_numbers) &  (v1_mesfunc6(C, A, B, k4_prob_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  & v1_xreal_0(D)) ) )  => k5_random_1(A, B, C, D)=k24_valued_1(C, D)) ) ).
fof(redefinition_m1_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m1_prob_1(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(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=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(spc2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k4_xcmplx_0(1))=k4_xcmplx_0(A)) ) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
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(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_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(t102_mesfunc6, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, B, k6_numbers) &  (v12_valued_0(C) &  (v6_supinf_2(C) &  (v4_measure1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k6_numbers)))) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers))))  =>  (! [E] :  (v1_xreal_0(E) =>  (r2_mesfunc6(A, B, C, D) =>  (r2_mesfunc6(A, B, C, k26_valued_1(A, k1_numbers, D, E)) & k1_mesfunc6(A, B, C, k26_valued_1(A, k1_numbers, D, E))=k4_xxreal_3(E, k1_mesfunc6(A, B, C, D))) ) ) ) ) ) ) ) ) ) ) ) ).
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(t26_random_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, A, k1_numbers) &  (v1_mesfunc6(E, A, B, k4_prob_1(A, B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  =>  ( (r1_random_1(A, B, D, C) & r1_random_1(A, B, E, C))  => k8_random_1(A, B, C, k3_random_1(A, B, D, E))=k2_xcmplx_0(k8_random_1(A, B, C, D), k8_random_1(A, B, C, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_random_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, k1_numbers) &  (v1_mesfunc6(D, A, B, k4_prob_1(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) )  =>  (! [E] :  (v1_xreal_0(E) =>  (r1_random_1(A, B, D, C) => k8_random_1(A, B, C, k5_random_1(A, B, D, E))=k3_xcmplx_0(E, k8_random_1(A, B, C, D))) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
