% Mizar problem: t32_waybel27,waybel27,1592,58 fof(t32_waybel27,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_waybel_9(A) ) => k1_waybel26(A,k9_waybel18) = k2_waybel27(A,k3_yellow_1(1)) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v1_waybel_9,antisymmetry_r2_hidden,cc10_waybel25,cc10_waybel_0,cc10_waybel_1,cc11_waybel_0,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc1_fraenkel,cc1_funct_1,cc1_lattice3,cc1_monoid_0,cc1_relat_1,cc1_relset_1,cc1_tops_1,cc1_waybel25,cc1_waybel27,cc1_waybel_2,cc1_waybel_8,cc1_yellow_0,cc1_yellow_2,cc1_yellow_3,cc1_yellow_9,cc2_funct_1,cc2_lattice3,cc2_tops_1,cc2_waybel25,cc2_waybel_2,cc2_waybel_8,cc2_yellow_0,cc2_yellow_3,cc2_yellow_9,cc3_tops_1,cc3_waybel27,cc3_waybel_2,cc3_waybel_8,cc3_yellow_0,cc3_yellow_3,cc3_yellow_9,cc4_tops_1,cc4_waybel25,cc4_waybel_2,cc4_waybel_8,cc4_yellow_0,cc4_yellow_9,cc5_tops_1,cc5_waybel_0,cc5_waybel_1,cc5_waybel_2,cc5_yellow_0,cc5_yellow_9,cc6_tops_1,cc6_waybel25,cc6_waybel_1,cc6_waybel_2,cc6_yellow_0,cc6_yellow_9,cc7_waybel25,cc7_waybel_1,cc7_waybel_2,cc7_yellow_0,cc8_waybel_1,cc8_yellow_0,cc9_waybel_0,cc9_waybel_1,d1_waybel26,d2_waybel25,dt_g1_orders_2,dt_g1_pre_topc,dt_g1_waybel_9,dt_k1_tarski,dt_k1_waybel25,dt_k1_waybel26,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_waybel17,dt_k2_waybel27,dt_k2_zfmisc_1,dt_k3_waybel24,dt_k3_yellow_1,dt_k6_pre_topc,dt_k6_yellow_1,dt_k7_yellow_1,dt_k9_waybel18,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_9,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m1_yellow_9,dt_m2_relset_1,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_9,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m1_yellow_9,existence_m2_relset_1,fc10_waybel24,fc10_waybel25,fc10_waybel_8,fc11_waybel24,fc11_waybel_8,fc11_yellow_1,fc12_relat_1,fc12_waybel_8,fc12_yellow_1,fc13_waybel24,fc13_yellow_1,fc13_yellow_3,fc14_waybel25,fc14_waybel_8,fc14_yellow_1,fc15_waybel25,fc15_yellow_1,fc16_yellow_1,fc17_yellow_1,fc18_yellow_1,fc1_struct_0,fc1_subset_1,fc1_waybel25,fc1_waybel_1,fc1_yellow_0,fc2_subset_1,fc2_tops_1,fc2_waybel17,fc2_waybel25,fc3_waybel17,fc3_waybel25,fc3_waybel27,fc4_relat_1,fc4_subset_1,fc4_waybel25,fc4_waybel27,fc4_waybel_8,fc5_waybel18,fc5_waybel25,fc5_waybel27,fc5_waybel_8,fc5_yellow16,fc6_waybel10,fc6_waybel18,fc6_waybel24,fc6_waybel25,fc6_waybel27,fc6_waybel_8,fc6_yellow16,fc7_waybel18,fc7_waybel24,fc7_waybel25,fc7_waybel27,fc7_waybel_8,fc7_yellow_1,fc8_waybel24,fc8_waybel25,fc8_waybel_8,fc8_yellow_1,fc9_waybel24,fc9_waybel25,fc9_waybel_1,fc9_waybel_8,free_g1_orders_2,free_g1_pre_topc,free_g1_waybel_9,rc12_waybel_0,rc13_waybel_0,rc1_fraenkel,rc1_funct_1,rc1_lattice3,rc1_monoid_0,rc1_partfun1,rc1_relat_1,rc1_subset_1,rc1_tops_1,rc1_waybel25,rc1_waybel27,rc1_waybel_2,rc1_waybel_8,rc1_yellow_0,rc1_yellow_3,rc2_funct_1,rc2_lattice3,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_tops_1,rc2_waybel25,rc2_waybel_2,rc2_yellow_0,rc3_funct_1,rc3_relat_1,rc3_struct_0,rc3_tops_1,rc3_waybel25,rc3_yellow_0,rc4_funct_1,rc4_tops_1,rc4_waybel27,rc4_waybel_1,rc4_yellow_0,rc5_struct_0,rc5_tops_1,rc5_waybel27,rc5_waybel_1,rc6_yellow_9,redefinition_m2_relset_1,reflexivity_r1_tarski,spc1_boole,t13_waybel25,t16_waybel25,t1_subset,t24_waybel27,t25_waybel27,t2_subset,t31_waybel27,t38_waybel24,t3_subset,t4_subset,t4_waybel26,t5_subset,t6_boole,t7_boole,t8_boole]), [file(waybel27,t32_waybel27)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(abstractness_v1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(A) => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ), file(pre_topc,v1_pre_topc), []). fof(abstractness_v1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( v1_waybel_9(A) => A = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) ), file(waybel_9,v1_waybel_9), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc10_waybel25), []). fof(cc10_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_0,cc10_waybel_0), []). fof(cc10_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v11_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ) ) ), file(waybel_1,cc10_waybel_1), []). fof(cc11_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_yellow_0(A) ) ) ) ), file(waybel_0,cc11_waybel_0), []). fof(cc12_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(waybel_0,cc12_waybel_0), []). fof(cc13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) ) ) ) ), file(waybel_0,cc13_waybel_0), []). fof(cc14_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc14_waybel_0), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). fof(cc1_monoid_0,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(monoid_0,cc1_monoid_0), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => ( v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ) ) ), file(tops_1,cc1_tops_1), []). fof(cc1_waybel25,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel25,cc1_waybel25), []). fof(cc1_waybel27,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel27(A) & v2_waybel27(A) & v3_waybel27(A) ) ) ), file(waybel27,cc1_waybel27), []). fof(cc1_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel_2,cc1_waybel_2), []). fof(cc1_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ) ) ), file(waybel_8,cc1_waybel_8), []). fof(cc1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(yellow_0,cc1_yellow_0), []). fof(cc1_yellow_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(yellow_2,cc1_yellow_2), []). fof(cc1_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_struct_0(A) => v1_yellow_3(A) ) ) ), file(yellow_3,cc1_yellow_3), []). fof(cc1_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ~ v3_struct_0(B) ) ) ), file(yellow_9,cc1_yellow_9), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc2_lattice3), []). fof(cc2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_tops_1(B,A) ) ) ) ), file(tops_1,cc2_tops_1), []). fof(cc2_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & ~ v1_yellow_3(B) & v2_waybel_3(B) & v3_waybel_3(B) & v2_waybel18(B) ) ) ) ) ), file(waybel25,cc2_waybel25), []). fof(cc2_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ), file(waybel_2,cc2_waybel_2), []). fof(cc2_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_8(A) ) ) ) ), file(waybel_8,cc2_waybel_8), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(cc2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v1_yellow_3(A) => ~ v3_struct_0(A) ) ) ), file(yellow_3,cc2_yellow_3), []). fof(cc2_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v2_orders_2(B) ) ) ), file(yellow_9,cc2_yellow_9), []). fof(cc3_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_tops_1(B,A) ) ) ) ), file(tops_1,cc3_tops_1), []). fof(cc3_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_monoid_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ~ v3_struct_0(B) => ( ~ v3_struct_0(B) & v1_monoid_0(B) ) ) ) ) ), file(waybel27,cc3_waybel27), []). fof(cc3_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc3_waybel_2), []). fof(cc3_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & v1_waybel_8(A) & v2_waybel_8(A) ) ) ) ), file(waybel_8,cc3_waybel_8), []). fof(cc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow_0,cc3_yellow_0), []). fof(cc3_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) ) => ( ~ v3_struct_0(A) & ~ v1_yellow_3(A) ) ) ) ), file(yellow_3,cc3_yellow_3), []). fof(cc3_yellow_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v3_orders_2(B) ) ) ), file(yellow_9,cc3_yellow_9), []). fof(cc4_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) => v2_tops_1(B,A) ) ) ) ), file(tops_1,cc4_tops_1), []). fof(cc4_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) => ( v3_pre_topc(B,k1_waybel25(A)) => v13_waybel_0(B,k1_waybel25(A)) ) ) ) ), file(waybel25,cc4_waybel25), []). fof(cc4_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc4_waybel_2), []). fof(cc4_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) ) ) ) ), file(waybel_8,cc4_waybel_8), []). fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(cc4_yellow_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v4_orders_2(B) ) ) ), file(yellow_9,cc4_yellow_9), []). fof(cc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_pre_topc(B,A) & v2_tops_1(B,A) ) => ( v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ) ) ), file(tops_1,cc5_tops_1), []). fof(cc5_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) ) ) ), file(waybel_0,cc5_waybel_0), []). fof(cc5_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel_1,cc5_waybel_1), []). fof(cc5_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc5_waybel_2), []). fof(cc5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) ), file(yellow_0,cc5_yellow_0), []). fof(cc5_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( ~ v3_struct_0(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ) ), file(yellow_9,cc5_yellow_9), []). fof(cc6_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(B,A) & v3_tops_1(B,A) ) => ( v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ) ) ), file(tops_1,cc6_tops_1), []). fof(cc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc6_waybel25), []). fof(cc6_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_waybel_1(A) ) ) ) ), file(waybel_1,cc6_waybel_1), []). fof(cc6_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v1_waybel_2(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc6_waybel_2), []). fof(cc6_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v2_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc6_yellow_0), []). fof(cc6_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ) ) ), file(yellow_9,cc6_yellow_9), []). fof(cc7_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v4_waybel11(B) & v1_waybel25(B) ) ) ) ) ), file(waybel25,cc7_waybel25), []). fof(cc7_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_yellow_0(A) ) ) ) ), file(waybel_1,cc7_waybel_1), []). fof(cc7_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_waybel_1(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ) ) ), file(waybel_2,cc7_waybel_2), []). fof(cc7_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v3_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc7_yellow_0), []). fof(cc8_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v11_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ), file(waybel_1,cc8_waybel_1), []). fof(cc8_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc8_yellow_0), []). fof(cc9_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v1_lattice3(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc9_waybel_0), []). fof(cc9_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) ) ) ) ), file(waybel_1,cc9_waybel_1), []). fof(d1_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => k1_waybel26(A,B) = k3_waybel24(A,k1_waybel25(B)) ) ) ), file(waybel26,d1_waybel26), []). fof(d2_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_waybel_9(B) & l1_waybel_9(B) ) => ( B = k1_waybel25(A) <=> ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & E = k1_tarski(D) & r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ) ) ), file(waybel25,d2_waybel25), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(pre_topc,g1_pre_topc), []). fof(dt_g1_waybel_9,axiom,( ! [A,B,C] : ( ( m1_relset_1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( v1_waybel_9(g1_waybel_9(A,B,C)) & l1_waybel_9(g1_waybel_9(A,B,C)) ) ) ), file(waybel_9,g1_waybel_9), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_waybel_9(k1_waybel25(A)) & l1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,k1_waybel25), []). fof(dt_k1_waybel26,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k1_waybel26(A,B)) & v1_orders_2(k1_waybel26(A,B)) & l1_orders_2(k1_waybel26(A,B)) ) ) ), file(waybel26,k1_waybel26), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_waybel17,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & l1_waybel_9(A) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & l1_waybel_9(B) ) => ( v1_orders_2(k2_waybel17(A,B)) & v4_yellow_0(k2_waybel17(A,B),k7_yellow_1(A,B)) & m1_yellow_0(k2_waybel17(A,B),k7_yellow_1(A,B)) ) ) ), file(waybel17,k2_waybel17), []). fof(dt_k2_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k2_waybel27(A,B)) & l1_orders_2(k2_waybel27(A,B)) ) ) ), file(waybel27,k2_waybel27), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_waybel24,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & ~ v3_struct_0(B) & l1_waybel_9(B) ) => ( v1_orders_2(k3_waybel24(A,B)) & l1_orders_2(k3_waybel24(A,B)) ) ) ), file(waybel24,k3_waybel24), []). fof(dt_k3_yellow_1,axiom,( ! [A] : ( v1_orders_2(k3_yellow_1(A)) & l1_orders_2(k3_yellow_1(A)) ) ), file(yellow_1,k3_yellow_1), []). fof(dt_k6_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k6_pre_topc), []). fof(dt_k6_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_orders_2(k6_yellow_1(A,B)) & l1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,k6_yellow_1), []). fof(dt_k7_yellow_1,axiom,( ! [A,B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k7_yellow_1(A,B)) & v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ), file(yellow_1,k7_yellow_1), []). fof(dt_k9_waybel18,axiom, ( v1_pre_topc(k9_waybel18) & l1_pre_topc(k9_waybel18) ), file(waybel18,k9_waybel18), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( l1_pre_topc(A) & l1_orders_2(A) ) ) ), file(waybel_9,l1_waybel_9), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) ), file(yellow_0,m1_yellow_0), []). fof(dt_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_9(B,A) => l1_waybel_9(B) ) ) ), file(yellow_9,m1_yellow_9), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pre_topc,u1_pre_topc), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) ), file(waybel_9,l1_waybel_9), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) ), file(yellow_0,m1_yellow_0), []). fof(existence_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_9(B,A) ) ), file(yellow_9,m1_yellow_9), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v4_orders_2(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc10_waybel24), []). fof(fc10_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v1_lattice3(k1_waybel25(A)) & v2_lattice3(k1_waybel25(A)) & v3_lattice3(k1_waybel25(A)) & v1_yellow_0(k1_waybel25(A)) & v2_yellow_0(k1_waybel25(A)) & v3_yellow_0(k1_waybel25(A)) & v24_waybel_0(k1_waybel25(A)) & v25_waybel_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) & v3_waybel_3(k1_waybel25(A)) ) ) ), file(waybel25,fc10_waybel25), []). fof(fc10_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc10_waybel_8), []). fof(fc11_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v1_monoid_0(k6_yellow_1(A,B)) ) ) ), file(waybel24,fc11_waybel24), []). fof(fc11_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc11_waybel_8), []). fof(fc11_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc11_yellow_1), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc12_waybel_8,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc12_waybel_8), []). fof(fc12_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v2_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc12_yellow_1), []). fof(fc13_waybel24,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v2_orders_2(k3_waybel24(A,B)) & v3_orders_2(k3_waybel24(A,B)) & v4_orders_2(k3_waybel24(A,B)) & v1_yellow_0(k3_waybel24(A,B)) & v2_yellow_0(k3_waybel24(A,B)) & v3_yellow_0(k3_waybel24(A,B)) & v24_waybel_0(k3_waybel24(A,B)) & v25_waybel_0(k3_waybel24(A,B)) & ~ v1_yellow_3(k3_waybel24(A,B)) & v1_lattice3(k3_waybel24(A,B)) & v2_lattice3(k3_waybel24(A,B)) & v3_lattice3(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc13_waybel24), []). fof(fc13_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ), file(yellow_1,fc13_yellow_1), []). fof(fc13_yellow_3,axiom,( ! [A] : ( ( ~ v1_yellow_3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(u1_orders_2(A)) & v1_relat_1(u1_orders_2(A)) ) ) ), file(yellow_3,fc13_yellow_3), []). fof(fc14_waybel25,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v4_waybel11(B) & m1_yellow_9(B,A) ) => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) & v1_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) & v2_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) & v1_waybel25(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) ) ) ), file(waybel25,fc14_waybel25), []). fof(fc14_waybel_8,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v9_waybel_1(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) & v11_waybel_1(k3_yellow_1(A)) & v2_waybel_3(k3_yellow_1(A)) & v3_waybel_3(k