% Mizar problem: t30_mesfun13,mesfun13,1128,5 
fof(t30_mesfun13, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, C, k6_numbers) &  (v12_valued_0(E) &  (v6_supinf_2(E) &  (v4_measure1(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, D, k6_numbers) &  (v12_valued_0(F) &  (v6_supinf_2(F) &  (v4_measure1(F, B, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(D, k6_numbers)))) ) ) ) )  =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  (! [H] :  (m2_subset_1(H, k1_zfmisc_1(A), C) =>  ~ ( (v4_measur11(E, A, C) &  (v4_measur11(F, B, D) &  (r1_mesfunc5(k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k8_mesfun12(A, B, C, D, E, F), G) &  (A=H &  (! [I] :  (m2_subset_1(I, k1_zfmisc_1(A), C) =>  ~ ( (k9_supinf_2(E, I)=k5_numbers &  ( (! [J] :  (m1_subset_1(J, A) =>  (r2_tarski(J, k3_subset_1(A, I)) => r1_mesfunc5(B, D, F, k2_mesfun12(A, B, k6_numbers, G, J))) ) )  &  ( (v1_funct_1(k2_partfun1(A, k6_numbers, k7_mesfun12(A, B, D, F, k9_mesfunc1(k2_zfmisc_1(A, B), G)), k3_subset_1(A, I))) & m1_subset_1(k2_partfun1(A, k6_numbers, k7_mesfun12(A, B, D, F, k9_mesfunc1(k2_zfmisc_1(A, B), G)), k3_subset_1(A, I)), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers))))  &  (v1_mesfunc1(k7_mesfun12(A, B, D, F, G), A, C, k3_measure1(A, C, H, I)) &  (r1_mesfunc5(A, C, E, k2_partfun1(A, k6_numbers, k7_mesfun12(A, B, D, F, G), k3_subset_1(A, I))) &  (r2_tarski(k2_partfun1(A, k6_numbers, k7_mesfun12(A, B, D, F, G), k3_subset_1(A, I)), k9_lpspace1(A, C, E)) &  (? [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, A, k6_numbers) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  &  (r1_mesfunc5(A, C, E, J) &  (r2_relset_1(A, k6_numbers, k2_partfun1(A, k6_numbers, J, k3_subset_1(A, I)), k2_partfun1(A, k6_numbers, k7_mesfun12(A, B, D, F, G), k3_subset_1(A, I))) & k7_mesfunc5(k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k8_mesfun12(A, B, C, D, E, F), G)=k7_mesfunc5(A, C, E, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_extreal1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k3_extreal1(A, B)=k3_extreal1(B, A)) ) ).
fof(commutativity_k3_mesfunc1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k6_numbers) & v1_funct_1(B)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, k6_numbers) & v1_funct_1(C)) ) ) ) )  => k3_mesfunc1(A, B, C)=k3_mesfunc1(A, C, B)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k4_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k4_xxreal_0(A, B)=k4_xxreal_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(commutativity_k9_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k9_xxreal_3(A, B)=k9_xxreal_3(B, A)) ) ).
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_mesfunc1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (C=k10_mesfunc1(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, k9_xtuple_0(A)) &  ~ (r1_xxreal_0(B, k1_funct_1(A, D))) ) ) ) ) ) ) ) ) ) ).
fof(d17_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))))  =>  (r1_mesfunc5(A, B, C, D) <=>  ( (? [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) &  (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E)) ) )  &  ( ~ (r1_xxreal_0(k1_supinf_1, k6_mesfunc5(A, B, C, k1_mesfunc2(A, D))))  &  ~ (r1_xxreal_0(k1_supinf_1, k6_mesfunc5(A, B, C, k2_mesfunc2(A, D)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_extreal1, axiom,  (! [A] :  (v1_xxreal_0(A) =>  ( (r1_xxreal_0(k5_numbers, A) => k1_extreal1(A)=A)  &  ( ~ (r1_xxreal_0(k5_numbers, A))  => k1_extreal1(A)=k2_xxreal_3(A)) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d1_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (v3_valued_0(B) <=>  (! [C] :  (m1_subset_1(C, A) =>  ~ ( (r2_tarski(C, k1_relset_1(A, B)) & r1_xxreal_0(k1_supinf_1, k1_extreal1(k9_supinf_2(B, C)))) ) ) ) ) ) ) ) ) ).
