% Mizar problem: t27_robbins3,robbins3,1362,5 
fof(t27_robbins3, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v6_oposet_1(A) &  (v10_oposet_1(A) &  (v10_robbins3(A) &  (v11_robbins3(A) & l4_robbins3(A)) ) ) ) ) ) ) )  => v10_robbins1(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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v19_lattices(B, A) => v21_lattices(B, A)) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_robbins3, axiom,  (! [A] :  (l4_robbins1(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v8_robbins1(A) &  (v10_robbins1(A) &  (v8_robbins3(A) & v9_robbins3(A)) ) ) ) ) ) ) ).
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_robbins3, axiom,  (! [A] :  (l2_qmax_1(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) &  (v6_oposet_1(A) &  (v7_oposet_1(A) & v10_oposet_1(A)) ) ) ) ) ) ) ).
fof(cc13_robbins3, axiom,  (! [A] :  (l3_robbins3(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) &  (v10_robbins3(A) & v11_robbins3(A)) ) ) ) ) ) ).
fof(cc14_robbins3, axiom,  (! [A] :  (l3_robbins3(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v10_robbins3(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) ) ) ) ) ).
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_partit_2, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) &  (v5_relat_2(A) & v8_relat_2(A)) ) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_robbins1(A) & v7_robbins1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v14_lattices(A)) ) ) ) ).
fof(cc1_robbins3, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_robbins3(A) &  (v2_robbins3(A) & v3_robbins3(A)) ) ) ) ) ) ).
fof(cc1_sheffer1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v17_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v11_lattices(A) &  (v1_sheffer1(A) &  (v2_sheffer1(A) &  (v3_sheffer1(A) & v4_sheffer1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v3_lattice3(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ).
fof(cc23_robbins3, axiom,  (! [A] :  (l3_robbins3(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & v10_robbins3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v3_orders_2(A)) ) ) ) ).
fof(cc24_robbins3, axiom,  (! [A] :  (l3_robbins3(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) & v10_robbins3(A)) )  =>  ( ~ (v2_struct_0(A))  & v4_orders_2(A)) ) ) ) ).
fof(cc25_robbins3, axiom,  (! [A] :  (l3_robbins3(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & v10_robbins3(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_orders_2(A)) ) ) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_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_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc2_oposet_1, axiom,  (! [A] :  (l2_qmax_1(A) =>  ( ( ~ (v2_struct_0(A))  & v6_oposet_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) ) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v6_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v7_robbins1(A)) ) ) ) ).
fof(cc2_robbins3, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v9_lattices(A) &  (v1_robbins3(A) &  (v2_robbins3(A) & v3_robbins3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc2_sheffer1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v11_lattices(A) &  (v1_sheffer1(A) &  (v2_sheffer1(A) &  (v3_sheffer1(A) & v4_sheffer1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v17_lattices(A)) ) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & v3_lattice3(A)) ) ) ) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_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_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  & v15_lattices(A)) ) ) ) ).
fof(cc3_oposet_1, axiom,  (! [A] :  (l2_qmax_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v6_oposet_1(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_robbins3, axiom,  (! [A] :  (l2_qmax_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_oposet_1(A) & v10_oposet_1(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v1_oposet_1(A) & v6_oposet_1(A)) ) ) ) ) ).
fof(cc3_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v3_lattice3(A))  =>  ( ~ (v2_struct_0(A))  & v3_yellow_0(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_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v15_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(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_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v5_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v6_robbins1(A)) ) ) ) ) ) ).
fof(cc4_sheffer1, axiom,  (! [A] :  (l2_lattices(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v4_lattices(A) & v5_lattices(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_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_yellow_0(A) =>  (v1_yellow_0(A) & v2_yellow_0(A)) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_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_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v17_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v11_lattices(A) &  (v15_lattices(A) & v16_lattices(A)) ) ) ) ) ) ).
fof(cc5_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) & v10_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v6_lattices(A)) ) ) ) ).
