% Mizar problem: t56_genealg1,genealg1,2266,5 
fof(t56_genealg1, conjecture,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  (m1_subset_1(C, k4_ordinal1) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) =>  (! [F] :  (m1_subset_1(F, k4_ordinal1) =>  (! [G] :  ( ( ~ (v1_xboole_0(G))  &  (v1_relat_1(G) &  (v2_relat_1(G) &  (v1_funct_1(G) & v1_finseq_1(G)) ) ) )  =>  (! [H] :  (m1_genealg1(H, G) =>  (! [I] :  (m1_genealg1(I, G) =>  (k12_genealg1(G, H, I, A, B, C, D, E, F)=k12_genealg1(G, H, I, B, A, C, D, E, F) &  (k12_genealg1(G, H, I, A, B, C, D, E, F)=k12_genealg1(G, H, I, C, B, A, D, E, F) &  (k12_genealg1(G, H, I, A, B, C, D, E, F)=k12_genealg1(G, H, I, D, B, C, A, E, F) &  (k12_genealg1(G, H, I, A, B, C, D, E, F)=k12_genealg1(G, H, I, E, B, C, D, A, F) & k12_genealg1(G, H, I, A, B, C, D, E, F)=k12_genealg1(G, H, I, F, B, C, D, E, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(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_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_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_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_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, 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_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_setfam_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_setfam_1(A))  =>  ~ (v2_setfam_1(A)) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_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_setfam_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v2_setfam_1(A)) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_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(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_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(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_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(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_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(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(d2_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m2_finseq_1(B, k3_card_3(A)) =>  (! [C] :  (m2_finseq_1(C, k3_card_3(A)) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) => k1_genealg1(A, B, C, D)=k8_finseq_1(k3_card_3(A), k17_finseq_1(k3_card_3(A), D, B), k2_rfinseq(k3_card_3(A), D, C))) ) ) ) ) ) ) ) ).
fof(d3_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m2_finseq_1(B, k3_card_3(A)) =>  (! [C] :  (m2_finseq_1(C, k3_card_3(A)) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) => k2_genealg1(A, B, C, D, E)=k1_genealg1(A, k1_genealg1(A, B, C, D), k1_genealg1(A, C, B, D), E)) ) ) ) ) ) ) ) ) ) ).
fof(d4_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m2_finseq_1(B, k3_card_3(A)) =>  (! [C] :  (m2_finseq_1(C, k3_card_3(A)) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) =>  (! [F] :  (m1_subset_1(F, k4_ordinal1) => k3_genealg1(A, B, C, D, E, F)=k1_genealg1(A, k2_genealg1(A, B, C, D, E), k2_genealg1(A, C, B, D, E), F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m2_finseq_1(B, k3_card_3(A)) =>  (! [C] :  (m2_finseq_1(C, k3_card_3(A)) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) =>  (! [F] :  (m1_subset_1(F, k4_ordinal1) =>  (! [G] :  (m1_subset_1(G, k4_ordinal1) => k4_genealg1(A, B, C, D, E, F, G)=k1_genealg1(A, k3_genealg1(A, B, C, D, E, F), k3_genealg1(A, C, B, D, E, F), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m2_finseq_1(B, k3_card_3(A)) =>  (! [C] :  (m2_finseq_1(C, k3_card_3(A)) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) =>  (! [F] :  (m1_subset_1(F, k4_ordinal1) =>  (! [G] :  (m1_subset_1(G, k4_ordinal1) =>  (! [H] :  (m1_subset_1(H, k4_ordinal1) => k5_genealg1(A, B, C, D, E, F, G, H)=k1_genealg1(A, k4_genealg1(A, B, C, D, E, F, G), k4_genealg1(A, C, B, D, E, F, G), H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m2_finseq_1(B, k3_card_3(A)) =>  (! [C] :  (m2_finseq_1(C, k3_card_3(A)) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) =>  (! [F] :  (m1_subset_1(F, k4_ordinal1) =>  (! [G] :  (m1_subset_1(G, k4_ordinal1) =>  (! [H] :  (m1_subset_1(H, k4_ordinal1) =>  (! [I] :  (m1_subset_1(I, k4_ordinal1) => k6_genealg1(A, B, C, D, E, F, G, H, I)=k1_genealg1(A, k5_genealg1(A, B, C, D, E, F, G, H), k5_genealg1(A, C, B, D, E, F, G, H), I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_genealg1, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) & m1_subset_1(G, k4_ordinal1)) ) ) ) ) )  => m1_genealg1(k10_genealg1(A, B, C, D, E, F, G), A)) ) ).
