% Mizar problem: t18_waybel33,waybel33,1034,68 fof(t18_waybel33,conjecture,( ! [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) & v1_waybel33(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(A))) & v3_waybel_7(C,k3_yellow_1(k2_pre_topc(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => ( r2_hidden(B,C) => r2_hidden(k1_waybel33(A,k2_pre_topc(A),C),B) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v6_waybel_0,antisymmetry_r2_hidden,cc10_waybel_0,cc11_waybel_0,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc14_yellow13,cc1_classes2,cc1_finset_1,cc1_funct_1,cc1_lattice3,cc1_relat_1,cc1_relset_1,cc1_tops_1,cc1_waybel19,cc1_waybel33,cc1_waybel_3,cc1_waybel_7,cc1_yellow11,cc1_yellow13,cc1_yellow_6,cc2_classes2,cc2_finset_1,cc2_funct_1,cc2_lattice3,cc2_tops_1,cc2_waybel19,cc2_waybel33,cc2_waybel_3,cc2_yellow13,cc2_yellow_6,cc3_classes2,cc3_tops_1,cc3_waybel_3,cc3_yellow13,cc4_tops_1,cc4_waybel_3,cc4_yellow11,cc5_tops_1,cc5_waybel_0,cc5_waybel_3,cc5_yellow11,cc6_tops_1,cc6_waybel_3,cc6_yellow13,cc7_yellow_6,cc9_waybel_0,commutativity_k2_tarski,commutativity_k3_xboole_0,commutativity_k5_subset_1,d11_waybel_0,d12_yellow_0,d14_yellow_6,d16_waybel_0,d1_classes1,d1_waybel12,d1_waybel28,d1_waybel33,d21_yellow_6,d27_waybel_0,d27_yellow_6,d28_waybel_0,d2_waybel28,d2_waybel33,d2_waybel_0,d2_waybel_9,d2_yellow_0,d3_pre_topc,d3_tarski,d3_waybel28,d3_xboole_0,d3_yellow_0,d3_yellow_6,d4_waybel28,d4_yellow19,d5_funct_1,d5_pre_topc,d5_tarski,d6_waybel_0,d6_yellow_2,d7_waybel_9,d8_waybel_0,d9_lattice3,dt_g1_orders_2,dt_g1_pre_topc,dt_g1_waybel_0,dt_k12_waybel_0,dt_k13_waybel_0,dt_k14_yellow_6,dt_k1_card_fil,dt_k1_classes1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_tarski,dt_k1_toler_1,dt_k1_waybel11,dt_k1_waybel28,dt_k1_waybel33,dt_k1_waybel_0,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_partfun1,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_tarski,dt_k2_waybel28,dt_k2_waybel_9,dt_k2_wellord1,dt_k2_yellow_0,dt_k2_yellow_6,dt_k2_zfmisc_1,dt_k3_subset_1,dt_k3_waybel28,dt_k3_waybel_0,dt_k3_xboole_0,dt_k3_yellow19,dt_k3_yellow_0,dt_k3_yellow_1,dt_k3_yellow_6,dt_k4_relset_1,dt_k4_tarski,dt_k4_waybel28,dt_k4_waybel_0,dt_k4_xboole_0,dt_k4_yellow_0,dt_k5_classes1,dt_k5_relat_1,dt_k5_subset_1,dt_k5_waybel_0,dt_k5_waybel_9,dt_k6_subset_1,dt_k6_waybel_9,dt_k6_yellow_2,dt_k7_funct_2,dt_k7_relat_1,dt_k7_yellow_2,dt_k7_yellow_6,dt_k8_funct_2,dt_k8_relset_1,dt_k8_yellow_2,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_0,dt_l1_waybel_9,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m1_yellow_6,dt_m2_relset_1,dt_m2_yellow_6,dt_m4_yellow_6,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,dt_u1_waybel_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_0,existence_l1_waybel_9,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m1_yellow_6,existence_m2_relset_1,existence_m2_yellow_6,existence_m4_yellow_6,fc10_finset_1,fc10_relat_1,fc11_finset_1,fc11_tops_1,fc11_waybel_0,fc12_finset_1,fc12_relat_1,fc12_waybel_0,fc13_relat_1,fc14_finset_1,fc15_waybel_0,fc15_yellow_6,fc16_waybel_0,fc17_waybel_0,fc18_waybel_0,fc18_yellow_6,fc19_waybel_0,fc1_classes2,fc1_finset_1,fc1_funct_1,fc1_relat_1,fc1_struct_0,fc1_subset_1,fc1_waybel28,fc1_waybel_7,fc1_yellow13,fc1_yellow_6,fc20_waybel_0,fc21_waybel_0,fc22_waybel_0,fc23_waybel_0,fc24_yellow_6,fc25_yellow_6,fc2_finset_1,fc2_subset_1,fc2_waybel28,fc2_waybel_0,fc2_waybel_7,fc2_yellow13,fc2_yellow_6,fc3_classes2,fc3_relat_1,fc3_subset_1,fc3_tops_1,fc3_waybel_0,fc3_yellow13,fc4_funct_1,fc4_relat_1,fc4_subset_1,fc4_tops_1,fc4_waybel_0,fc4_yellow19,fc5_classes2,fc5_relat_1,fc5_waybel_0,fc5_yellow19,fc6_classes2,fc6_relat_1,fc6_waybel_0,fc6_yellow19,fc6_yellow_6,fc7_relat_1,fc7_waybel_0,fc7_yellow_6,fc8_relat_1,fc8_tops_1,fc8_waybel_0,fc8_yellow_6,fc9_relat_1,fc9_tops_1,fraenkel_a_1_1_waybel33,fraenkel_a_2_10_waybel33,fraenkel_a_2_11_waybel33,fraenkel_a_2_12_waybel33,fraenkel_a_2_2_waybel33,fraenkel_a_2_3_waybel11,fraenkel_a_2_3_yellow_6,fraenkel_a_2_4_waybel_0,fraenkel_a_2_5_waybel_0,fraenkel_a_3_0_waybel33,fraenkel_a_3_0_waybel_9,fraenkel_a_3_10_waybel33,fraenkel_a_3_11_waybel33,fraenkel_a_3_1_yellow19,fraenkel_a_4_0_waybel33,fraenkel_a_4_1_waybel33,free_g1_orders_2,free_g1_pre_topc,free_g1_waybel_0,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k3_subset_1,rc10_waybel_0,rc11_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_classes2,rc1_finset_1,rc1_funct_1,rc1_lattice3,rc1_relat_1,rc1_subset_1,rc1_tops_1,rc1_waybel28,rc1_waybel33,rc1_waybel_0,rc1_waybel_3,rc1_waybel_7,rc1_yellow11,rc2_classes2,rc2_funct_1,rc2_lattice3,rc2_relat_1,rc2_subset_1,rc2_tops_1,rc2_waybel28,rc2_waybel_0,rc2_waybel_3,rc2_waybel_7,rc2_yellow13,rc3_finset_1,rc3_funct_1,rc3_relat_1,rc3_struct_0,rc3_tops_1,rc3_waybel28,rc3_waybel_7,rc4_finset_1,rc4_funct_1,rc4_tops_1,rc4_waybel_0,rc4_waybel_7,rc4_yellow_6,rc5_struct_0,rc5_tops_1,rc5_waybel_0,rc7_waybel_0,rc7_waybel_7,rc8_waybel_0,rc9_waybel_0,redefinition_k1_card_fil,redefinition_k1_toler_1,redefinition_k1_waybel_0,redefinition_k2_partfun1,redefinition_k2_waybel28,redefinition_k3_yellow_6,redefinition_k4_relset_1,redefinition_k5_subset_1,redefinition_k6_subset_1,redefinition_k6_waybel_9,redefinition_k7_funct_2,redefinition_k7_yellow_2,redefinition_k8_funct_2,redefinition_k8_relset_1,redefinition_k8_yellow_2,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,s14_funct_2__e5_32_2_7__waybel33,s1_wellord2__e8_32_2_3__waybel33,t106_zfmisc_1,t10_subset_1,t10_waybel_0,t10_yellow_6,t11_waybel33,t12_funct_1,t12_waybel_9,t13_waybel33,t13_waybel_7,t14_waybel28,t14_waybel33,t16_waybel33,t16_waybel_0,t16_waybel_9,t17_pre_topc,t17_waybel33,t17_yellow_0,t18_yellow_1,t19_waybel11,t19_yellow_1,t19_yellow_6,t1_subset,t1_waybel_0,t1_xboole_1,t20_yellow_1,t23_funct_1,t24_yellow_6,t26_finset_1,t2_boole,t2_subset,t2_tarski,t2_yellow_1,t30_waybel_7,t32_yellow_0,t34_yellow_0,t3_boole,t3_subset,t3_waybel28,t3_waybel_7,t3_xboole_1,t4_boole,t4_subset,t4_waybel_7,t50_waybel_0,t5_subset,t67_funct_2,t68_funct_1,t6_boole,t6_setfam_1,t76_funct_1,t7_boole,t7_mcart_1,t7_waybel28,t8_boole,t8_waybel_7]), [file(waybel33,t18_waybel33)]). 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_v6_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v6_waybel_0(B,A) => B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) ) ) ), file(waybel_0,v6_waybel_0), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). 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(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(cc14_yellow13,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_yellow13(A) ) ) ) ), file(yellow13,cc14_yellow13), []). fof(cc1_classes2,axiom,( ! [A] : ( v2_classes1(A) => v1_classes1(A) ) ), file(classes2,cc1_classes2), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). 