% Mizar problem: t22_pralg_3,pralg_3,783,5 
fof(t22_pralg_3, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) =>  ( ~ (k1_msualg_1(B, D)=k1_xboole_0)  =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(B, D, k14_pralg_2(A, B, C))) =>  (! [F] :  (m1_subset_1(F, A) =>  (! [G] :  ( (v1_relat_1(G) & v1_funct_1(G))  =>  (G=k3_funct_2(k3_msualg_1(B, D, k14_pralg_2(A, B, C)), k4_msualg_1(B, D, k14_pralg_2(A, B, C)), k5_msualg_1(B, D, k14_pralg_2(A, B, C)), E) => k1_funct_1(G, F)=k1_funct_1(k5_msualg_1(B, D, k5_pralg_2(A, B, C, F)), k1_funct_1(k9_funct_6(E), F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v3_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  & l3_msualg_1(B, A))  =>  (v3_msualg_1(B, A) => B=g3_msualg_1(A, u3_msualg_1(A, B), u4_msualg_1(A, B))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k4_card_3(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc10_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) & v5_funct_1(C, B)) )  =>  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) ) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ~ (v2_struct_0(A))  => v14_struct_0(A)) ) ) ).
fof(cc13_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k4_card_3(B)) => v1_partfun1(C, A)) ) ) ) ).
fof(cc13_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v14_struct_0(A)) ) ) ).
fof(cc14_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k4_card_3(B)) => v1_partfun1(C, A)) ) ) ) ).
fof(cc14_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( (v2_struct_0(A) & v14_struct_0(A))  => v11_struct_0(A)) ) ) ).
fof(cc15_card_3, axiom,  (! [A] :  ( ~ (v4_card_3(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc15_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ( ~ (v11_struct_0(A))  & v14_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc16_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v15_struct_0(A)) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_card_3, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (! [C] :  (m1_subset_1(C, k10_xtuple_0(u3_msualg_1(A, B))) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, A)) ) ) ) ).
fof(cc1_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc1_pralg_2, axiom,  (! [A] :  ( (v4_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v2_card_3(A)) )  =>  (! [B] :  (m1_subset_1(B, A) => v4_relat_1(B, k9_card_3(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_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_card_3, axiom,  (! [A, B] :  (v1_setfam_1(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v2_relat_1(C) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (! [C] :  (m1_subset_1(C, k10_xtuple_0(k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, B)))) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
fof(cc2_partfun1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ~ (v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v2_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc2_pralg_2, axiom,  (! [A] :  ( (v4_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v2_card_3(A)) )  =>  (! [B] :  (m1_subset_1(B, A) => v1_partfun1(B, k9_card_3(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_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_card_3, axiom,  (! [A] :  (v3_card_3(A) =>  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) => v1_funcop_1(D)) ) ) ) ).
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_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  ~ (v2_setfam_1(A)) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_card_3, axiom,  (! [A] :  (v5_card_3(A) =>  ( ~ (v1_finset_1(A))  & v4_card_3(A)) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc4_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_setfam_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v2_setfam_1(A)) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc5_card_3, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v4_card_3(A))  => v5_card_3(A)) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc5_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_card_3, axiom,  (! [A] :  (v1_finset_1(A) => v4_card_3(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_card_3, axiom,  (! [A] :  (v4_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_card_3(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_card_3, axiom,  (! [A] :  (v2_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_card_3(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k4_card_3(A)) => v5_funct_1(B, A)) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(d12_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) => k12_pralg_2(A, B, C, D)=k1_funct_1(k9_funct_6(k11_pralg_2(A, B, C)), D)) ) ) ) ) ) ) ).