fof(d2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  ( (r2_hidden(B, k9_xtuple_0(A)) =>  (C=k1_funct_1(A, B) <=> r2_hidden(k4_tarski(B, C), A)) )  &  ( ~ (r2_hidden(B, k9_xtuple_0(A)))  =>  (C=k1_funct_1(A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d2_mesfun13, 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))))  =>  (r2_mesfun13(A, B, C, D) <=>  (? [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) &  (k9_supinf_2(C, E)=k5_numbers &  (r1_tarski(E, k1_relset_1(A, D)) &  (v1_funct_1(k2_partfun1(A, k6_numbers, D, k3_subset_1(A, E))) & m1_subset_1(k2_partfun1(A, k6_numbers, D, k3_subset_1(A, E)), k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (C=k1_mesfunc2(A, B) <=>  (k1_relset_1(A, C)=k1_relset_1(A, B) &  (! [D] :  (m1_subset_1(D, A) =>  (r2_tarski(D, k1_relset_1(A, C)) => k9_supinf_2(C, D)=k3_extreal1(k9_supinf_2(B, D), k1_supinf_2)) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_mesfun12, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))))  =>  (! [E] :  (m1_subset_1(E, A) =>  (! [F] :  ( (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(B, C))))  =>  (F=k2_mesfun12(A, B, C, D, E) <=>  (k1_relset_1(B, F)=k7_measur11(A, B, k1_relset_1(k2_zfmisc_1(A, B), D), E) &  (! [G] :  (m1_subset_1(G, B) =>  (r2_hidden(k4_tarski(E, G), k1_relset_1(k2_zfmisc_1(A, B), D)) => k1_funct_1(F, G)=k1_binop_1(D, E, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (C=k2_mesfunc2(A, B) <=>  (k1_relset_1(A, C)=k1_relset_1(A, B) &  (! [D] :  (m1_subset_1(D, A) =>  (r2_tarski(D, k1_relset_1(A, C)) => k9_supinf_2(C, D)=k3_extreal1(k7_xxreal_3(k9_supinf_2(B, D)), k1_supinf_2)) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_mesfunc1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k6_numbers) & v1_funct_1(B)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, k6_numbers) & v1_funct_1(C)) ) )  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (D=k4_mesfunc1(A, B, C) <=>  (k9_xtuple_0(D)=k6_subset_1(k3_xboole_0(k9_xtuple_0(B), k9_xtuple_0(C)), k2_xboole_0(k3_xboole_0(k8_relat_1(B, k1_tarski(k1_supinf_1)), k8_relat_1(C, k1_tarski(k1_supinf_1))), k3_xboole_0(k8_relat_1(B, k1_tarski(k2_supinf_1)), k8_relat_1(C, k1_tarski(k2_supinf_1))))) &  (! [E] :  (m1_subset_1(E, A) =>  (r2_tarski(E, k9_xtuple_0(D)) => k9_supinf_2(D, E)=k10_xxreal_3(k9_supinf_2(B, E), k9_supinf_2(C, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k3_subset_1(A, B)=k4_xboole_0(A, B)) ) ) ).
fof(d5_mesfunc5, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (v3_mesfunc5(B) <=>  (! [C] :  ~ (r1_xxreal_0(k1_funct_1(B, C), k2_supinf_1)) ) ) ) ) ) ) ).
fof(d6_measur11, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [E] :  (m2_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D))) =>  (! [F] : k9_measur11(A, B, C, D, E, F)=k7_measur11(A, B, E, F)) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_mesfunc5, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (v4_mesfunc5(B) <=>  (! [C] :  ~ (r1_xxreal_0(k1_supinf_1, k1_funct_1(B, C))) ) ) ) ) ) ) ).
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(d8_lpspace1, 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)))) ) ) ) )  => k9_lpspace1(A, B, C)=a_3_0_lpspace1(A, B, C)) ) ) ) ) ) ).
fof(d8_mesfun12, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, B) &  (v4_prob_1(C, B) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, C, k6_numbers) &  (v12_valued_0(D) &  (v6_supinf_2(D) &  (v4_measure1(D, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, A, k6_numbers) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  =>  (F=k7_mesfun12(A, B, C, D, E) <=>  (! [G] :  (m1_subset_1(G, A) => k9_supinf_2(F, G)=k7_mesfunc5(B, C, D, k2_mesfun12(A, B, k6_numbers, E, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_measur11, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  & m1_subset_1(E, k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)))) ) ) )  => m2_subset_1(k10_measur11(A, B, C, D, E, F), k1_zfmisc_1(A), C)) ) ).
fof(dt_k10_mesfunc1, axiom, $true).
fof(dt_k10_relat_1, axiom, $true).
fof(dt_k10_xtuple_0, axiom, $true).
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_k13_mesfunc1, axiom, $true).
fof(dt_k15_measur11, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v4_mesfunc5(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  &  (v1_funct_1(C) &  (v3_mesfunc5(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) )  =>  (v1_funct_1(k15_measur11(A, B, C)) &  (v4_mesfunc5(k15_measur11(A, B, C)) & m1_subset_1(k15_measur11(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ) ).
fof(dt_k17_mesfunc1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  & v1_xxreal_0(C))  => m1_subset_1(k17_mesfunc1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k18_mesfunc1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  & v1_xxreal_0(C))  => m1_subset_1(k18_mesfunc1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_extreal1, axiom,  (! [A] :  (v1_xxreal_0(A) => m1_subset_1(k1_extreal1(A), k6_numbers)) ) ).
fof(dt_k1_funct_1, axiom, $true).
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_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_supinf_1, axiom, m1_subset_1(k1_supinf_1, k6_numbers)).
fof(dt_k1_supinf_2, axiom, m1_subset_1(k1_supinf_2, k6_numbers)).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xxreal_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_k2_mesfun12, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))))  & m1_subset_1(E, A)) ) )  =>  (v1_funct_1(k2_mesfun12(A, B, C, D, E)) & m1_subset_1(k2_mesfun12(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(B, C)))) ) ) ).
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_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (v1_funct_1(k2_partfun1(A, B, C, D)) & m1_subset_1(k2_partfun1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ).