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_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_waybel19,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_pre_topc(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_pre_topc(A) & ~ v1_yellow_3(A) & v1_waybel19(A) ) ) ) ), file(waybel19,cc1_waybel19), []). fof(cc1_waybel33,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v1_waybel33(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) ) ) ) ), file(waybel33,cc1_waybel33), []). fof(cc1_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ) ), file(waybel_3,cc1_waybel_3), []). fof(cc1_waybel_7,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) & v3_waybel_7(B,A) ) => ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ) ) ), file(waybel_7,cc1_waybel_7), []). fof(cc1_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v2_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v1_yellow11(A) ) ) ) ), file(yellow11,cc1_yellow11), []). fof(cc1_yellow13,axiom,( ! [A] : ( v1_realset1(A) => v1_finset_1(A) ) ), file(yellow13,cc1_yellow13), []). fof(cc1_yellow_6,axiom,( ! [A] : ( v1_classes2(A) => ( v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) ) ) ), file(yellow_6,cc1_yellow_6), []). fof(cc2_classes2,axiom,( ! [A] : ( v1_classes2(A) => ( v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A) ) ) ), file(classes2,cc2_classes2), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). 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_waybel19,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_waybel19(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v2_t_0topsp(A) & ~ v1_yellow_3(A) ) ) ) ), file(waybel19,cc2_waybel19), []). fof(cc2_waybel33,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_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_waybel33(A) ) ) ) ), file(waybel33,cc2_waybel33), []). fof(cc2_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v16_waybel_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) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_3,cc2_waybel_3), []). fof(cc2_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_realset2(A) => v6_group_1(A) ) ) ), file(yellow13,cc2_yellow13), []). fof(cc2_yellow_6,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_classes1(A) ) => ( v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) ) ) ), file(yellow_6,cc2_yellow_6), []). fof(cc3_classes2,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_classes1(A) ) => v1_classes2(A) ) ), file(classes2,cc3_classes2), []). 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_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) & v2_orders_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc3_waybel_3), []). fof(cc3_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v3_realset2(A) => ~ v3_struct_0(A) ) ) ), file(yellow13,cc3_yellow13), []). 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_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc4_waybel_3), []). fof(cc4_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v6_group_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) ) ) ) ), file(yellow11,cc4_yellow11), []). 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_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) ) ) ) ), file(waybel_3,cc5_waybel_3), []). fof(cc5_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v6_group_1(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(yellow11,cc5_yellow11), []). 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_waybel_3,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) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc6_waybel_3), []). fof(cc6_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v6_group_1(A) ) => ( v2_pre_topc(A) & v2_compts_1(A) ) ) ) ), file(yellow13,cc6_yellow13), []). fof(cc7_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => v1_relat_1(B) ) ) ), file(yellow_6,cc7_yellow_6), []). 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(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). fof(d11_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r1_waybel_0(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,D,E) => r2_hidden(k3_waybel_0(A,B,E),C) ) ) ) ) ) ) ), file(waybel_0,d11_waybel_0), []). fof(d12_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => k4_yellow_0(A) = k2_yellow_0(A,k1_xboole_0) ) ), file(yellow_0,d12_yellow_0), []). fof(d14_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( B = k7_yellow_6(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( ~ v3_struct_0(D) & v3_orders_2(D) & v6_waybel_0(D,A) & v7_waybel_0(D) & l1_waybel_0(D,A) & D = C & r2_hidden(u1_struct_0(D),k2_yellow_6(u1_struct_0(A))) ) ) ) ) ), file(yellow_6,d14_yellow_6), []). fof(d16_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k5_waybel_0(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_orders_2(A,E,D) & r2_hidden(E,B) ) ) ) ) ) ) ) ), file(waybel_0,d16_waybel_0), []). fof(d1_classes1,axiom,( ! [A] : ( v1_classes1(A) <=> ! [B,C] : ( ( r2_hidden(B,A) & r1_tarski(C,B) ) => r2_hidden(C,A) ) ) ), file(classes1,d1_classes1), []). fof(d1_waybel12,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ), file(waybel12,d1_waybel12), []). fof(d1_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( v1_waybel28(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_orders_2(A,C,k3_yellow_6(u1_struct_0(A),A,B,C)) ) ) ) ) ), file(waybel28,d1_waybel28), []). fof(d1_waybel33,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) ), file(waybel33,d1_waybel33), []). fof(d21_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) <=> r1_tarski(B,k2_zfmisc_1(k7_yellow_6(A),u1_struct_0(A))) ) ) ), file(yellow_6,d21_yellow_6), []). fof(d27_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k12_waybel_0(A,B) = a_2_4_waybel_0(A,B) ) ) ), file(waybel_0,d27_waybel_0), []). fof(d27_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ! [C] : ( ( v1_pre_topc(C) & l1_pre_topc(C) ) => ( C = k14_yellow_6(A,B) <=> ( u1_struct_0(C) = u1_struct_0(A) & u1_pre_topc(C) = a_2_3_yellow_6(A,B) ) ) ) ) ) ), file(yellow_6,d27_yellow_6), []). fof(d28_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k13_waybel_0(A,B) = a_2_5_waybel_0(A,B) ) ) ), file(waybel_0,d28_waybel_0), []). fof(d2_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => ! [D] : ( ( ~ v3_struct_0(D) & v6_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( D = k1_waybel28(A,B,C) <=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & u1_waybel_0(A,D) = k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,u1_waybel_0(A,B)) ) ) ) ) ) ) ), file(waybel28,d2_waybel28), []). fof(d2_waybel33,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_waybel_9(A) ) => ( v1_waybel33(A) <=> u1_pre_topc(A) = k4_waybel28(A) ) ) ), file(waybel33,d2_waybel33), []). fof(d2_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r1_orders_2(A,E,C) & r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ), file(waybel_0,d2_waybel_0), []). fof(d2_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => k2_waybel_9(A,B) = k6_yellow_2(A,u1_waybel_0(A,B)) ) ) ), file(waybel_9,d2_waybel_9), []). fof(d2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_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,C,D) ) => r1_orders_2(A,B,D) ) ) ) ) ) ) ), file(yellow_0,d2_yellow_0), []). fof(d3_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => k2_pre_topc(A) = u1_struct_0(A) ) ), file(pre_topc,d3_pre_topc), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( B = k3_waybel28(A) <=> ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( r2_hidden(C,k7_yellow_6(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ! [E] : ( m2_yellow_6(E,A,C) => D = k1_waybel11(A,E) ) ) ) ) ) ) ) ) ), file(waybel28,d3_waybel28), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). fof(d3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v4_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 ) ) ) ) ) ), file(yellow_0,d3_yellow_0), []). fof(d3_yellow_6,axiom,( ! [A] : k2_yellow_6(A) = k1_classes1(k5_classes1(A)) ), file(yellow_6,d3_yellow_6), []). fof(d4_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => k4_waybel28(A) = u1_pre_topc(k14_yellow_6(A,k3_waybel28(A))) ) ), file(waybel28,d4_waybel28), []). fof(d4_yellow19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ! [D] : ( ( ~ v3_struct_0(D) & v6_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( D = k3_yellow19(A,B,C) <=> ( u1_struct_0(D) = a_3_1_yellow19(A,B,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( r1_orders_2(D,E,F) <=> r1_tarski(k2_mcart_1(F),k2_mcart_1(E)) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => k3_waybel_0(A,D,E) = k1_mcart_1(E) ) ) ) ) ) ) ) ), file(yellow19,d4_yellow19), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> r2_hidden(B,u1_pre_topc(A)) ) ) ) ), file(pre_topc,d5_pre_topc), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v7_waybel_0(A) <=> v1_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,d6_waybel_0), []). fof(d6_yellow_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( v1_relat_1(B) => k6_yellow_2(A,B) = k2_yellow_0(A,k2_relat_1(B)) ) ) ), file(yellow_2,d6_yellow_2), []). fof(d7_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v6_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( D = k5_waybel_9(A,B,C) <=> ( ! [E] : ( r2_hidden(E,u1_struct_0(D)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & F = E & r1_orders_2(B,C,F) ) ) & u1_orders_2(D) = k1_toler_1(u1_orders_2(B),u1_struct_0(D)) & u1_waybel_0(A,D) = k2_partfun1(u1_struct_0(B),u1_struct_0(A),u1_waybel_0(A,B),u1_struct_0(D)) ) ) ) ) ) ) ), file(waybel_9,d7_waybel_9), []). fof(d8_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_waybel_0(A,B,C) = k1_waybel_0(B,A,u1_waybel_0(A,B),C) ) ) ) ), file(waybel_0,d8_waybel_0), []). fof(d9_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B,C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r1_orders_2(A,D,C) ) ) ) ) ) ), file(lattice3,d9_lattice3), []). 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_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( v6_waybel_0(g1_waybel_0(A,B,C,D),A) & l1_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,g1_waybel_0), []). fof(dt_k12_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k12_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k12_waybel_0), []). fof(dt_k13_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k13_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k13_waybel_0), []). fof(dt_k14_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( v1_pre_topc(k14_yellow_6(A,B)) & l1_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,k14_yellow_6), []). fof(dt_k1_card_fil,axiom,( ! [A,B] : m1_subset_1(k1_card_fil(A,B),k1_zfmisc_1(A)) ), file(card_fil,k1_card_fil), []). fof(dt_k1_classes1,axiom,( $true ), file(classes1,k1_classes1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_setfam_1,axiom,( $true ), file(setfam_1,k1_setfam_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_toler_1,axiom,( ! [A,B] : ( v1_relat_1(A) => m2_relset_1(k1_toler_1(A,B),B,B) ) ), file(toler_1,k1_toler_1), []). fof(dt_k1_waybel11,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(k1_waybel11(A,B),u1_struct_0(A)) ) ), file(waybel11,k1_waybel11), []). fof(dt_k1_waybel28,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => ( ~ v3_struct_0(k1_waybel28(A,B,C)) & v6_waybel_0(k1_waybel28(A,B,C),A) & l1_waybel_0(k1_waybel28(A,B,C),A) ) ) ), file(waybel28,k1_waybel28), []). fof(dt_k1_waybel33,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) ), file(waybel33,k1_waybel33), []). fof(dt_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ), file(waybel_0,k1_waybel_0), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k1_yellow_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k2_pre_topc), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_waybel28,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v1_waybel28(C,B) & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => ( v6_waybel_0(k2_waybel28(A,B,C),A) & m2_yellow_6(k2_waybel28(A,B,C),A,B) ) ) ), file(waybel28,k2_waybel28), []). fof(dt_k2_waybel_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & l1_waybel_0(B,A) ) => m1_subset_1(k2_waybel_9(A,B),u1_struct_0(A)) ) ), file(waybel_9,k2_waybel_9), []). fof(dt_k2_wellord1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k2_wellord1(A,B)) ) ), file(wellord1,k2_wellord1), []). fof(dt_k2_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k2_yellow_0), []). fof(dt_k2_yellow_6,axiom,( $true ), file(yellow_6,k2_yellow_6), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ), file(subset_1,k3_subset_1), []). fof(dt_k3_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => m4_yellow_6(k3_waybel28(A),A) ) ), file(waybel28,k3_waybel28), []). fof(dt_k3_waybel_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)) ) ), file(waybel_0,k3_waybel_0), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_yellow19,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ( ~ v3_struct_0(k3_yellow19(A,B,C)) & v6_waybel_0(k3_yellow19(A,B,C),A) & l1_waybel_0(k3_yellow19(A,B,C),A) ) ) ), file(yellow19,k3_yellow19), []). fof(dt_k3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ), file(yellow_0,k3_yellow_0), []). 