% Mizar problem: t50_glib_012,glib_012,3156,5 
fof(t50_glib_012, conjecture,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (! [B] :  (m2_glib_012(B, A) =>  (! [C] :  (m2_glib_012(C, A) => v20_glib_010(C, B)) ) ) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_msafree5, axiom,  (! [A] :  (v6_membered(A) => v6_ordinal1(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc36_glib_010, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) & v20_glib_010(B, A)) ) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) & v19_glib_010(B, A)) ) ) ) ) ) ) ) ) ).
fof(cc37_glib_010, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) & v19_glib_010(B, A)) ) ) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v1_glib_000(C) & v19_glib_010(C, B)) ) ) ) )  =>  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v1_glib_000(C) & v19_glib_010(C, A)) ) ) ) ) ) ) ) ) ).
fof(cc38_glib_010, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) & v20_glib_010(B, A)) ) ) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v1_glib_000(C) & v20_glib_010(C, B)) ) ) ) )  =>  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v1_glib_000(C) & v20_glib_010(C, A)) ) ) ) ) ) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(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(cc9_msafree5, axiom,  (! [A] :  (v6_membered(A) =>  (v5_finset_1(A) & v1_ordinal6(A)) ) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_m2_glib_012, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (! [B] :  (m2_glib_012(B, A) =>  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) & v6_glib_000(B)) ) ) ) ) ) ) ) ) ).
fof(existence_m2_glib_012, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (? [B] : m2_glib_012(B, A)) ) ) ).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_glib_000, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_glib_000, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc8_glib_010, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) &  (v19_glib_010(B, A) & v20_glib_010(B, A)) ) ) ) ) ) ) ) ) ).
fof(t49_glib_012, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_glib_000(B) & v20_glib_010(B, A)) ) ) ) )  =>  (! [C] :  (m2_glib_012(C, A) =>  (! [D] :  (m2_glib_012(D, B) => v20_glib_010(D, C)) ) ) ) ) ) ) ) ).
fof(t53_glib_010, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_glib_000(A)) ) ) )  =>  (v20_glib_010(A, A) & v19_glib_010(A, A)) ) ) ).