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_supinf_1, axiom, m1_subset_1(k2_supinf_1, k6_numbers)).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xxreal_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_k3_extreal1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => m1_subset_1(k3_extreal1(A, B), k6_numbers)) ) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_measur10, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v2_finsub_1(C) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v2_finsub_1(D) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) ) )  => m2_srings_3(k3_measur10(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k3_measure1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  &  (v2_finsub_1(B) &  (v1_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  (m1_subset_1(C, B) & m1_subset_1(D, B)) )  => m2_subset_1(k3_measure1(A, B, C, D), k1_zfmisc_1(A), B)) ) ).
fof(dt_k3_mesfun12, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))))  & m1_subset_1(E, B)) ) )  =>  (v1_funct_1(k3_mesfun12(A, B, C, D, E)) & m1_subset_1(k3_mesfun12(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ).
fof(dt_k3_mesfunc1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k6_numbers) & v1_funct_1(B)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, k6_numbers) & v1_funct_1(C)) ) ) ) )  =>  (v1_funct_1(k3_mesfunc1(A, B, C)) & m1_subset_1(k3_mesfunc1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_subset_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k3_xboole_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_k4_mesfunc1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k6_numbers) & v1_funct_1(B)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, k6_numbers) & v1_funct_1(C)) ) ) ) )  =>  (v1_funct_1(k4_mesfunc1(A, B, C)) & m1_subset_1(k4_mesfunc1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k4_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k4_xxreal_0(A, B))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k6_mesfun12, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, C, k6_numbers) &  (v12_valued_0(D) &  (v6_supinf_2(D) &  (v4_measure1(D, A, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers)))) ) ) ) )  =>  (v1_funct_1(k6_mesfun12(A, B, C, D, E)) &  (v1_funct_2(k6_mesfun12(A, B, C, D, E), B, k6_numbers) & m1_subset_1(k6_mesfun12(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(B, k6_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_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_lpspace1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v2_struct_0(k7_lpspace1(A)))  & l1_rlvect_1(k7_lpspace1(A))) ) ) ).
fof(dt_k7_measur11, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k7_measur11(A, B, C, D), k1_zfmisc_1(B))) ) ).
fof(dt_k7_mesfun12, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, B) &  (v4_prob_1(C, B) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, C, k6_numbers) &  (v12_valued_0(D) &  (v6_supinf_2(D) &  (v4_measure1(D, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers)))) ) ) ) )  =>  (v1_funct_1(k7_mesfun12(A, B, C, D, E)) &  (v1_funct_2(k7_mesfun12(A, B, C, D, E), A, k6_numbers) & m1_subset_1(k7_mesfun12(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ) ).
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_k7_prob_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (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_subset_1(C, B) & m1_subset_1(D, B)) )  => m1_prob_1(k7_prob_1(A, B, C, D), A, B)) ) ).
fof(dt_k7_xxreal_3, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => m1_subset_1(k7_xxreal_3(A), k6_numbers)) ) ).
fof(dt_k8_mesfun12, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, C, k6_numbers) &  (v12_valued_0(E) &  (v6_supinf_2(E) &  (v4_measure1(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  &  (v1_funct_1(F) &  (v1_funct_2(F, D, k6_numbers) &  (v12_valued_0(F) &  (v6_supinf_2(F) &  (v4_measure1(F, B, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(D, k6_numbers)))) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k8_mesfun12(A, B, C, D, E, F)) &  (v1_funct_2(k8_mesfun12(A, B, C, D, E, F), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k6_numbers) &  (v12_valued_0(k8_mesfun12(A, B, C, D, E, F)) &  (v6_supinf_2(k8_mesfun12(A, B, C, D, E, F)) &  (v4_measure1(k8_mesfun12(A, B, C, D, E, F), k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D))) & m1_subset_1(k8_mesfun12(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k6_numbers)))) ) ) ) ) ) ) ).
fof(dt_k8_relat_1, axiom, $true).
fof(dt_k9_lpspace1, 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)))) ) )  &  (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_xboole_0(k9_lpspace1(A, B, C)))  & m1_subset_1(k9_lpspace1(A, B, C), k1_zfmisc_1(u1_struct_0(k7_lpspace1(A))))) ) ) ).
fof(dt_k9_measur11, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  & m1_subset_1(E, k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)))) ) ) )  => m2_subset_1(k9_measur11(A, B, C, D, E, F), k1_zfmisc_1(B), D)) ) ).
fof(dt_k9_mesfunc1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k6_numbers) & v1_funct_1(B)) ) ) )  =>  (v1_funct_1(k9_mesfunc1(A, B)) & m1_subset_1(k9_mesfunc1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) ).
fof(dt_k9_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( ~ (v1_xboole_0(k9_prob_1(A, B)))  &  (v1_prob_1(k9_prob_1(A, B), A) &  (v4_prob_1(k9_prob_1(A, B), A) & m1_subset_1(k9_prob_1(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ) ) ).
fof(dt_k9_relat_1, axiom, $true).
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_supinf_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => m1_subset_1(k9_supinf_2(A, B), k6_numbers)) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_k9_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => m1_subset_1(k9_xxreal_3(A, B), k6_numbers)) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) => l2_algstr_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
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_srings_3, axiom,  (! [A] :  (! [B] :  (m2_srings_3(B, A) =>  ( ~ (v1_setfam_1(B))  &  (v2_finsub_1(B) &  (v1_srings_3(B) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ) ) ) ).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_rlvect_1, axiom,  (? [A] : l1_rlvect_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
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_srings_3, axiom,  (! [A] :  (? [B] : m2_srings_3(B, A)) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc100_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v7_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc101_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v10_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc102_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v8_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc103_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v9_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ( ~ (v1_xboole_0(k5_relat_1(A, B)))  & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc10_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  &  (v1_relat_1(B) & v4_valued_0(B)) )  => v4_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(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(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc11_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  &  (v1_relat_1(B) & v5_valued_0(B)) )  => v5_valued_0(k2_xboole_0(A, B))) ) ).
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(fc12_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  &  (v1_relat_1(B) & v6_valued_0(B)) )  => v6_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(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(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(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_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  & v1_relat_1(B))  => v1_valued_0(k4_xboole_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(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_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(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_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc16_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  & v1_relat_1(B))  => v2_valued_0(k4_xboole_0(A, B))) ) ).