fof(cc5_sheffer1, axiom,  (! [A] :  (l1_lattices(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v6_lattices(A) & v7_lattices(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_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v1_yellow_0(A) & v2_yellow_0(A))  => v3_yellow_0(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(cc6_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v11_lattices(A) &  (v15_lattices(A) & v16_lattices(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v17_lattices(A)) ) ) ) ).
fof(cc6_oposet_1, axiom,  (! [A] :  (l2_qmax_1(A) =>  ( ( ~ (v2_struct_0(A))  & v6_oposet_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) ) ) ) ) ).
fof(cc6_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v17_lattices(A) & v8_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v6_robbins1(A) & v8_robbins1(A)) ) ) ) ) ) ).
fof(cc6_sheffer1, axiom,  (! [A] :  (l3_lattices(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v8_lattices(A) &  (v9_lattices(A) & v17_lattices(A)) ) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v11_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v12_lattices(A)) ) ) ) ) ).
fof(cc7_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v6_robbins1(A) & v10_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v17_lattices(A) & v10_robbins1(A)) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
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_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(cc8_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v5_robbins1(A) & v10_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v17_lattices(A)) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_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_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v18_lattices(B, A) => v20_lattices(B, A)) ) ) ) ) ).
fof(cc9_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v17_lattices(A) & v8_robbins1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v5_robbins1(A) & v8_robbins1(A)) ) ) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k12_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k12_lattice3(A, B, C)=k12_lattice3(A, C, B)) ) ).
fof(commutativity_k13_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k13_lattice3(A, B, C)=k13_lattice3(A, C, B)) ) ).
fof(commutativity_k4_robbins3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) & l1_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k4_robbins3(A, B, C)=k4_robbins3(A, C, B)) ) ).
fof(commutativity_k5_robbins3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k5_robbins3(A, B, C)=k5_robbins3(A, C, B)) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d1_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_lattices(A, B, C)=k4_binop_1(u1_struct_0(A), u2_lattices(A), B, C)) ) ) ) ) ) ).
fof(d23_robbins1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l4_robbins1(A))  =>  (v10_robbins1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_lattices(A, B, C)=k3_robbins1(A, k1_lattices(A, k3_robbins1(A, B), k3_robbins1(A, C)))) ) ) ) ) ) ) ).
fof(d2_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_lattices(A, B, C)=k4_binop_1(u1_struct_0(A), u1_lattices(A), B, C)) ) ) ) ) ) ).
fof(dt_k10_lattice3, axiom,  (! [A, B, C] :  ( (l1_orders_2(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k10_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k11_lattice3, axiom,  (! [A, B, C] :  ( (l1_orders_2(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k11_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k12_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k12_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k13_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k13_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_robbins1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_robbins1(A))  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k3_robbins1(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_robbins3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) & l1_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k4_robbins3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_robbins3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_robbins3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => l1_struct_0(A)) ) ).
fof(dt_l1_robbins1, axiom,  (! [A] :  (l1_robbins1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_robbins3, axiom,  (! [A] :  (l1_robbins3(A) =>  (l2_lattices(A) & l1_orders_2(A)) ) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_lattices, axiom,  (! [A] :  (l2_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l2_qmax_1, axiom,  (! [A] :  (l2_qmax_1(A) =>  (l1_orders_2(A) & l1_robbins1(A)) ) ) ).
fof(dt_l2_robbins1, axiom,  (! [A] :  (l2_robbins1(A) =>  (l2_lattices(A) & l1_robbins1(A)) ) ) ).
fof(dt_l2_robbins3, axiom,  (! [A] :  (l2_robbins3(A) =>  (l1_lattices(A) & l1_orders_2(A)) ) ) ).
fof(dt_l3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (l1_lattices(A) & l2_lattices(A)) ) ) ).
fof(dt_l3_robbins3, axiom,  (! [A] :  (l3_robbins3(A) =>  (l2_robbins3(A) &  (l1_robbins3(A) & l3_lattices(A)) ) ) ) ).