fof(d13_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m2_pboole(D, u4_struct_0(B), k3_relat_1(u1_msualg_1(B), k6_finseq_2(u1_struct_0(B), k10_pralg_2(A, B, C))), k3_relat_1(u2_msualg_1(B), k10_pralg_2(A, B, C))) =>  ( ( ~ (A=k1_xboole_0)  =>  (D=k13_pralg_2(A, B, C) <=>  (! [E] :  (m1_subset_1(E, u4_struct_0(B)) => k1_funct_1(D, E)=k15_funcop_1(k1_msualg_1(B, E), k1_xboole_0, k9_funct_6(k12_pralg_2(A, B, C, E)), k1_pralg_2(k2_pralg_2(k12_pralg_2(A, B, C, E))))) ) ) )  &  (A=k1_xboole_0 => D=k13_pralg_2(A, B, C)) ) ) ) ) ) ) ) ) ).
fof(d14_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) => k14_pralg_2(A, B, C)=g3_msualg_1(B, k10_pralg_2(A, B, C), k13_pralg_2(A, B, C))) ) ) ) ) ).
fof(d19_pralg_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (C=k17_pralg_1(A, B) <=>  (k9_xtuple_0(C)=k3_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B)) &  (! [D] :  (r2_tarski(D, k9_xtuple_0(C)) => k1_funct_1(C, D)=k1_funct_1(k1_funct_1(A, D), k1_funct_1(B, D))) ) ) ) ) ) ) ) ) ) ).
fof(d1_pralg_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (B=k1_pralg_2(A) <=>  ( (! [C] :  (r2_hidden(C, k9_xtuple_0(B)) <=>  (? [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  &  (r2_tarski(D, k9_xtuple_0(A)) & C=k9_funct_6(D)) ) ) ) )  &  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_tarski(C, k9_xtuple_0(B)) => k1_funct_1(B, C)=k1_funct_1(A, k9_funct_6(C))) ) ) ) ) ) ) ) ) ).
fof(d2_partfun1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_partfun1(B, A) <=> k1_relset_1(A, B)=A) ) ) ) ).
fof(d2_pralg_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_card_3(k1_funct_6(A))) &  (v1_funct_1(B) &  (v1_partfun1(B, k4_card_3(k1_funct_6(A))) & v1_funcop_1(B)) ) ) )  =>  (B=k2_pralg_2(A) <=>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_tarski(C, k4_card_3(k1_funct_6(A))) => k1_funct_1(B, C)=k17_pralg_1(A, C)) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d6_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k5_msualg_1(A, B, C)=k1_funct_1(u4_msualg_1(A, C), B)) ) ) ) ) ) ).
fof(d8_funcop_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (A=B => k14_funcop_1(A, B, C, D)=C)  &  ( ~ (A=B)  => k14_funcop_1(A, B, C, D)=D) ) ) ) ) ) ).
fof(dt_g3_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  & m2_pboole(C, u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), B)), k3_relat_1(u2_msualg_1(A), B))) )  =>  (v3_msualg_1(g3_msualg_1(A, B, C), A) & l3_msualg_1(g3_msualg_1(A, B, C), A)) ) ) ).
fof(dt_k10_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  & m1_pralg_2(C, A, B))  =>  (v1_relat_1(k10_pralg_2(A, B, C)) &  (v4_relat_1(k10_pralg_2(A, B, C), u1_struct_0(B)) &  (v1_funct_1(k10_pralg_2(A, B, C)) & v1_partfun1(k10_pralg_2(A, B, C), u1_struct_0(B))) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  & m1_pralg_2(C, A, B))  =>  (v1_relat_1(k11_pralg_2(A, B, C)) &  (v4_relat_1(k11_pralg_2(A, B, C), A) &  (v1_funct_1(k11_pralg_2(A, B, C)) &  (v1_partfun1(k11_pralg_2(A, B, C), A) & v1_funcop_1(k11_pralg_2(A, B, C))) ) ) ) ) ) ).
fof(dt_k12_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  &  (m1_pralg_2(C, A, B) & m1_subset_1(D, u4_struct_0(B))) )  =>  (v1_relat_1(k12_pralg_2(A, B, C, D)) &  (v4_relat_1(k12_pralg_2(A, B, C, D), A) &  (v1_funct_1(k12_pralg_2(A, B, C, D)) &  (v1_partfun1(k12_pralg_2(A, B, C, D), A) & v1_funcop_1(k12_pralg_2(A, B, C, D))) ) ) ) ) ) ).