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_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
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(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_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  & v1_relat_1(B))  => v3_valued_0(k4_xboole_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(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_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(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_mesfunc7, 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(k9_mesfunc1(A, B)) & v6_supinf_2(k9_mesfunc1(A, B))) ) ) ).
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_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
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(fc1_xxreal_0, axiom, v1_xxreal_0(k1_xxreal_0)).
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_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  & v1_relat_1(B))  => v4_valued_0(k4_xboole_0(A, B))) ) ).
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_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  => v1_xboole_0(k8_relat_1(A, B))) ) ).
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(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_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  => v1_xboole_0(k8_relat_1(A, B))) ) ).
fof(fc22_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  & v1_relat_1(B))  => v5_valued_0(k4_xboole_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(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_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
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(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_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc24_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  & v1_relat_1(B))  => v6_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc2_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  => v2_membered(k10_xtuple_0(A))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc2_xreal_0, axiom,  ~ (v1_xreal_0(k1_xxreal_0)) ).
fof(fc2_xxreal_0, axiom, v1_xxreal_0(k2_xxreal_0)).
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(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc36_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k4_xxreal_0(A, B)) & v1_xreal_0(k4_xxreal_0(A, B))) ) ) ).
fof(fc37_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_valued_0(A))  => v1_membered(k9_relat_1(A, B))) ) ).
fof(fc38_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_valued_0(A))  => v2_membered(k9_relat_1(A, B))) ) ).
fof(fc39_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_valued_0(A))  => v3_membered(k9_relat_1(A, B))) ) ).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  => v3_membered(k10_xtuple_0(A))) ) ).
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_0, axiom, v2_xxreal_0(k1_xxreal_0)).
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(fc40_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v4_valued_0(A))  => v4_membered(k9_relat_1(A, B))) ) ).
fof(fc41_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v5_valued_0(A))  => v5_membered(k9_relat_1(A, B))) ) ).
fof(fc42_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v6_valued_0(A))  => v6_membered(k9_relat_1(A, B))) ) ).
fof(fc43_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_valued_0(k5_relat_1(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_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc45_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc46_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v4_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc47_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v5_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc48_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v6_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(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_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  => v4_membered(k10_xtuple_0(A))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_xxreal_0, axiom, v3_xxreal_0(k2_xxreal_0)).
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(fc5_numbers, axiom,  ~ (v1_xboole_0(k6_numbers)) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
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_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(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(fc61_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => v1_xcmplx_0(k1_funct_1(A, B))) ) ).
fof(fc62_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => v1_xxreal_0(k1_funct_1(A, B))) ) ).
fof(fc63_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  => v1_xreal_0(k1_funct_1(A, B))) ) ).
fof(fc64_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  => v1_rat_1(k1_funct_1(A, B))) ) ).
fof(fc65_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  => v1_int_1(k1_funct_1(A, B))) ) ).
fof(fc66_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  => v7_ordinal1(k1_funct_1(A, B))) ) ).
fof(fc6_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v7_ordinal1(k4_xxreal_0(A, B)) & v1_xxreal_0(k4_xxreal_0(A, B))) ) ) ).
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_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  => v6_membered(k10_xtuple_0(A))) ) ).
fof(fc6_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k4_xxreal_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_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  &  (v1_relat_1(B) & v1_valued_0(B)) )  => v1_valued_0(k2_xboole_0(A, B))) ) ).
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(fc85_valued_0, axiom,  (! [A, B] :  (v1_membered(B) => v1_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc86_valued_0, axiom,  (! [A, B] :  (v2_membered(B) => v2_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc87_valued_0, axiom,  (! [A, B] :  (v3_membered(B) => v3_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc88_valued_0, axiom,  (! [A, B] :  (v4_membered(B) => v4_valued_0(k2_zfmisc_1(A, B))) ) ).
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_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
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_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  &  (v1_relat_1(B) & v2_valued_0(B)) )  => v2_valued_0(k2_xboole_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_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
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_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  &  (v1_relat_1(B) & v3_valued_0(B)) )  => v3_valued_0(k2_xboole_0(A, B))) ) ).
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(fraenkel_a_3_0_lpspace1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, B) &  (v4_prob_1(C, B) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, C, k6_numbers) &  (v12_valued_0(D) &  (v6_supinf_2(D) &  (v4_measure1(D, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) ) ) )  =>  (r2_hidden(A, a_3_0_lpspace1(B, C, D)) <=>  (? [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, k1_numbers))))  &  (A=E &  (? [F] :  (m2_subset_1(F, k1_zfmisc_1(B), C) &  (k3_funct_2(C, k6_numbers, D, F)=k5_numbers &  (k1_relset_1(B, E)=k3_subset_1(B, F) & r2_mesfunc6(B, C, D, E)) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_mesfun13, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, B) &  (v4_prob_1(C, B) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, C, k6_numbers) &  (v12_valued_0(D) &  (v6_supinf_2(D) &  (v4_measure1(D, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) ) ) )  =>  (r2_hidden(A, a_3_0_mesfun13(B, C, D)) <=>  (? [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, k1_numbers))))  &  (A=E &  (? [F] :  (m2_subset_1(F, k1_zfmisc_1(B), C) &  (k9_supinf_2(D, F)=k5_numbers &  (k1_relset_1(B, E)=k3_subset_1(B, F) & r2_mesfunc6(B, C, D, E)) ) ) ) ) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_extreal1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k3_extreal1(A, A)=A) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k4_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k4_xxreal_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(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(involutiveness_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k2_xxreal_3(k2_xxreal_3(A))=A) ) ).
fof(involutiveness_k3_subset_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k3_subset_1(A, k3_subset_1(A, B))=B) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(involutiveness_k7_xxreal_3, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => k7_xxreal_3(k7_xxreal_3(A))=A) ) ).