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_k3_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => m1_subset_1(k3_yellow_6(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_6,k3_yellow_6), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k4_waybel28(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(waybel28,k4_waybel28), []). fof(dt_k4_waybel_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k4_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k4_waybel_0), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k4_yellow_0(A),u1_struct_0(A)) ) ), file(yellow_0,k4_yellow_0), []). fof(dt_k5_classes1,axiom,( $true ), file(classes1,k5_classes1), []). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(dt_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_1), []). fof(dt_k5_waybel_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k5_waybel_0), []). fof(dt_k5_waybel_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => ( v6_waybel_0(k5_waybel_9(A,B,C),A) & l1_waybel_0(k5_waybel_9(A,B,C),A) ) ) ), file(waybel_9,k5_waybel_9), []). fof(dt_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_1), []). fof(dt_k6_waybel_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => ( v6_waybel_0(k6_waybel_9(A,B,C),A) & m2_yellow_6(k6_waybel_9(A,B,C),A,B) ) ) ), file(waybel_9,k6_waybel_9), []). fof(dt_k6_yellow_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v1_relat_1(B) ) => m1_subset_1(k6_yellow_2(A,B),u1_struct_0(A)) ) ), file(yellow_2,k6_yellow_2), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_2,k7_yellow_2), []). fof(dt_k7_yellow_6,axiom,( $true ), file(yellow_6,k7_yellow_6), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ), file(relset_1,k8_relset_1), []). fof(dt_k8_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ), file(yellow_2,k8_yellow_2), []). 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_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => l1_orders_2(B) ) ) ), file(waybel_0,l1_waybel_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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_yellow_6,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ! [C] : ( m1_yellow_6(C,A,B) => l1_waybel_0(C,A) ) ) ), file(yellow_6,m1_yellow_6), []). 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_m2_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) ) ) ), file(yellow_6,m2_yellow_6), []). fof(dt_m4_yellow_6,axiom,( $true ), file(yellow_6,m4_yellow_6), []). 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(dt_u1_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(waybel_0,u1_waybel_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_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_waybel_0(B,A) ) ), file(waybel_0,l1_waybel_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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_yellow_6,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ? [C] : m1_yellow_6(C,A,B) ) ), file(yellow_6,m1_yellow_6), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : m2_yellow_6(C,A,B) ) ), file(yellow_6,m2_yellow_6), []). fof(existence_m4_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : m4_yellow_6(B,A) ) ), file(yellow_6,m4_yellow_6), []). fof(fc10_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ), file(tops_1,fc11_tops_1), []). fof(fc11_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v12_waybel_0(k4_waybel_0(A,B),A) ) ), file(waybel_0,fc11_waybel_0), []). fof(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_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_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v13_waybel_0(k5_waybel_0(A,B),A) ) ), file(waybel_0,fc12_waybel_0), []). fof(fc13_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)) ) ) ), file(relat_1,fc13_relat_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc15_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v12_waybel_0(k2_pre_topc(A),A) & v13_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc15_waybel_0), []). fof(fc15_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ( ~ v1_xboole_0(u1_waybel_0(A,B)) & v1_relat_1(u1_waybel_0(A,B)) & v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(yellow_6,fc15_yellow_6), []). fof(fc16_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_waybel_0(k4_waybel_0(A,B),A) & v12_waybel_0(k4_waybel_0(A,B),A) ) ) ), file(waybel_0,fc16_waybel_0), []). fof(fc17_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_waybel_0(k5_waybel_0(A,B),A) & v13_waybel_0(k5_waybel_0(A,B),A) ) ) ), file(waybel_0,fc17_waybel_0), []). fof(fc18_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k12_waybel_0(A,B)) ) ), file(waybel_0,fc18_waybel_0), []). fof(fc18_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k7_yellow_6(A)) ) ), file(yellow_6,fc18_yellow_6), []). fof(fc19_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k13_waybel_0(A,B)) ) ), file(waybel_0,fc19_waybel_0), []). fof(fc1_classes2,axiom,( ! [A] : ( ~ v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) ) ), file(classes2,fc1_classes2), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_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_waybel28,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) ) => ( ~ v3_struct_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) & v3_orders_2(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) & v6_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A) & v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) ) ) ), file(waybel28,fc1_waybel28), []). fof(fc1_waybel_7,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)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & ~ v1_yellow_3(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)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(waybel_7,fc1_waybel_7), []). fof(fc1_yellow13,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) ), file(yellow13,fc1_yellow13), []). fof(fc1_yellow_6,axiom,( ! [A] : ( v1_ordinal1(k2_yellow_6(A)) & v1_classes1(k2_yellow_6(A)) & v2_classes1(k2_yellow_6(A)) & v1_classes2(k2_yellow_6(A)) ) ), file(yellow_6,fc1_yellow_6), []). fof(fc20_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k12_waybel_0(A,B)) ) ), file(waybel_0,fc20_waybel_0), []). fof(fc21_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k13_waybel_0(A,B)) ) ), file(waybel_0,fc21_waybel_0), []). fof(fc22_waybel_0,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_waybel_0(k12_waybel_0(A,B),A) ) ), file(waybel_0,fc22_waybel_0), []). fof(fc23_waybel_0,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v2_waybel_0(k13_waybel_0(A,B),A) ) ), file(waybel_0,fc23_waybel_0), []). fof(fc24_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( ~ v3_struct_0(k14_yellow_6(A,B)) & v1_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,fc24_yellow_6), []). fof(fc25_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( ~ v3_struct_0(k14_yellow_6(A,B)) & v1_pre_topc(k14_yellow_6(A,B)) & v2_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,fc25_yellow_6), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_waybel28,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => ( ~ v3_struct_0(k1_waybel28(A,B,C)) & v3_orders_2(k1_waybel28(A,B,C)) & v6_waybel_0(k1_waybel28(A,B,C),A) & v7_waybel_0(k1_waybel28(A,B,C)) ) ) ), file(waybel28,fc2_waybel28), []). fof(fc2_waybel_0,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v1_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc2_waybel_0), []). fof(fc2_waybel_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v3_struct_0(k3_yellow_1(A)) & ~ v3_realset2(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)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & ~ v1_yellow_3(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)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ) ), file(waybel_7,fc2_waybel_7), []). fof(fc2_yellow13,axiom,( ! [A] : ( ( v3_realset2(A) & l1_struct_0(A) ) => v1_realset1(u1_struct_0(A)) ) ), file(yellow13,fc2_yellow13), []). fof(fc2_yellow_6,axiom,( ! [A] : ( ~ v1_xboole_0(k2_yellow_6(A)) & v1_ordinal1(k2_yellow_6(A)) & v1_classes1(k2_yellow_6(A)) & v2_classes1(k2_yellow_6(A)) & v1_classes2(k2_yellow_6(A)) ) ), file(yellow_6,fc2_yellow_6), []). fof(fc3_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( v1_ordinal1(k1_classes1(A)) & ~ v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) ) ) ), file(classes2,fc3_classes2), []). fof(fc3_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k4_xboole_0(A,B)) ) ), file(relat_1,fc3_relat_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ), file(tops_1,fc3_tops_1), []). fof(fc3_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v1_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc3_waybel_0), []). fof(fc3_yellow13,axiom,( ! [A] : ( ( v2_compts_1(A) & l1_pre_topc(A) ) => ( v1_tops_1(k2_pre_topc(A),A) & v6_compts_1(k2_pre_topc(A),A) ) ) ), file(yellow13,fc3_yellow13), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). 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_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ), file(tops_1,fc4_tops_1), []). fof(fc4_waybel_0,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v2_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc4_waybel_0), []). fof(fc4_yellow19,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ( ~ v3_struct_0(k3_yellow19(A,B,C)) & v2_orders_2(k3_yellow19(A,B,C)) & v3_orders_2(k3_yellow19(A,B,C)) & v6_waybel_0(k3_yellow19(A,B,C),A) ) ) ), file(yellow19,fc4_yellow19), []). fof(fc5_classes2,axiom,( ! [A] : v1_ordinal1(k5_classes1(A)) ), file(classes2,fc5_classes2), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc5_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v2_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc5_waybel_0), []). fof(fc5_yellow19,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ( ~ v3_struct_0(k3_yellow19(A,B,C)) & v2_orders_2(k3_yellow19(A,B,C)) & v3_orders_2(k3_yellow19(A,B,C)) & v6_waybel_0(k3_yellow19(A,B,C),A) & v7_waybel_0(k3_yellow19(A,B,C)) ) ) ), file(yellow19,fc5_yellow19), []). fof(fc6_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => ( v1_ordinal1(k1_classes1(A)) & ~ v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) ) ) ), file(classes2,fc6_classes2), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc6_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & ~ v1_xboole_0(B) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( ~ v3_struct_0(g1_waybel_0(A,B,C,D)) & v6_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,fc6_waybel_0), []). fof(fc6_yellow19,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => ( ~ v3_struct_0(k3_yellow19(A,k2_pre_topc(A),B)) & v2_orders_2(k3_yellow19(A,k2_pre_topc(A),B)) & v3_orders_2(k3_yellow19(A,k2_pre_topc(A),B)) & v6_waybel_0(k3_yellow19(A,k2_pre_topc(A),B),A) & v7_waybel_0(k3_yellow19(A,k2_pre_topc(A),B)) & v1_yellow19(k3_yellow19(A,k2_pre_topc(A),B),A) ) ) ), file(yellow19,fc6_yellow19), []). fof(fc6_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v13_waybel_0(k3_subset_1(u1_struct_0(A),B),A) ) ), file(yellow_6,fc6_yellow_6), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k4_waybel_0(A,B)) ) ), file(waybel_0,fc7_waybel_0), []). fof(fc7_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v12_waybel_0(k3_subset_1(u1_struct_0(A),B),A) ) ), file(yellow_6,fc7_yellow_6), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc8_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A) ) ) ), file(tops_1,fc8_tops_1), []). fof(fc8_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k5_waybel_0(A,B)) ) ), file(waybel_0,fc8_waybel_0), []). fof(fc8_yellow_6,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)) & v7_waybel_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & ~ v1_yellow_3(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(yellow_6,fc8_yellow_6), []). fof(fc9_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fc9_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A),A) ) ), file(tops_1,fc9_tops_1), []). fof(fraenkel_a_1_1_waybel33,axiom,( ! [A,B] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_1_waybel33(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => ! [E] : ( ( ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(k4_tarski(E,D),k3_waybel28(B)) => r1_waybel_0(B,E,C) ) ) ) ) ) ) ) ), file(waybel33,a_1_1_waybel33), []). fof(fraenkel_a_2_10_waybel33,axiom,( ! [A,B,C] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v3_waybel_7(C,k3_yellow_1(k2_pre_topc(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) ) => ( r2_hidden(A,a_2_10_waybel33(B,C)) <=> ? [D,E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_struct_0(E,k3_yellow_1(k2_pre_topc(B)),C) & A = k4_tarski(D,E) & r2_hidden(D,E) ) ) ) ), file(waybel33,a_2_10_waybel33), []). fof(fraenkel_a_2_11_waybel33,axiom,( ! [A,B,C] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) ) => ( r2_hidden(A,a_2_11_waybel33(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k2_yellow_0(k3_yellow_1(k2_pre_topc(B)),D) & r2_yellow_0(k3_yellow_1(k2_pre_topc(B)),D) ) ) ) ), file(waybel33,a_2_11_waybel33), []). fof(fraenkel_a_2_12_waybel33,axiom,( ! [A,B,C] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) ) => ( r2_hidden(A,a_2_12_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(D,C) ) ) ) ), file(waybel33,a_2_12_waybel33), []). fof(fraenkel_a_2_2_waybel33,axiom,( ! [A,B,C] : ( ( 