fof(dt_l4_robbins1, axiom,  (! [A] :  (l4_robbins1(A) =>  (l2_robbins1(A) & l3_lattices(A)) ) ) ).
fof(dt_l4_robbins3, axiom,  (! [A] :  (l4_robbins3(A) =>  (l3_robbins3(A) &  (l4_robbins1(A) & l2_qmax_1(A)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_lattices, axiom,  (! [A] :  (l1_lattices(A) =>  (v1_funct_1(u1_lattices(A)) &  (v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_lattices(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_lattices, axiom,  (! [A] :  (l2_lattices(A) =>  (v1_funct_1(u2_lattices(A)) &  (v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_lattices(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_orders_2, axiom,  (? [A] : l1_orders_2(A)) ).
fof(existence_l1_robbins1, axiom,  (? [A] : l1_robbins1(A)) ).
fof(existence_l1_robbins3, axiom,  (? [A] : l1_robbins3(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l2_qmax_1, axiom,  (? [A] : l2_qmax_1(A)) ).
fof(existence_l2_robbins1, axiom,  (? [A] : l2_robbins1(A)) ).
fof(existence_l2_robbins3, axiom,  (? [A] : l2_robbins3(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_l3_robbins3, axiom,  (? [A] : l3_robbins3(A)) ).
fof(existence_l4_robbins1, axiom,  (? [A] : l4_robbins1(A)) ).
fof(existence_l4_robbins3, axiom,  (? [A] : l4_robbins3(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
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_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc11_robbins3, axiom,  (? [A] :  (l4_robbins1(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v8_struct_0(A) &  (v13_struct_0(A, 1) &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v10_lattices(A) &  (v11_lattices(A) &  (v12_lattices(A) &  (v13_lattices(A) &  (v14_lattices(A) &  (v15_lattices(A) &  (v16_lattices(A) &  (v17_lattices(A) &  (v10_robbins1(A) &  (v1_sheffer1(A) &  (v2_sheffer1(A) &  (v3_sheffer1(A) &  (v4_sheffer1(A) &  (v1_robbins3(A) &  (v2_robbins3(A) &  (v3_robbins3(A) &  (v8_robbins3(A) & v9_robbins3(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc13_robbins3, axiom,  (? [A] :  (l3_robbins3(A) &  (v13_struct_0(A, 1) & v3_orders_2(A)) ) ) ).
fof(rc14_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc14_robbins3, axiom,  (? [A] :  (l4_robbins3(A) &  (v13_struct_0(A, 1) & v3_orders_2(A)) ) ) ).
fof(rc15_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc15_oposet_1, axiom,  (? [A] :  (l2_qmax_1(A) &  ( ~ (v2_struct_0(A))  &  (v6_oposet_1(A) &  (v7_oposet_1(A) & v10_oposet_1(A)) ) ) ) ) ).
fof(rc15_robbins3, axiom,  (? [A] :  (l2_qmax_1(A) &  (v13_struct_0(A, 1) & v3_orders_2(A)) ) ) ).
fof(rc16_robbins3, axiom,  (? [A] :  (l4_robbins3(A) &  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v10_robbins1(A) &  (v6_oposet_1(A) &  (v7_oposet_1(A) &  (v10_oposet_1(A) &  (v10_robbins3(A) & v11_robbins3(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc17_robbins3, axiom,  (? [A] :  (l3_robbins3(A) &  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v10_robbins3(A) & v11_robbins3(A)) ) ) ) ) ) ) ).
fof(rc19_robbins3, axiom,  (? [A] :  (l4_robbins3(A) &  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v8_robbins1(A) &  (v10_robbins1(A) &  (v8_robbins3(A) &  (v9_robbins3(A) & v10_robbins3(A)) ) ) ) ) ) ) ) ).