fof(projectivity_k1_extreal1, axiom,  (! [A] :  (v1_xxreal_0(A) => k1_extreal1(k1_extreal1(A))=k1_extreal1(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_mesfun13, 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)))) ) )  & m1_subset_1(C, B)) )  =>  (? [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))) &  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v5_relat_1(D, k6_numbers) &  (v1_funct_1(D) &  (v2_valued_0(D) & v1_mesfunc1(D, A, B, C)) ) ) ) ) ) ) ) ) ).
fof(rc1_mesfunc7, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))) &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k6_numbers) &  (v1_funct_1(B) &  (v2_valued_0(B) & v6_supinf_2(B)) ) ) ) ) ) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_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_xboole_0, axiom,  (? [A] : v1_xboole_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_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_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_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(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_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_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_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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_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(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
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_k15_measur11, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v4_mesfunc5(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  &  (v1_funct_1(C) &  (v3_mesfunc5(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) ) ) )  => k15_measur11(A, B, C)=k4_mesfunc1(A, B, C)) ) ).
fof(redefinition_k17_mesfunc1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  & v1_xxreal_0(C))  => k17_mesfunc1(A, B, C)=k13_mesfunc1(B, C)) ) ).
fof(redefinition_k18_mesfunc1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  & v1_xxreal_0(C))  => k18_mesfunc1(A, B, C)=k10_relat_1(B, C)) ) ).
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_k1_supinf_1, axiom, k1_supinf_1=k1_xxreal_0).
fof(redefinition_k1_supinf_2, axiom, k1_supinf_2=k5_ordinal1).
fof(redefinition_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => k2_partfun1(A, B, C, D)=k5_relat_1(C, D)) ) ).
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_k2_supinf_1, axiom, k2_supinf_1=k2_xxreal_0).
fof(redefinition_k3_extreal1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k3_extreal1(A, B)=k4_xxreal_0(A, B)) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k3_measure1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(B))  &  (v2_finsub_1(B) &  (v1_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  &  (m1_subset_1(C, B) & m1_subset_1(D, B)) )  => k3_measure1(A, B, C, D)=k4_xboole_0(C, D)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k7_measur11, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k7_measur11(A, B, C, D)=k9_relat_1(C, D)) ) ).
fof(redefinition_k7_prob_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (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_subset_1(C, B) & m1_subset_1(D, B)) )  => k7_prob_1(A, B, C, D)=k4_xboole_0(C, D)) ) ).
fof(redefinition_k7_xxreal_3, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => k7_xxreal_3(A)=k2_xxreal_3(A)) ) ).
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_k9_supinf_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => k9_supinf_2(A, B)=k1_funct_1(A, B)) ) ).
fof(redefinition_k9_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k9_xxreal_3(A, B)=k1_xxreal_3(A, B)) ) ).
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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r1_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (r1_relset_1(A, B, C, D) <=> r1_tarski(C, D)) ) ) ).
fof(redefinition_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => r1_relset_1(A, B, C, C)) ) ).
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(reflexivity_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => r2_relset_1(A, B, C, C)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(symmetry_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) => r2_relset_1(A, B, D, C)) ) ) ).
fof(t100_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))))  =>  ( (? [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) &  (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E)) ) )  =>  (r1_mesfunc5(A, B, C, D) <=> r1_mesfunc5(A, B, C, k9_mesfunc1(A, D))) ) ) ) ) ) ) ) ) ) ).
fof(t101_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))))  =>  (r1_mesfunc5(A, B, C, D) => r1_xxreal_0(k1_extreal1(k7_mesfunc5(A, B, C, D)), k7_mesfunc5(A, B, C, k9_mesfunc1(A, D)))) ) ) ) ) ) ) ) ) ).
fof(t102_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))))  =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ( (k1_relset_1(A, D)=k1_relset_1(A, E) &  (r1_mesfunc5(A, B, C, E) &  (! [F] :  (m1_subset_1(F, A) =>  (r2_tarski(F, k1_relset_1(A, D)) => r1_xxreal_0(k1_extreal1(k9_supinf_2(D, F)), k9_supinf_2(E, F))) ) ) ) )  =>  ( (! [F] :  (m2_subset_1(F, k1_zfmisc_1(A), B) =>  ~ ( (F=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, F)) ) ) )  |  (r1_mesfunc5(A, B, C, D) & r1_xxreal_0(k7_mesfunc5(A, B, C, k9_mesfunc1(A, D)), k7_mesfunc5(A, B, C, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_mesfun11, 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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [D] :  (m1_subset_1(D, B) =>  (r1_tarski(D, k1_relset_1(A, C)) =>  (v1_mesfunc1(C, A, B, D) <=>  (v1_mesfunc1(k1_mesfunc2(A, C), A, B, D) & v1_mesfunc1(k2_mesfunc2(A, C), A, B, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_mesfun10, 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))))  =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ( (r1_mesfunc5(A, B, C, D) & r1_mesfunc5(A, B, C, E))  => r1_mesfunc5(A, B, C, k4_mesfunc1(A, D, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  (m1_subset_1(C, A) => r1_xxreal_0(k1_supinf_2, k9_supinf_2(k1_mesfunc2(A, B), C))) ) ) ) ) ) ).
fof(t13_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  (m1_subset_1(C, A) => r1_xxreal_0(k1_supinf_2, k9_supinf_2(k2_mesfunc2(A, B), C))) ) ) ) ) ) ).