3_yellow_1(A)) & v1_waybel_8(k3_yellow_1(A)) & v2_waybel_8(k3_yellow_1(A)) ) ), file(waybel_8,fc14_waybel_8), []). fof(fc14_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v2_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_orders_2(k6_yellow_1(k1_xboole_0,A)) & v4_orders_2(k6_yellow_1(k1_xboole_0,A)) & v1_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v2_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v3_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_lattice3(k6_yellow_1(k1_xboole_0,A)) & v2_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ), file(yellow_1,fc14_yellow_1), []). fof(fc15_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v24_waybel_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc15_waybel25), []). fof(fc15_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v3_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc15_yellow_1), []). fof(fc16_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc16_yellow_1), []). fof(fc17_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v2_lattice3(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc17_yellow_1), []). fof(fc18_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v1_lattice3(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc18_yellow_1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_waybel25,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) & ~ v1_urysohn1(k9_waybel18) & v2_waybel18(k9_waybel18) ), file(waybel25,fc1_waybel25), []). fof(fc1_waybel_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) ) ), file(waybel_1,fc1_waybel_1), []). fof(fc1_yellow_0,axiom,( ! [A,B] : ( m1_relset_1(B,k1_tarski(A),k1_tarski(A)) => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ), file(yellow_0,fc1_yellow_0), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v4_pre_topc(k6_pre_topc(A,B),A) ) ), file(tops_1,fc2_tops_1), []). fof(fc2_waybel17,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( v1_orders_2(k6_yellow_1(A,B)) & v3_lattice3(k6_yellow_1(A,B)) ) ) ), file(waybel17,fc2_waybel17), []). fof(fc2_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v2_waybel18(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ), file(waybel25,fc2_waybel25), []). fof(fc3_waybel17,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & l1_waybel_9(A) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k2_waybel17(A,B)) & v1_orders_2(k2_waybel17(A,B)) & v4_yellow_0(k2_waybel17(A,B),k7_yellow_1(A,B)) ) ) ), file(waybel17,fc3_waybel17), []). fof(fc3_waybel25,axiom,( ! [A] : ( ( v3_struct_0(A) & l1_pre_topc(A) ) => ( v3_struct_0(k1_waybel25(A)) & v1_yellow_0(k1_waybel25(A)) & v2_yellow_0(k1_waybel25(A)) & v3_yellow_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc3_waybel25), []). fof(fc3_waybel27,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => v1_fraenkel(u1_struct_0(A)) ) ), file(waybel27,fc3_waybel27), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc4_waybel25), []). fof(fc4_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v1_monoid_0(k6_yellow_1(A,B)) ) ) ), file(waybel27,fc4_waybel27), []). fof(fc4_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc4_waybel_8), []). fof(fc5_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) ), file(waybel18,fc5_waybel18), []). fof(fc5_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_pre_topc(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc5_waybel25), []). fof(fc5_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k2_waybel27(A,B)) & v1_orders_2(k2_waybel27(A,B)) & v2_orders_2(k2_waybel27(A,B)) & v4_orders_2(k2_waybel27(A,B)) & ~ v1_yellow_3(k2_waybel27(A,B)) & v1_monoid_0(k2_waybel27(A,B)) ) ) ), file(waybel27,fc5_waybel27), []). fof(fc5_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc5_waybel_8), []). fof(fc5_yellow16,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) ) => ( ~ v3_struct_0(k6_yellow_1(B,A)) & v1_orders_2(k6_yellow_1(B,A)) & v2_orders_2(k6_yellow_1(B,A)) & v3_orders_2(k6_yellow_1(B,A)) & v4_orders_2(k6_yellow_1(B,A)) & v24_waybel_0(k6_yellow_1(B,A)) ) ) ), file(yellow16,fc5_yellow16), []). fof(fc6_waybel10,axiom,( ! [A,B] : ( ( l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k7_yellow_1(A,B)) & v1_orders_2(k7_yellow_1(A,B)) & v2_orders_2(k7_yellow_1(A,B)) & v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ), file(waybel10,fc6_waybel10), []). fof(fc6_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) ), file(waybel18,fc6_waybel18), []). fof(fc6_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) ) ) ), file(waybel24,fc6_waybel24), []). fof(fc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc6_waybel25), []). fof(fc6_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k2_waybel27(A,B)) & v1_orders_2(k2_waybel27(A,B)) & v2_orders_2(k2_waybel27(A,B)) & v3_orders_2(k2_waybel27(A,B)) & v4_orders_2(k2_waybel27(A,B)) & ~ v1_yellow_3(k2_waybel27(A,B)) & v1_monoid_0(k2_waybel27(A,B)) ) ) ), file(waybel27,fc6_waybel27), []). fof(fc6_waybel_8,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc6_waybel_8), []). fof(fc6_yellow16,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(u1_pre_topc(A)) ) ), file(yellow16,fc6_yellow16), []). fof(fc7_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) & v2_waybel18(k9_waybel18) ), file(waybel18,fc7_waybel18), []). fof(fc7_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc7_waybel24), []). fof(fc7_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc7_waybel25), []). fof(fc7_waybel27,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k2_waybel27(A,B)) & v1_orders_2(k2_waybel27(A,B)) & v2_orders_2(k2_waybel27(A,B)) & v3_orders_2(k2_waybel27(A,B)) & v4_orders_2(k2_waybel27(A,B)) & v1_yellow_0(k2_waybel27(A,B)) & v2_yellow_0(k2_waybel27(A,B)) & v3_yellow_0(k2_waybel27(A,B)) & v24_waybel_0(k2_waybel27(A,B)) & v25_waybel_0(k2_waybel27(A,B)) & ~ v1_yellow_3(k2_waybel27(A,B)) & v1_lattice3(k2_waybel27(A,B)) & v2_lattice3(k2_waybel27(A,B)) & v3_lattice3(k2_waybel27(A,B)) & v1_monoid_0(k2_waybel27(A,B)) ) ) ), file(waybel27,fc7_waybel27), []). fof(fc7_waybel_8,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc7_waybel_8), []). fof(fc7_yellow_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) ) ), file(yellow_1,fc7_yellow_1), []). fof(fc8_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v2_orders_2(k3_waybel24(A,B)) & ~ v1_yellow_3(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc8_waybel24), []). fof(fc8_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc8_waybel25), []). fof(fc8_waybel_8,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc8_waybel_8), []). fof(fc8_yellow_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(yellow_1,fc8_yellow_1), []). fof(fc9_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v3_orders_2(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc9_waybel24), []). fof(fc9_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v1_lattice3(k1_waybel25(A)) & v2_lattice3(k1_waybel25(A)) & v3_lattice3(k1_waybel25(A)) & v1_yellow_0(k1_waybel25(A)) & v2_yellow_0(k1_waybel25(A)) & v3_yellow_0(k1_waybel25(A)) & v24_waybel_0(k1_waybel25(A)) & v25_waybel_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc9_waybel25), []). fof(fc9_waybel_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) ) ), file(waybel_1,fc9_waybel_1), []). fof(fc9_waybel_8,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc9_waybel_8), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). fof(free_g1_waybel_9,axiom,( ! [A,B,C] : ( ( m1_relset_1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [D,E,F] : ( g1_waybel_9(A,B,C) = g1_waybel_9(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(waybel_9,g1_waybel_9), []). fof(rc12_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) ) ), file(waybel_0,rc12_waybel_0), []). fof(rc13_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ), file(waybel_0,rc13_waybel_0), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ), file(lattice3,rc1_lattice3), []). fof(rc1_monoid_0,axiom,( ? [A] : ( l1_struct_0(A) & v1_monoid_0(A) ) ), file(monoid_0,rc1_monoid_0), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) ) ) ), file(tops_1,rc1_tops_1), []). fof(rc1_waybel25,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) ) ), file(waybel25,rc1_waybel25), []). fof(rc1_waybel27,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel27(A) & v2_waybel27(A) & v3_waybel27(A) ) ), file(waybel27,rc1_waybel27), []). fof(rc1_waybel_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v3_realset2(A) ) ), file(waybel_2,rc1_waybel_2), []). fof(rc1_waybel_8,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v2_waybel_3(A) & v3_waybel_3(A) & v3_realset2(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) ) ), file(waybel_8,rc1_waybel_8), []). fof(rc1_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) ), file(yellow_0,rc1_yellow_0), []). fof(rc1_yellow_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v1_yellow_3(A) ) ), file(yellow_3,rc1_yellow_3), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ), file(lattice3,rc2_lattice3), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc2_tops_1), []). fof(rc2_waybel25,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_waybel_9(A) & v4_waybel11(A) ) ), file(waybel25,rc2_waybel25), []). fof(rc2_waybel_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v3_realset2(A) & v1_waybel_2(A) & v2_waybel_2(A) ) ), file(waybel_2,rc2_waybel_2), []). fof(rc2_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ), file(yellow_0,rc2_yellow_0), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_tops_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc3_tops_1), []). fof(rc3_waybel25,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v3_realset2(A) & v1_waybel25(A) ) ), file(waybel25,rc3_waybel25), []). fof(rc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc3_yellow_0), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) ) ) ), file(tops_1,rc4_tops_1), []). fof(rc4_waybel27,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_monoid_0(A) ) ), file(waybel27,rc4_waybel27), []). fof(rc4_waybel_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) ) ), file(waybel_1,rc4_waybel_1), []). fof(rc4_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc4_yellow_0), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ), file(tops_1,rc5_tops_1), []). fof(rc5_waybel27,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) & v1_monoid_0(A) ) ), file(waybel27,rc5_waybel27), []). fof(rc5_waybel_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ), file(waybel_1,rc5_waybel_1), []). fof(rc6_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_9(B,A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v1_waybel_9(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ), file(yellow_9,rc6_yellow_9), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(t13_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) => k1_waybel25(A) = k1_waybel25(B) ) ) ) ), file(waybel25,t13_waybel25), []). fof(t16_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => g1_orders_2(u1_struct_0(k1_waybel25(B)),u1_orders_2(k1_waybel25(B))) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(waybel25,t16_waybel25), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t24_waybel27,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_waybel_9(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_waybel_9(B) ) => k2_waybel27(A,B) = k2_waybel17(A,B) ) ) ), file(waybel27,t24_waybel27), []). fof(t25_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v2_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v3_struct_0(D) & v2_orders_2(D) & v4_orders_2(D) & l1_orders_2(D) ) => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) ) => k2_waybel27(A,C) = k2_waybel27(B,D) ) ) ) ) ) ), file(waybel27,t25_waybel27), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t31_waybel27,axiom,( v4_waybel11(k1_waybel25(k9_waybel18)) ), file(waybel27,t31_waybel27), []). fof(t38_waybel24,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_waybel_9(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_waybel_9(B) ) => k2_waybel17(A,B) = k3_waybel24(A,B) ) ) ), file(waybel24,t38_waybel24), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t4_waybel26,axiom,( m1_yellow_9(k1_waybel25(k9_waybel18),k3_yellow_1(1)) ), file(waybel26,t4_waybel26), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).