fof(dt_k11_genealg1, axiom,  (! [A, B, C, D, E, F, G, H] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) &  (m1_subset_1(G, k4_ordinal1) & m1_subset_1(H, k4_ordinal1)) ) ) ) ) ) )  => m1_genealg1(k11_genealg1(A, B, C, D, E, F, G, H), A)) ) ).
fof(dt_k12_genealg1, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) &  (m1_subset_1(G, k4_ordinal1) &  (m1_subset_1(H, k4_ordinal1) & m1_subset_1(I, k4_ordinal1)) ) ) ) ) ) ) )  => m1_genealg1(k12_genealg1(A, B, C, D, E, F, G, H, I), A)) ) ).
fof(dt_k16_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ).
fof(dt_k17_finseq_1, axiom,  (! [A, B, C] :  ( (v7_ordinal1(B) & m1_finseq_1(C, A))  => m2_finseq_1(k17_finseq_1(A, B, C), A)) ) ).
fof(dt_k1_genealg1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_finseq_1(B, k3_card_3(A)) &  (m1_finseq_1(C, k3_card_3(A)) & m1_subset_1(D, k4_ordinal1)) ) )  => m2_finseq_1(k1_genealg1(A, B, C, D), k3_card_3(A))) ) ).
fof(dt_k1_rfinseq, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k1_rfinseq(A, B)) &  (v1_funct_1(k1_rfinseq(A, B)) & v1_finseq_1(k1_rfinseq(A, B))) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_genealg1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_finseq_1(B, k3_card_3(A)) &  (m1_finseq_1(C, k3_card_3(A)) &  (m1_subset_1(D, k4_ordinal1) & m1_subset_1(E, k4_ordinal1)) ) ) )  => m2_finseq_1(k2_genealg1(A, B, C, D, E), k3_card_3(A))) ) ).
fof(dt_k2_rfinseq, axiom,  (! [A, B, C] :  ( (v7_ordinal1(B) &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  => m2_finseq_1(k2_rfinseq(A, B, C), A)) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_genealg1, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_finseq_1(B, k3_card_3(A)) &  (m1_finseq_1(C, k3_card_3(A)) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) & m1_subset_1(F, k4_ordinal1)) ) ) ) )  => m2_finseq_1(k3_genealg1(A, B, C, D, E, F), k3_card_3(A))) ) ).
fof(dt_k4_genealg1, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_finseq_1(B, k3_card_3(A)) &  (m1_finseq_1(C, k3_card_3(A)) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) & m1_subset_1(G, k4_ordinal1)) ) ) ) ) )  => m2_finseq_1(k4_genealg1(A, B, C, D, E, F, G), k3_card_3(A))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_genealg1, axiom,  (! [A, B, C, D, E, F, G, H] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_finseq_1(B, k3_card_3(A)) &  (m1_finseq_1(C, k3_card_3(A)) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) &  (m1_subset_1(G, k4_ordinal1) & m1_subset_1(H, k4_ordinal1)) ) ) ) ) ) )  => m2_finseq_1(k5_genealg1(A, B, C, D, E, F, G, H), k3_card_3(A))) ) ).
fof(dt_k6_genealg1, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_finseq_1(B, k3_card_3(A)) &  (m1_finseq_1(C, k3_card_3(A)) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) &  (m1_subset_1(G, k4_ordinal1) &  (m1_subset_1(H, k4_ordinal1) & m1_subset_1(I, k4_ordinal1)) ) ) ) ) ) ) )  => m2_finseq_1(k6_genealg1(A, B, C, D, E, F, G, H, I), k3_card_3(A))) ) ).
fof(dt_k7_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ).
fof(dt_k7_genealg1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) & m1_subset_1(D, k4_ordinal1)) ) )  => m1_genealg1(k7_genealg1(A, B, C, D), A)) ) ).
fof(dt_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => m2_finseq_1(k8_finseq_1(A, B, C), A)) ) ).
fof(dt_k8_genealg1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) & m1_subset_1(E, k4_ordinal1)) ) ) )  => m1_genealg1(k8_genealg1(A, B, C, D, E), 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_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (! [B] :  (m1_genealg1(B, A) => m2_finseq_1(B, k3_card_3(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(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  =>  (? [B] : m1_genealg1(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(fc1_genealg1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  =>  ~ (v1_xboole_0(k3_card_3(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc24_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  ( ~ (v1_xboole_0(k7_finseq_1(A, B)))  & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc25_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, A)) &  (v1_funct_1(k7_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k7_finseq_1(B, A)))  & v1_finseq_1(k7_finseq_1(B, A))) ) ) ) ) ).