fof(t17_mesfun13, 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))))  =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ( (r1_mesfunc5(A, B, C, D) & r1_mesfunc5(A, B, C, E))  =>  (k7_mesfunc5(A, B, C, k3_mesfunc1(A, D, E))=k9_xxreal_3(k7_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, D, k9_subset_1(A, k1_relset_1(A, D), k1_relset_1(A, E)))), k7_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, E, k9_subset_1(A, k1_relset_1(A, D), k1_relset_1(A, E))))) & k7_mesfunc5(A, B, C, k4_mesfunc1(A, D, E))=k10_xxreal_3(k7_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, D, k9_subset_1(A, k1_relset_1(A, D), k1_relset_1(A, E)))), k7_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, E, k9_subset_1(A, k1_relset_1(A, D), k1_relset_1(A, E)))))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_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(t23_mesfun11, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ( (v3_mesfunc5(B) & v4_mesfunc5(B))  =>  (k1_relset_1(A, k3_mesfunc1(A, B, C))=k9_subset_1(A, k1_relset_1(A, B), k1_relset_1(A, C)) &  (k1_relset_1(A, k4_mesfunc1(A, B, C))=k9_subset_1(A, k1_relset_1(A, B), k1_relset_1(A, C)) & k1_relset_1(A, k4_mesfunc1(A, C, B))=k9_subset_1(A, k1_relset_1(A, B), k1_relset_1(A, C))) ) ) ) ) ) ) ) ) ).
fof(t23_mesfun13, 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))))  =>  (r1_mesfunc5(A, B, C, D) =>  (k9_supinf_2(C, k18_mesfunc1(A, D, k1_xxreal_0))=k5_numbers &  (k9_supinf_2(C, k18_mesfunc1(A, D, k2_xxreal_0))=k5_numbers &  (r2_mesfun13(A, B, C, D) &  (! [E] :  (v1_xreal_0(E) =>  ~ ( ( ~ (r1_xxreal_0(E, k5_numbers))  & r1_xxreal_0(k1_xxreal_0, k9_supinf_2(C, k17_mesfunc1(A, k9_mesfunc1(A, D), E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  => r2_relset_1(A, k6_numbers, B, k4_mesfunc1(A, k1_mesfunc2(A, B), k2_mesfunc2(A, B)))) ) ) ) ).
fof(t24_mesfun13, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, C, k6_numbers) &  (v12_valued_0(E) &  (v6_supinf_2(E) &  (v4_measure1(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, D, k6_numbers) &  (v12_valued_0(F) &  (v6_supinf_2(F) &  (v4_measure1(F, B, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(D, k6_numbers)))) ) ) ) )  =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  ( (v4_measur11(E, A, C) &  (v4_measur11(F, B, D) & r1_mesfunc5(k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k8_mesfun12(A, B, C, D, E, F), G)) )  =>  (r1_mesfunc5(B, D, F, k6_mesfun12(A, B, C, E, k1_mesfunc2(k2_zfmisc_1(A, B), G))) &  (r1_mesfunc5(A, C, E, k7_mesfun12(A, B, D, F, k1_mesfunc2(k2_zfmisc_1(A, B), G))) &  (r1_mesfunc5(B, D, F, k6_mesfun12(A, B, C, E, k2_mesfunc2(k2_zfmisc_1(A, B), G))) &  (r1_mesfunc5(A, C, E, k7_mesfun12(A, B, D, F, k2_mesfunc2(k2_zfmisc_1(A, B), G))) &  (r1_mesfunc5(B, D, F, k6_mesfun12(A, B, C, E, k9_mesfunc1(k2_zfmisc_1(A, B), G))) & r1_mesfunc5(A, C, E, k7_mesfun12(A, B, D, F, k9_mesfunc1(k2_zfmisc_1(A, B), G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  (m1_subset_1(D, C) =>  (v1_mesfunc1(B, A, C, D) => v1_mesfunc1(k1_mesfunc2(A, B), A, C, D)) ) ) ) ) ) ) ) ) ).
fof(t26_mesfun13, 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] :  (m2_subset_1(D, k1_zfmisc_1(A), B) =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ~ ( (k9_supinf_2(C, D)=k5_numbers &  (r1_tarski(D, k1_relset_1(A, E)) &  (r1_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, E, k3_subset_1(A, D))) &  (! [F] :  ( (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ~ ( (k1_relset_1(A, F)=k1_relset_1(A, E) &  (r2_relset_1(A, k6_numbers, k2_partfun1(A, k6_numbers, E, k3_subset_1(A, D)), k2_partfun1(A, k6_numbers, F, k3_subset_1(A, D))) &  (r1_mesfunc5(A, B, C, F) & k7_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, E, k3_subset_1(A, D)))=k7_mesfunc5(A, B, C, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  (m1_subset_1(D, C) =>  ( (v1_mesfunc1(B, A, C, D) & r1_tarski(D, k1_relset_1(A, B)))  => v1_mesfunc1(k2_mesfunc2(A, B), A, C, D)) ) ) ) ) ) ) ) ) ).
fof(t27_mesfunc2, 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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [D] :  (m1_subset_1(D, B) =>  ( (v1_mesfunc1(C, A, B, D) & r1_tarski(D, k1_relset_1(A, C)))  => v1_mesfunc1(k9_mesfunc1(A, C), A, B, D)) ) ) ) ) ) ) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_mesfunc2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  ( (v3_valued_0(B) | v3_valued_0(C))  =>  (k1_relset_1(A, k3_mesfunc1(A, B, C))=k9_subset_1(A, k1_relset_1(A, B), k1_relset_1(A, C)) & k1_relset_1(A, k4_mesfunc1(A, B, C))=k9_subset_1(A, k1_relset_1(A, B), k1_relset_1(A, C))) ) ) ) ) ) ) ) ).