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(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_2_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_9(B,k6_waybel_9(B,C,D)) ) ) ) ), file(waybel33,a_2_2_waybel33), []). fof(fraenkel_a_2_3_waybel11,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & ~ v3_struct_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_3_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k3_waybel_0(B,C,D) ) ) ) ), file(waybel11,a_2_3_waybel11), []). fof(fraenkel_a_2_3_yellow_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & m4_yellow_6(C,B) ) => ( r2_hidden(A,a_2_3_yellow_6(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) => ! [F] : ( ( ~ v3_struct_0(F) & v3_orders_2(F) & v7_waybel_0(F) & l1_waybel_0(F,B) ) => ( r2_hidden(k4_tarski(F,E),C) => r1_waybel_0(B,F,D) ) ) ) ) ) ) ) ), file(yellow_6,a_2_3_yellow_6), []). fof(fraenkel_a_2_4_waybel_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_waybel_0(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) ), file(waybel_0,a_2_4_waybel_0), []). fof(fraenkel_a_2_5_waybel_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_waybel_0(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k2_yellow_0(B,D) & r2_yellow_0(B,D) ) ) ) ), file(waybel_0,a_2_5_waybel_0), []). fof(fraenkel_a_3_0_waybel33,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k3_yellow_1(C)) & v13_waybel_0(D,k3_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) ) => ( r2_hidden(A,a_3_0_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,E) & r2_hidden(E,D) ) ) ) ), file(waybel33,a_3_0_waybel33), []). fof(fraenkel_a_3_0_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & ~ v3_struct_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_orders_2(C,D,E) ) ) ) ), file(waybel_9,a_3_0_waybel_9), []). fof(fraenkel_a_3_10_waybel33,axiom,( ! [A,B,C,D] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & v6_waybel_0(D,B) & m2_yellow_6(D,B,C) ) => ( r2_hidden(A,a_3_10_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & A = k8_yellow_2(u1_struct_0(k6_waybel_9(B,D,E)),B,u1_waybel_0(B,k6_waybel_9(B,D,E))) ) ) ) ), file(waybel33,a_3_10_waybel33), []). fof(fraenkel_a_3_11_waybel33,axiom,( ! [A,B,C,D] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & v6_waybel_0(D,B) & m2_yellow_6(D,B,C) ) => ( r2_hidden(A,a_3_11_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & A = k2_waybel_9(B,k6_waybel_9(B,D,E)) ) ) ) ), file(waybel33,a_3_11_waybel33), []). fof(fraenkel_a_3_1_yellow19,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k3_yellow_1(C)) & v13_waybel_0(D,k3_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) ) => ( r2_hidden(A,a_3_1_yellow19(B,C,D)) <=> ? [E,F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_struct_0(F,k3_yellow_1(C),D) & A = k4_tarski(E,F) & r2_hidden(E,F) ) ) ) ), file(yellow19,a_3_1_yellow19), []). fof(fraenkel_a_4_0_waybel33,axiom,( ! [A,B,C,D,E] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & v6_waybel_0(D,B) & m2_yellow_6(D,B,C) & m1_subset_1(E,u1_struct_0(D)) ) => ( r2_hidden(A,a_4_0_waybel33(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = F & r1_orders_2(D,E,F) ) ) ) ), file(waybel33,a_4_0_waybel33), []). fof(fraenkel_a_4_1_waybel33,axiom,( ! [A,B,C,D,E] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_waybel33(B) & l1_waybel_9(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & v6_waybel_0(D,B) & m2_yellow_6(D,B,C) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(D),u1_struct_0(D)) & m2_relset_1(E,u1_struct_0(D),u1_struct_0(D)) ) => ( r2_hidden(A,a_4_1_waybel33(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k1_waybel28(B,D,E))) & A = k3_waybel_0(B,k1_waybel28(B,D,E),F) ) ) ) ), file(waybel33,a_4_1_waybel33), []). 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_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ! [E,F,G,H] : ( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(waybel_0,g1_waybel_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(involutiveness_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,k3_subset_1(A,B)) = B ) ), file(subset_1,k3_subset_1), []). fof(rc10_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc10_waybel_0), []). fof(rc11_waybel_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc11_waybel_0), []). 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_classes2,axiom,( ? [A] : ( v1_ordinal1(A) & ~ v1_xboole_0(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) ) ), file(classes2,rc1_classes2), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). 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_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_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v7_waybel_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_waybel28(B,A) ) ) ), file(waybel28,rc1_waybel28), []). fof(rc1_waybel33,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v3_struct_0(A) & v2_pre_topc(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) & v2_waybel_3(A) & v3_waybel_3(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_waybel33(A) ) ), file(waybel33,rc1_waybel33), []). fof(rc1_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ), file(waybel_0,rc1_waybel_0), []). fof(rc1_waybel_3,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) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ), file(waybel_3,rc1_waybel_3), []). fof(rc1_waybel_7,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & ~ v3_realset2(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) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v1_lattice3(A) & v2_lattice3(A) ) ), file(waybel_7,rc1_waybel_7), []). fof(rc1_yellow11,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) & v6_group_1(A) ) ), file(yellow11,rc1_yellow11), []). fof(rc2_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & ~ v1_xboole_0(B) ) ) ), file(classes2,rc2_classes2), []). 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_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_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_waybel28(B,A) ) ) ), file(waybel28,rc2_waybel28), []). fof(rc2_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ), file(waybel_0,rc2_waybel_0), []). fof(rc2_waybel_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_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) & v2_waybel_3(A) & v3_waybel_3(A) ) ), file(waybel_3,rc2_waybel_3), []). fof(rc2_waybel_7,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ), file(waybel_7,rc2_waybel_7), []). fof(rc2_yellow13,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v6_group_1(A) & v3_realset2(A) ) ), file(yellow13,rc2_yellow13), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). 