fof(dt_k13_finseq_1, axiom, $true).
fof(dt_k13_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => m2_pboole(k13_pralg_2(A, B, C), u4_struct_0(B), k3_relat_1(u1_msualg_1(B), k6_finseq_2(u1_struct_0(B), k10_pralg_2(A, B, C))), k3_relat_1(u2_msualg_1(B), k10_pralg_2(A, B, C)))) ) ).
fof(dt_k14_funcop_1, axiom, $true).
fof(dt_k14_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => l3_msualg_1(k14_pralg_2(A, B, C), B)) ) ).
fof(dt_k15_funcop_1, axiom, $true).
fof(dt_k17_pralg_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k17_pralg_1(A, B)) & v1_funct_1(k17_pralg_1(A, B))) ) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_funct_6, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_6(A)) & v1_funct_1(k1_funct_6(A))) ) ) ).
fof(dt_k1_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & m1_subset_1(B, u4_struct_0(A)))  => m2_finseq_2(k1_msualg_1(A, B), u1_struct_0(A), k3_finseq_2(u1_struct_0(A)))) ) ).
fof(dt_k1_pralg_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k1_pralg_2(A)) & v1_funct_1(k1_pralg_2(A))) ) ) ).
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_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_pralg_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k2_pralg_2(A)) &  (v4_relat_1(k2_pralg_2(A), k4_card_3(k1_funct_6(A))) &  (v1_funct_1(k2_pralg_2(A)) &  (v1_partfun1(k2_pralg_2(A), k4_card_3(k1_funct_6(A))) & v1_funcop_1(k2_pralg_2(A))) ) ) ) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_finseq_2, axiom,  (! [A] : m1_finseq_2(k3_finseq_2(A), A)) ).
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_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & l3_msualg_1(C, A)) )  => m1_subset_1(k3_msualg_1(A, B, C), k10_xtuple_0(k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, C))))) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_card_3, axiom, $true).
fof(dt_k4_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & l3_msualg_1(C, A)) )  => m1_subset_1(k4_msualg_1(A, B, C), k10_xtuple_0(u3_msualg_1(A, C)))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & l3_msualg_1(C, A)) )  =>  (v1_funct_1(k5_msualg_1(A, B, C)) &  (v1_funct_2(k5_msualg_1(A, B, C), k3_msualg_1(A, B, C), k4_msualg_1(A, B, C)) & m1_subset_1(k5_msualg_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k3_msualg_1(A, B, C), k4_msualg_1(A, B, C))))) ) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  &  (m1_pralg_2(C, A, B) & m1_subset_1(D, A)) ) )  =>  (v4_msualg_1(k5_pralg_2(A, B, C, D), B) & l3_msualg_1(k5_pralg_2(A, B, C, D), B)) ) ) ).
fof(dt_k6_finseq_2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k6_finseq_2(A, B)) &  (v4_relat_1(k6_finseq_2(A, B), k3_finseq_2(A)) &  (v1_funct_1(k6_finseq_2(A, B)) & v1_partfun1(k6_finseq_2(A, B), k3_finseq_2(A))) ) ) ) ) ).
fof(dt_k6_funct_6, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k6_funct_6(A)) & v1_funct_1(k6_funct_6(A))) ) ) ).
fof(dt_k9_card_3, axiom, $true).
fof(dt_k9_funct_6, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k9_funct_6(A)) &  (v1_funct_1(k9_funct_6(A)) & v1_funcop_1(k9_funct_6(A))) ) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) => l5_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_msualg_1, axiom, $true).
fof(dt_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (! [B] :  (l3_msualg_1(B, A) => l2_msualg_1(B, A)) ) ) ) ).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_finseq_2, axiom, $true).
fof(dt_m1_pralg_2, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) => m2_finseq_1(C, A)) ) ) ) ).