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(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t2_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(B, C))  => r1_xxreal_0(A, C)) ) ) ) ) ) ) ).
fof(t31_mesfun11, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v6_supinf_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  => r2_relset_1(A, k6_numbers, B, k1_mesfunc2(A, B))) ) ) ) ).
fof(t36_mesfun12, 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))))  =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [F] :  (m2_subset_1(F, k1_zfmisc_1(A), B) =>  ( (r2_relset_1(A, k6_numbers, k2_partfun1(A, k6_numbers, D, F), k2_partfun1(A, k6_numbers, E, F)) &  (r1_tarski(F, k1_relset_1(A, D)) &  (r1_tarski(F, k1_relset_1(A, E)) & v1_mesfunc1(D, A, B, F)) ) )  => v1_mesfunc1(E, A, B, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_extreal1, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) =>  (r1_xxreal_0(k5_numbers, A) => k1_extreal1(A)=A) ) ) ).
fof(t3_partfun1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, C))))  =>  ~ ( (r2_hidden(A, k10_xtuple_0(D)) &  (! [E] :  (m1_subset_1(E, B) =>  ~ ( (r2_tarski(E, k1_relset_1(B, D)) & A=k1_funct_1(D, E)) ) ) ) ) ) ) ) ) ) ) ).
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(t41_extreal1, axiom,  (! [A] :  (v1_xxreal_0(A) =>  ( ~ (r1_xxreal_0(k1_supinf_1, k1_extreal1(A)))  <=> r2_hidden(A, k1_numbers)) ) ) ).
fof(t45_mesfun12, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  (! [D] :  (m1_subset_1(D, A) =>  (r2_relset_1(B, k6_numbers, k2_mesfun12(A, B, k6_numbers, k1_mesfunc2(k2_zfmisc_1(A, B), C), D), k1_mesfunc2(B, k2_mesfun12(A, B, k6_numbers, C, D))) & r2_relset_1(B, k6_numbers, k2_mesfun12(A, B, k6_numbers, k2_mesfunc2(k2_zfmisc_1(A, B), C), D), k2_mesfunc2(B, k2_mesfun12(A, B, k6_numbers, C, D)))) ) ) ) ) ) ) ) ) ).
fof(t47_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, k9_xtuple_0(k5_relat_1(C, A))) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t47_mesfun12, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  (! [F] :  (m1_subset_1(F, A) =>  (! [G] :  (m1_subset_1(G, B) =>  (! [H] :  (m2_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(A, B)), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D))) =>  ( (r1_relset_1(A, B, H, k1_relset_1(k2_zfmisc_1(A, B), E)) & v1_mesfunc1(E, k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), H))  =>  (v1_mesfunc1(k2_mesfun12(A, B, k6_numbers, E, F), B, D, k9_measur11(A, B, C, D, H, F)) & v1_mesfunc1(k3_mesfun12(A, B, k6_numbers, E, G), A, C, k10_measur11(A, B, C, D, H, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, A) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t4_partfun1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) &  (v5_relat_1(C, B) & v1_funct_1(C)) )  =>  (r2_hidden(A, k9_xtuple_0(C)) => r2_tarski(k1_funct_1(C, A), B)) ) ) ) ) ).
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(t53_mesfun11, 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) &  (v6_supinf_2(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  =>  (! [E] :  (m1_subset_1(E, B) =>  ( (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E))  =>  (k7_mesfunc5(A, B, C, k2_mesfunc2(A, D))=k5_numbers & k6_mesfunc5(A, B, C, k2_mesfunc2(A, D))=k5_numbers) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t54_mesfun11, 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))))  =>  (! [E] :  (m1_subset_1(E, B) =>  ( (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E))  => k7_mesfunc5(A, B, C, D)=k10_xxreal_3(k7_mesfunc5(A, B, C, k1_mesfunc2(A, D)), k7_mesfunc5(A, B, C, k2_mesfunc2(A, D)))) ) ) ) ) ) ) ) ) ) ) ).
fof(t57_relat_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) =>  (r2_hidden(B, k9_xtuple_0(k5_relat_1(C, A))) <=>  (r2_hidden(B, A) & r2_hidden(B, k9_xtuple_0(C))) ) ) ) ) ) ).
fof(t5_mesfun11, 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))))  =>  (v6_supinf_2(k1_mesfunc2(A, D)) &  (v6_supinf_2(k2_mesfunc2(A, D)) & v6_supinf_2(k9_mesfunc1(A, D))) ) ) ) ) ) ) ) ) ) ).
fof(t5_partfun1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  ( (k1_relset_1(A, C)=k1_relset_1(A, D) &  (! [E] :  (m1_subset_1(E, A) =>  (r2_tarski(E, k1_relset_1(A, C)) => k1_funct_1(C, E)=k1_funct_1(D, E)) ) ) )  => C=D) ) ) ) ) ) ) ).