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_oposet_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (v1_relat_1(B) &  (v2_relat_2(B) &  (v5_relat_2(B) & v8_relat_2(B)) ) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_sheffer1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v8_struct_0(A) &  (v13_struct_0(A, 1) &  (v10_lattices(A) &  (v17_lattices(A) &  (v7_robbins1(A) &  (v1_sheffer1(A) &  (v2_sheffer1(A) &  (v3_sheffer1(A) & v4_sheffer1(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(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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_oposet_1, axiom,  (? [A] :  (l2_qmax_1(A) &  ( ~ (v2_struct_0(A))  & v1_oposet_1(A)) ) ) ).
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(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_robbins3, axiom,  (? [A] :  (l1_robbins3(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_robbins3, axiom,  (? [A] :  (l2_robbins3(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_robbins3, axiom,  (? [A] :  (l3_robbins3(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_robbins3, axiom,  (? [A] :  (l3_robbins3(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_robbins3, axiom,  (? [A] :  (l3_robbins3(A) &  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ).
fof(rd1_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k1_lattices(A, B, B)=B) ) ).
fof(redefinition_k12_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k12_lattice3(A, B, C)=k11_lattice3(A, B, C)) ) ).
fof(redefinition_k13_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k13_lattice3(A, B, C)=k10_lattice3(A, B, C)) ) ).
fof(redefinition_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k4_robbins3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) & l1_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k4_robbins3(A, B, C)=k2_lattices(A, B, C)) ) ).
fof(redefinition_k5_robbins3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k5_robbins3(A, B, C)=k1_lattices(A, B, C)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_orders_2(A, B, C) <=> r1_orders_2(A, B, C)) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_orders_2(A, B, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t13_lattice3, axiom,  (! [A] :  ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k10_lattice3(A, B, C)=k10_lattice3(A, C, B)) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_waybel_1, axiom,  (! [A] :  ( (v4_orders_2(A) &  (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_orders_2(A, B, C) => r1_orders_2(A, k12_lattice3(A, B, D), k12_lattice3(A, C, D))) ) ) ) ) ) ) ) ) ).
fof(t22_yellow_0, axiom,  (! [A] :  ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (D=k13_lattice3(A, B, C) <=>  (r1_orders_2(A, B, D) &  (r1_orders_2(A, C, D) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (r1_orders_2(A, B, E) & r1_orders_2(A, C, E))  => r1_orders_2(A, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_yellow_0, axiom,  (! [A] :  ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (D=k12_lattice3(A, B, C) <=>  (r1_orders_2(A, D, B) &  (r1_orders_2(A, D, C) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (r1_orders_2(A, E, B) & r1_orders_2(A, E, C))  => r1_orders_2(A, E, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_robbins3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v6_oposet_1(A) & l2_qmax_1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_orders_2(A, B, C) =>  (C=k10_lattice3(A, B, C) & B=k11_lattice3(A, B, C)) ) ) ) ) ) ) ) ).
fof(t25_robbins3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v10_robbins3(A) & l4_robbins3(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k10_lattice3(A, B, C)=k5_robbins3(A, B, C)) ) ) ) ) ) ).
fof(t26_robbins3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v10_robbins3(A) & l4_robbins3(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k11_lattice3(A, B, C)=k4_robbins3(A, B, C)) ) ) ) ) ) ).
fof(t2_orders_2, axiom,  (! [A] :  ( (v5_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( (r1_orders_2(A, B, C) & r1_orders_2(A, C, B))  => B=C) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_waybel_1, axiom,  (! [A] :  ( (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_orders_2(A, B, C) => r1_orders_2(A, k13_lattice3(A, B, D), k13_lattice3(A, C, D))) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_robbins3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_oposet_1(A) & l2_qmax_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k3_robbins1(A, k3_robbins1(A, B))=B) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_robbins3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v6_oposet_1(A) &  (v10_oposet_1(A) & l2_qmax_1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_orders_2(A, B, C) => r3_orders_2(A, k3_robbins1(A, C), k3_robbins1(A, B))) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