fof(dt_m2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) ) ) ) ) ).
fof(dt_u1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v1_funct_1(u1_msualg_1(A)) &  (v1_funct_2(u1_msualg_1(A), u4_struct_0(A), k3_finseq_2(u1_struct_0(A))) & m1_subset_1(u1_msualg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), k3_finseq_2(u1_struct_0(A)))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v1_funct_1(u2_msualg_1(A)) &  (v1_funct_2(u2_msualg_1(A), u4_struct_0(A), u1_struct_0(A)) & m1_subset_1(u2_msualg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_u3_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l2_msualg_1(B, A))  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), u1_struct_0(A))) ) ) ) ) ).
fof(dt_u4_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  & l3_msualg_1(B, A))  => m2_pboole(u4_msualg_1(A, B), u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, B))), k3_relat_1(u2_msualg_1(A), u3_msualg_1(A, B)))) ) ).
fof(dt_u4_struct_0, axiom, $true).
fof(existence_l1_msualg_1, axiom,  (? [A] : l1_msualg_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_msualg_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l2_msualg_1(B, A)) ) ) ).
fof(existence_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] : l3_msualg_1(B, A)) ) ) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, A)) ) ).
fof(existence_m1_pralg_2, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (? [C] : m1_pralg_2(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (? [C] : m2_finseq_2(C, A, B)) ) ) ).
fof(existence_m2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (? [D] : m2_pboole(D, A, B, C)) ) ) ).
fof(fc10_card_3, axiom, v5_card_3(k4_ordinal1)).
fof(fc10_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, A))) ) ) ).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc13_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  ~ (v1_xboole_0(k3_tarski(A))) ) ) ).
fof(fc13_struct_0, axiom,  (! [A] :  ( (v11_struct_0(A) & l5_struct_0(A))  => v1_xboole_0(u4_struct_0(A))) ) ).
fof(fc14_struct_0, axiom,  (! [A] :  ( ( ~ (v11_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_xboole_0(u4_struct_0(A))) ) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc1_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v4_msualg_1(B, A) & l2_msualg_1(B, A)) )  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v2_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), u1_struct_0(A))) ) ) ) ) ) ).
fof(fc1_msualg_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  & m1_subset_1(C, u4_struct_0(A))) )  => v4_funct_1(k3_msualg_1(A, C, B))) ) ).
fof(fc1_pboole, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_relat_1(D) &  (v4_relat_1(D, B) &  (v1_funct_1(D) & v1_partfun1(D, B)) ) ) ) )  =>  (v1_relat_1(k3_relat_1(C, D)) &  (v4_relat_1(k3_relat_1(C, D), A) &  (v1_funct_1(k3_relat_1(C, D)) & v1_partfun1(k3_relat_1(C, D), A)) ) ) ) ) ).
fof(fc1_pralg_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => v4_msualg_1(k14_pralg_2(A, B, C), B)) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_struct_0, axiom,  (! [A] :  ( (v15_struct_0(A) & l5_struct_0(A))  => v1_zfmisc_1(u4_struct_0(A))) ) ).
fof(fc21_struct_0, axiom,  (! [A] :  ( ( ~ (v15_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_zfmisc_1(u4_struct_0(A))) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  & m1_subset_1(C, A)) )  =>  ~ (v1_xboole_0(k1_funct_1(B, C))) ) ) ).
fof(fc2_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_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc4_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k4_card_3(A))) ) ).
fof(fc5_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_xboole_0(k4_card_3(A))) ) ) ).
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(fc6_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  & m1_pralg_2(C, A, B))  =>  (v1_relat_1(k10_pralg_2(A, B, C)) &  (v2_relat_1(k10_pralg_2(A, B, C)) &  (v4_relat_1(k10_pralg_2(A, B, C), u1_struct_0(B)) &  (v1_funct_1(k10_pralg_2(A, B, C)) & v1_partfun1(k10_pralg_2(A, B, C), u1_struct_0(B))) ) ) ) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => v3_msualg_1(k14_pralg_2(A, B, C), B)) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_card_3, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_card_3(A))) ) ).