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(t60_mesfun12, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, D, k6_numbers) &  (v12_valued_0(E) &  (v6_supinf_2(E) &  (v4_measure1(E, B, D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(D, k6_numbers)))) ) ) ) )  =>  (! [F] :  ( (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  (! [G] :  (m2_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(A, B)), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D))) =>  (! [H] :  (m2_subset_1(H, k1_zfmisc_1(A), C) =>  ( (v4_measur11(E, B, D) &  (r2_relset_1(A, B, G, k1_relset_1(k2_zfmisc_1(A, B), F)) & v1_mesfunc1(F, k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), G)) )  =>  ( ( ~ (v6_supinf_2(F))  &  ~ (v2_mesfunc5(F)) )  | v1_mesfunc1(k7_mesfun12(A, B, D, E, F), A, C, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t61_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) => k9_xtuple_0(k5_relat_1(B, A))=k3_xboole_0(k9_xtuple_0(B), A)) ) ) ).
fof(t62_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (r1_tarski(A, k9_xtuple_0(B)) => k9_xtuple_0(k5_relat_1(B, A))=A) ) ) ) ).
fof(t66_measur11, 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_subset_1(C, k1_zfmisc_1(A), B) =>  (! [D] :  ( (v1_funct_1(D) &  (v4_mesfunc5(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v3_mesfunc5(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers)))) )  =>  ( (v1_mesfunc1(D, A, B, C) &  (v1_mesfunc1(E, A, B, C) & r1_tarski(C, k1_relset_1(A, k15_measur11(A, D, E)))) )  => v1_mesfunc1(k15_measur11(A, D, E), A, B, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_mesfun13, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k6_numbers))))  =>  (! [C] :  (m1_subset_1(C, A) =>  (r1_xxreal_0(k9_supinf_2(k1_mesfunc2(A, B), C), k9_supinf_2(k9_mesfunc1(A, B), C)) & r1_xxreal_0(k9_supinf_2(k2_mesfunc2(A, B), C), k9_supinf_2(k9_mesfunc1(A, B), C))) ) ) ) ) ) ) ).
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(t6_relset_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (r1_tarski(k10_xtuple_0(D), C) => m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) ) ) ).
fof(t79_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))))  =>  (v6_supinf_2(D) =>  ( (! [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) =>  ~ ( (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E)) ) ) )  | r1_xxreal_0(k5_numbers, k6_mesfunc5(A, B, C, D))) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_mesfun13, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, B) =>  (r2_relset_1(B, k6_numbers, k2_mesfun12(A, B, k6_numbers, k9_mesfunc1(k2_zfmisc_1(A, B), C), D), k9_mesfunc1(B, k2_mesfun12(A, B, k6_numbers, C, D))) & r2_relset_1(A, k6_numbers, k3_mesfun12(A, B, k6_numbers, k9_mesfunc1(k2_zfmisc_1(A, B), C), E), k9_mesfunc1(A, k3_mesfun12(A, B, k6_numbers, C, E)))) ) ) ) ) ) ) ) ) ) ) ).
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(t84_mesfun12, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_prob_1(C, A) &  (v4_prob_1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v1_prob_1(D, B) &  (v4_prob_1(D, B) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(B)))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, C, k6_numbers) &  (v12_valued_0(E) &  (v6_supinf_2(E) &  (v4_measure1(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(C, k6_numbers)))) ) ) ) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, D, k6_numbers) &  (v12_valued_0(F) &  (v6_supinf_2(F) &  (v4_measure1(F, B, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(D, k6_numbers)))) ) ) ) )  =>  (! [G] :  (m2_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(A, B)), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D))) =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k6_numbers))))  =>  ( (v4_measur11(E, A, C) &  (v4_measur11(F, B, D) &  (r2_relset_1(A, B, G, k1_relset_1(k2_zfmisc_1(A, B), H)) & v1_mesfunc1(H, k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), G)) ) )  =>  ( ( ~ (v6_supinf_2(H))  &  ~ (v2_mesfunc5(H)) )  |  (k7_mesfunc5(k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k8_mesfun12(A, B, C, D, E, F), H)=k7_mesfunc5(B, D, F, k6_mesfun12(A, B, C, E, H)) & k7_mesfunc5(k2_zfmisc_1(A, B), k9_prob_1(k2_zfmisc_1(A, B), k3_measur10(A, B, C, D)), k8_mesfun12(A, B, C, D, E, F), H)=k7_mesfunc5(A, C, E, k7_mesfun12(A, B, D, F, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t88_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))))  =>  (v6_supinf_2(D) =>  ( (! [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) =>  ~ ( (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E)) ) ) )  | k7_mesfunc5(A, B, C, D)=k6_mesfunc5(A, B, C, D)) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ) ) ) ).
fof(t90_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))))  =>  (v6_supinf_2(D) =>  ( (! [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) =>  ~ ( (E=k1_relset_1(A, D) & v1_mesfunc1(D, A, B, E)) ) ) )  | r1_xxreal_0(k5_numbers, k7_mesfunc5(A, B, C, D))) ) ) ) ) ) ) ) ) ) ).
fof(t95_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))))  =>  (! [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) =>  (! [F] :  (m2_subset_1(F, k1_zfmisc_1(A), B) =>  ( (E=k1_relset_1(A, D) &  (v1_mesfunc1(D, A, B, E) & k9_supinf_2(C, F)=k5_numbers) )  => k7_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, D, k7_prob_1(A, B, E, F)))=k7_mesfunc5(A, B, C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t97_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))))  =>  (! [E] :  (m2_subset_1(E, k1_zfmisc_1(A), B) =>  (r1_mesfunc5(A, B, C, D) =>  (r1_xxreal_0(k6_mesfunc5(A, B, C, k1_mesfunc2(A, k2_partfun1(A, k6_numbers, D, E))), k6_mesfunc5(A, B, C, k1_mesfunc2(A, D))) &  (r1_xxreal_0(k6_mesfunc5(A, B, C, k2_mesfunc2(A, k2_partfun1(A, k6_numbers, D, E))), k6_mesfunc5(A, B, C, k2_mesfunc2(A, D))) & r1_mesfunc5(A, B, C, k2_partfun1(A, k6_numbers, D, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  ~ ( (r2_hidden(A, k1_numbers) & r1_xxreal_0(k1_xxreal_0, A)) ) ) ) ).