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_waybel28,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m2_yellow_6(C,A,B) & ~ v3_struct_0(C) & v3_orders_2(C) & v6_waybel_0(C,A) & v7_waybel_0(C) ) ) ), file(waybel28,rc3_waybel28), []). fof(rc3_waybel_7,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(waybel_7,rc3_waybel_7), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). 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_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) ) ) ), file(waybel_0,rc4_waybel_0), []). fof(rc4_waybel_7,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_7,rc4_waybel_7), []). fof(rc4_yellow_6,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v7_waybel_0(A) ) ), file(yellow_6,rc4_yellow_6), []). 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_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) ) ) ), file(waybel_0,rc5_waybel_0), []). fof(rc7_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc7_waybel_0), []). fof(rc7_waybel_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) & ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) & v2_waybel_0(B,k3_yellow_1(A)) & v13_waybel_0(B,k3_yellow_1(A)) & v3_waybel_7(B,k3_yellow_1(A)) ) ) ), file(waybel_7,rc7_waybel_7), []). fof(rc8_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc8_waybel_0), []). fof(rc9_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & v12_waybel_0(B,A) ) ) ), file(waybel_0,rc9_waybel_0), []). fof(redefinition_k1_card_fil,axiom,( ! [A,B] : k1_card_fil(A,B) = k4_xboole_0(A,B) ), file(card_fil,k1_card_fil), []). fof(redefinition_k1_toler_1,axiom,( ! [A,B] : ( v1_relat_1(A) => k1_toler_1(A,B) = k2_wellord1(A,B) ) ), file(toler_1,k1_toler_1), []). fof(redefinition_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_0,k1_waybel_0), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). fof(redefinition_k2_waybel28,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v1_waybel28(C,B) & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => k2_waybel28(A,B,C) = k1_waybel28(A,B,C) ) ), file(waybel28,k2_waybel28), []). fof(redefinition_k3_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => k3_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_6,k3_yellow_6), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). fof(redefinition_k6_waybel_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => k6_waybel_9(A,B,C) = k5_waybel_9(A,B,C) ) ), file(waybel_9,k6_waybel_9), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), []). fof(redefinition_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_2,k7_yellow_2), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ), file(relset_1,k8_relset_1), []). fof(redefinition_k8_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => k8_yellow_2(A,B,C) = k2_relat_1(C) ) ), file(yellow_2,k8_yellow_2), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). 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(redefinition_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_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) ) ) ), file(orders_2,r3_orders_2), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_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) ) ), file(orders_2,r3_orders_2), []). fof(s14_funct_2__e5_32_2_7__waybel33,axiom,( ! [A,B,C,D] : ( ( 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) & v1_waybel33(A) & l1_waybel_9(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & v6_waybel_0(C,A) & m2_yellow_6(C,A,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & r1_orders_2(C,E,F) & r2_hidden(k3_waybel_0(A,C,F),D) ) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(C)) & ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( r1_orders_2(C,F,k8_funct_2(u1_struct_0(C),u1_struct_0(C),E,F)) & r2_hidden(k3_waybel_0(A,C,k8_funct_2(u1_struct_0(C),u1_struct_0(C),E,F)),D) ) ) ) ) ) ), file(waybel33,s14_funct_2__e5_32_2_7__waybel33), []). fof(s1_wellord2__e8_32_2_3__waybel33,axiom,( ! [A,B,C,D] : ( ( 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) & v1_waybel33(A) & l1_waybel_9(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & v6_waybel_0(C,A) & m2_yellow_6(C,A,B) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => ( ! [E] : ~ ( r2_hidden(E,D) & ! [F] : ~ ( r2_hidden(F,u1_struct_0(C)) & ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & G = F & E = k8_yellow_2(u1_struct_0(k6_waybel_9(A,C,G)),A,u1_waybel_0(A,k6_waybel_9(A,C,G))) ) ) ) => ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & k1_relat_1(E) = D & r1_tarski(k2_relat_1(E),u1_struct_0(C)) & ! [F] : ( r2_hidden(F,D) => ? [H] : ( m1_subset_1(H,u1_struct_0(C)) & H = k1_funct_1(E,F) & F = k8_yellow_2(u1_struct_0(k6_waybel_9(A,C,H)),A,u1_waybel_0(A,k6_waybel_9(A,C,H))) ) ) ) ) ) ), file(waybel33,s1_wellord2__e8_32_2_3__waybel33), []). fof(t106_zfmisc_1,axiom,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), []). fof(t10_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ r2_hidden(C,B) ) ) ) ), file(subset_1,t10_subset_1), []). fof(t10_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r2_waybel_0(A,B,C) <=> ~ r1_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) ) ) ) ), file(waybel_0,t10_waybel_0), []). fof(t10_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r2_hidden(C,B) <=> r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) ) ) ) ) ), file(yellow_6,t10_yellow_6), []). fof(t11_waybel33,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] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => k1_waybel11(A,B) = k1_yellow_0(A,a_2_2_waybel33(A,B)) ) ) ), file(waybel33,t11_waybel33), []). fof(t12_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k1_relat_1(B)) => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ), file(funct_1,t12_funct_1), []). fof(t12_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => u1_struct_0(k5_waybel_9(A,B,C)) = a_3_0_waybel_9(A,B,C) ) ) ) ), file(waybel_9,t12_waybel_9), []). fof(t13_waybel33,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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) ), file(waybel33,t13_waybel33), []). fof(t13_waybel_7,axiom,( ! [A,B] : ( ( v13_waybel_0(B,k3_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) ) => ( v2_waybel_0(B,k3_yellow_1(A)) <=> ! [C,D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k3_xboole_0(C,D),B) ) ) ) ), file(waybel_7,t13_waybel_7), []). fof(t14_waybel28,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] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r2_hidden(B,k7_yellow_6(A)) & C = k1_waybel11(A,B) & ! [D] : ( m2_yellow_6(D,A,B) => ( r2_hidden(D,k7_yellow_6(A)) => r1_orders_2(A,k2_waybel_9(A,D),C) ) ) ) => ( C = k1_waybel11(A,B) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(B)) & v1_waybel28(D,B) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) ) => r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,B,D)),C) ) ) ) ) ) ) ), file(waybel28,t14_waybel28), []). fof(t14_waybel33,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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => r2_hidden(k3_yellow19(A,k2_pre_topc(A),B),k7_yellow_6(A)) ) ) ), file(waybel33,t14_waybel33), []). fof(t16_waybel33,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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v3_waybel_7(B,k3_yellow_1(k2_pre_topc(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => ! [C] : ( m2_yellow_6(C,A,k3_yellow19(A,k2_pre_topc(A),B)) => k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,C) ) ) ) ), file(waybel33,t16_waybel33), []). fof(t16_waybel_0,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,k4_waybel_0(A,B)) & r1_tarski(B,k5_waybel_0(A,B)) ) ) ) ), file(waybel_0,t16_waybel_0), []). fof(t16_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_waybel_9(A,B,C))) => ( D = E => k3_waybel_0(A,B,D) = k3_waybel_0(A,k5_waybel_9(A,B,C),E) ) ) ) ) ) ) ), file(waybel_9,t16_waybel_9), []). fof(t17_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_subset_1(u1_struct_0(A),B) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) ) ) ), file(pre_topc,t17_pre_topc), []). fof(t17_waybel33,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ~ ( r2_waybel_0(A,B,C) & ! [D] : ( ( v6_waybel_0(D,A) & m2_yellow_6(D,A,B) ) => ~ ( r1_tarski(k8_yellow_2(u1_struct_0(D),A,u1_waybel_0(A,D)),C) & m1_yellow_6(D,A,B) ) ) ) ) ) ), file(waybel33,t17_waybel33), []). fof(t17_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( r1_yellow_0(A,B) & r2_yellow_0(A,B) ) ) ), file(yellow_0,t17_yellow_0), []). fof(t18_yellow_1,axiom,( ! [A] : k3_yellow_0(k3_yellow_1(A)) = k1_xboole_0 ), file(yellow_1,t18_yellow_1), []). fof(t19_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => k8_yellow_2(u1_struct_0(B),A,u1_waybel_0(A,B)) = a_2_3_waybel11(A,B) ) ) ), file(waybel11,t19_waybel11), []). fof(t19_yellow_1,axiom,( ! [A] : k4_yellow_0(k3_yellow_1(A)) = A ), file(yellow_1,t19_yellow_1), []). fof(t19_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ( m1_yellow_6(C,A,B) => r1_tarski(u1_struct_0(C),u1_struct_0(B)) ) ) ) ), file(yellow_6,t19_yellow_6), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) ) <=> ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & r2_lattice3(A,C,D) ) ) ) ) ) ), file(waybel_0,t1_waybel_0), []). fof(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t20_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) ) => k2_yellow_0(k3_yellow_1(A),B) = k1_setfam_1(B) ) ), file(yellow_1,t20_yellow_1), []). fof(t23_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), []). fof(t24_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ( ( m2_yellow_6(B,A,C) & m2_yellow_6(C,A,D) ) => m2_yellow_6(B,A,D) ) ) ) ) ) ), file(yellow_6,t24_yellow_6), []). fof(t26_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_finset_1(k1_relat_1(A)) => v1_finset_1(k2_relat_1(A)) ) ) ), file(finset_1,t26_finset_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_yellow_1,axiom,( ! [A,B] : ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_1(A))) => ( r3_orders_2(k3_yellow_1(A),B,C) <=> r1_tarski(B,C) ) ) ) ), file(yellow_1,t2_yellow_1), []). fof(t30_waybel_7,axiom,( ! [A] : ( ( ~ v3_realset2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v11_waybel_1(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(B,A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( ~ v1_xboole_0(C) & v2_waybel_0(C,A) & v13_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,C) & v3_waybel_7(C,A) ) ) ) ), file(waybel_7,t30_waybel_7), []). fof(t32_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( B = k1_yellow_0(A,C) <=> ( r2_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,C,D) => r1_orders_2(A,B,D) ) ) ) ) ) ) ), file(yellow_0,t32_yellow_0), []). fof(t34_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B,C] : ( ( r1_tarski(B,C) & r1_yellow_0(A,B) & r1_yellow_0(A,C) ) => r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ), file(yellow_0,t34_yellow_0), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_waybel28,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] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r2_hidden(B,k7_yellow_6(A)) & ! [D] : ( m2_yellow_6(D,A,B) => ( r2_hidden(D,k7_yellow_6(A)) => C = k1_waybel11(A,D) ) ) ) => ( C = k1_waybel11(A,B) & ! [D] : ( m2_yellow_6(D,A,B) => ( r2_hidden(D,k7_yellow_6(A)) => r1_orders_2(A,k2_waybel_9(A,D),C) ) ) ) ) ) ) ) ), file(waybel28,t3_waybel28), []). fof(t3_waybel_7,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,C] : ( r1_tarski(B,C) => ( r3_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) & r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)) ) ) ) ), file(waybel_7,t3_waybel_7), []). fof(t3_xboole_1,axiom,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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_waybel_7,axiom,( ! [A] : u1_struct_0(k3_yellow_1(A)) = k1_zfmisc_1(A) ), file(waybel_7,t4_waybel_7), []). fof(t50_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,k12_waybel_0(A,B)) & r1_tarski(B,k13_waybel_0(A,B)) ) ) ) ), file(waybel_0,t50_waybel_0), []). 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(t67_funct_2,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) ) => ( k4_relset_1(A,A,B) = A & r1_tarski(k2_relat_1(B),A) ) ) ), file(funct_2,t67_funct_2), []). fof(t68_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( B = k7_relat_1(C,A) <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A) & ! [D] : ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ), file(funct_1,t68_funct_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_setfam_1,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) => r1_tarski(B,C) ) => ( A = k1_xboole_0 | r1_tarski(B,k1_setfam_1(A)) ) ) ), file(setfam_1,t6_setfam_1), []). fof(t76_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ) ), file(funct_1,t76_funct_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_mcart_1,axiom,( ! [A,B] : ( k1_mcart_1(k4_tarski(A,B)) = A & k2_mcart_1(k4_tarski(A,B)) = B ) ), file(mcart_1,t7_mcart_1), []). fof(t7_waybel28,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => u1_struct_0(k1_waybel28(A,B,C)) = u1_struct_0(B) ) ) ) ), file(waybel28,t7_waybel28), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_waybel_7,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) <=> ~ r2_hidden(k3_yellow_0(A),B) ) ) ) ), file(waybel_7,t8_waybel_7), []).