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_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v3_card_3(k4_card_3(A))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_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_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_3_1_pralg_3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  & l1_msualg_1(C)) )  & m1_pralg_2(D, B, C)) )  =>  (r2_hidden(A, a_3_1_pralg_3(B, C, D)) <=>  (? [E, F] :  ( (m1_subset_1(E, B) & m1_subset_1(F, u1_struct_0(C)))  & A=k1_funct_1(u3_msualg_1(C, k5_pralg_2(B, C, D, E)), F)) ) ) ) ) ).
fof(free_g3_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  & m2_pboole(C, u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), B)), k3_relat_1(u2_msualg_1(A), B))) )  =>  (! [D, E, F] :  (g3_msualg_1(A, B, C)=g3_msualg_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(rc1_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_partfun1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ) ).
fof(rc1_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_setfam_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_setfam_1(A)) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(A)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_setfam_1, axiom,  (? [A] :  ~ (v2_setfam_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(rc3_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_partfun1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  ~ (v1_xboole_0(C)) ) ) ) ) ) ) ) ) ).
fof(rc3_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_card_3(A)) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc5_card_3, axiom,  (? [A] : v5_card_3(A)) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] :  (l3_msualg_1(B, A) & v3_msualg_1(B, 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(rc6_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] :  (l3_msualg_1(B, A) &  (v3_msualg_1(B, A) & v4_msualg_1(B, A)) ) ) ) ) ).
fof(rc6_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v5_funct_1(C, B) & v1_partfun1(C, 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_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_pboole, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, B)) ) ) ) ) ) ) ).
fof(rc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (? [C] :  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v5_funct_1(C, B)) ) ) ) ) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(redefinition_k15_funcop_1, axiom,  (! [A, B, C, D] : k15_funcop_1(A, B, C, D)=k14_funcop_1(A, B, C, D)) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_pralg_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  => k2_pralg_2(A)=k6_funct_6(A)) ) ).
fof(redefinition_k3_finseq_2, axiom,  (! [A] : k3_finseq_2(A)=k13_finseq_1(A)) ).
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_k5_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  &  (m1_pralg_2(C, A, B) & m1_subset_1(D, A)) ) )  => k5_pralg_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t14_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(B, D, k14_pralg_2(A, B, C))) => r2_tarski(E, k1_funct_2(k1_relset_1(k4_ordinal1, k1_msualg_1(B, D)), k1_funct_2(A, k3_tarski(a_3_1_pralg_3(A, B, C)))))) ) ) ) ) ) ) ) ) ) ).
fof(t17_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(B, D, k14_pralg_2(A, B, C))) =>  ( ~ (k1_msualg_1(B, D)=k1_xboole_0)  => r2_tarski(k9_funct_6(E), k4_card_3(k1_funct_6(k12_pralg_2(A, B, C, D))))) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(B, D, k14_pralg_2(A, B, C))) =>  ( ~ (k1_msualg_1(B, D)=k1_xboole_0)  => r2_tarski(E, k9_xtuple_0(k1_pralg_2(k2_pralg_2(k12_pralg_2(A, B, C, D)))))) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_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(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t55_funct_6, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (r2_tarski(D, k1_funct_2(A, k1_funct_2(B, C))) =>  (A=k1_xboole_0 |  (B=k1_xboole_0 | r2_tarski(k9_funct_6(D), k1_funct_2(B, k1_funct_2(A, C)))) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_pralg_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  & l1_msualg_1(C)) )  =>  (! [D] :  (m1_pralg_2(D, A, C) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(C)) => k1_funct_1(k12_pralg_2(A, C, D, E), B)=k5_msualg_1(C, E, k5_pralg_2(A, C, D, B))) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t92_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_tarski(C, k1_funct_2(A, B)) =>  (k9_xtuple_0(C)=A & r1_tarski(k10_xtuple_0(C), B)) ) ) ) ) ) ).