fof(fc30_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finseq_1(A)) ) )  &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  (v1_relat_1(k16_finseq_1(B, A)) &  (v1_funct_1(k16_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k16_finseq_1(B, A)))  & v1_finseq_1(k16_finseq_1(B, A))) ) ) ) ) ).
fof(fc42_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v6_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc43_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k4_ordinal1) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc54_finseq_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, C)) &  (v5_relat_1(k7_finseq_1(B, C), A) &  (v1_funct_1(k7_finseq_1(B, C)) & v1_finseq_1(k7_finseq_1(B, C))) ) ) ) ) ).
fof(fc55_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v6_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v6_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(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(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc15_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(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_setfam_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_setfam_1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(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_setfam_1, axiom,  (? [A] :  ~ (v2_setfam_1(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(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_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(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_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k10_genealg1, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) & m1_subset_1(G, k4_ordinal1)) ) ) ) ) )  => k10_genealg1(A, B, C, D, E, F, G)=k4_genealg1(A, B, C, D, E, F, G)) ) ).
fof(redefinition_k11_genealg1, axiom,  (! [A, B, C, D, E, F, G, H] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) &  (m1_subset_1(G, k4_ordinal1) & m1_subset_1(H, k4_ordinal1)) ) ) ) ) ) )  => k11_genealg1(A, B, C, D, E, F, G, H)=k5_genealg1(A, B, C, D, E, F, G, H)) ) ).
fof(redefinition_k12_genealg1, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) &  (m1_subset_1(E, k4_ordinal1) &  (m1_subset_1(F, k4_ordinal1) &  (m1_subset_1(G, k4_ordinal1) &  (m1_subset_1(H, k4_ordinal1) & m1_subset_1(I, k4_ordinal1)) ) ) ) ) ) ) )  => k12_genealg1(A, B, C, D, E, F, G, H, I)=k6_genealg1(A, B, C, D, E, F, G, H, I)) ) ).
fof(redefinition_k17_finseq_1, axiom,  (! [A, B, C] :  ( (v7_ordinal1(B) & m1_finseq_1(C, A))  => k17_finseq_1(A, B, C)=k16_finseq_1(B, C)) ) ).
fof(redefinition_k2_rfinseq, axiom,  (! [A, B, C] :  ( (v7_ordinal1(B) &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  => k2_rfinseq(A, B, C)=k1_rfinseq(B, C)) ) ).
fof(redefinition_k7_genealg1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) & m1_subset_1(D, k4_ordinal1)) ) )  => k7_genealg1(A, B, C, D)=k1_genealg1(A, B, C, D)) ) ).
fof(redefinition_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => k8_finseq_1(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k8_genealg1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) )  &  (m1_genealg1(B, A) &  (m1_genealg1(C, A) &  (m1_subset_1(D, k4_ordinal1) & m1_subset_1(E, k4_ordinal1)) ) ) )  => k8_genealg1(A, B, C, D, E)=k2_genealg1(A, B, C, D, E)) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
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(t13_genealg1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  =>  (! [D] :  (m1_genealg1(D, C) =>  (! [E] :  (m1_genealg1(E, C) => k8_genealg1(C, D, E, A, B)=k8_genealg1(C, D, E, B, A)) ) ) ) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t51_genealg1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  (m1_subset_1(C, k4_ordinal1) =>  (! [D] :  (m1_subset_1(D, k4_ordinal1) =>  (! [E] :  (m1_subset_1(E, k4_ordinal1) =>  (! [F] :  ( ( ~ (v1_xboole_0(F))  &  (v1_relat_1(F) &  (v2_relat_1(F) &  (v1_funct_1(F) & v1_finseq_1(F)) ) ) )  =>  (! [G] :  (m1_genealg1(G, F) =>  (! [H] :  (m1_genealg1(H, F) =>  (k11_genealg1(F, G, H, A, B, C, D, E)=k11_genealg1(F, G, H, B, A, C, D, E) &  (k11_genealg1(F, G, H, A, B, C, D, E)=k11_genealg1(F, G, H, C, B, A, D, E) &  (k11_genealg1(F, G, H, A, B, C, D, E)=k11_genealg1(F, G, H, D, B, C, A, E) & k11_genealg1(F, G, H, A, B, C, D, E)=k11_genealg1(F, G, H, E, B, C, D, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
