% Mizar problem: t35_waybel26,waybel26,1362,25 fof(t35_waybel26,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_waybel26(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18)))),u1_struct_0(k5_yellow_1(B,k2_pre_circ(B,k1_waybel26(A,k9_waybel18))))) & m2_relset_1(C,u1_struct_0(k1_waybel26(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18)))),u1_struct_0(k5_yellow_1(B,k2_pre_circ(B,k1_waybel26(A,k9_waybel18))))) & v23_waybel_0(C,k1_waybel26(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18))),k5_yellow_1(B,k2_pre_circ(B,k1_waybel26(A,k9_waybel18)))) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_waybel18(B,k2_pre_circ(B,k9_waybel18)))) & v5_pre_topc(D,A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18))) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_waybel18(B,k2_pre_circ(B,k9_waybel18)))) ) => k1_funct_1(C,D) = k10_funct_6(D) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v1_waybel_9,antisymmetry_r2_hidden,cc10_tsp_1,cc10_waybel25,cc10_waybel_0,cc11_waybel_0,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc1_finset_1,cc1_funct_1,cc1_lattice3,cc1_monoid_0,cc1_relset_1,cc1_tops_1,cc1_tsp_1,cc1_waybel10,cc1_waybel17,cc1_waybel18,cc1_waybel24,cc1_waybel_2,cc1_waybel_3,cc1_yellow16,cc1_yellow_0,cc1_yellow_1,cc1_yellow_2,cc2_finset_1,cc2_funct_1,cc2_lattice3,cc2_tops_1,cc2_tsp_1,cc2_waybel_2,cc2_waybel_3,cc2_yellow14,cc2_yellow_0,cc3_tops_1,cc3_tsp_1,cc3_waybel25,cc3_waybel_2,cc3_waybel_3,cc3_yellow14,cc3_yellow_0,cc4_borsuk_2,cc4_tops_1,cc4_tsp_1,cc4_waybel25,cc4_waybel_2,cc4_waybel_3,cc4_yellow_0,cc5_tops_1,cc5_tsp_1,cc5_waybel_0,cc5_waybel_2,cc5_waybel_3,cc5_yellow_0,cc6_tops_1,cc6_tsp_1,cc6_waybel25,cc6_waybel_0,cc6_waybel_2,cc6_waybel_3,cc7_tsp_1,cc7_waybel_0,cc7_waybel_2,cc8_tsp_1,cc8_waybel_0,cc9_tsp_1,cc9_waybel25,cc9_waybel_0,d1_funct_2,d1_waybel26,d1_yellow_2,d2_funct_2,d2_waybel_1,d3_pboole,d3_tarski,d3_waybel18,d5_funct_1,d5_yellow_1,dt_g1_orders_2,dt_g1_pre_topc,dt_g1_waybel_9,dt_k10_funct_6,dt_k12_pralg_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_relat_1,dt_k1_waybel25,dt_k1_waybel26,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_waybel18,dt_k2_yellow16,dt_k2_zfmisc_1,dt_k3_waybel18,dt_k3_waybel24,dt_k3_waybel_3,dt_k4_card_3,dt_k4_relset_1,dt_k4_waybel18,dt_k4_waybel_3,dt_k5_relat_1,dt_k5_waybel18,dt_k5_yellow_1,dt_k6_waybel_3,dt_k6_yellow_1,dt_k7_funct_2,dt_k7_grcat_1,dt_k7_waybel_3,dt_k7_yellow_2,dt_k8_funct_2,dt_k8_yellow_2,dt_k9_waybel18,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_9,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cantor_1,dt_m2_relset_1,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_9,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_cantor_1,existence_m2_relset_1,fc10_waybel18,fc10_waybel24,fc10_waybel25,fc10_yellow_1,fc11_waybel18,fc11_waybel24,fc11_yellow_1,fc12_waybel18,fc12_yellow_1,fc13_waybel18,fc13_yellow_1,fc14_finset_1,fc14_yellow_1,fc15_waybel25,fc15_yellow_1,fc16_yellow_1,fc17_yellow_1,fc18_yellow_1,fc1_borsuk_2,fc1_funct_1,fc1_struct_0,fc1_subset_1,fc1_waybel10,fc1_waybel17,fc1_waybel18,fc1_waybel25,fc1_waybel26,fc1_xboole_0,fc1_yellow16,fc2_waybel17,fc2_waybel18,fc2_waybel25,fc2_waybel26,fc2_yellow16,fc3_waybel10,fc3_waybel25,fc3_waybel26,fc3_yellow_6,fc4_subset_1,fc4_waybel10,fc4_waybel25,fc4_yellow_6,fc5_waybel18,fc5_waybel25,fc5_waybel26,fc5_yellow14,fc5_yellow16,fc5_yellow_6,fc6_funct_1,fc6_waybel18,fc6_waybel24,fc6_waybel25,fc6_yellow14,fc6_yellow16,fc7_waybel18,fc7_waybel24,fc7_waybel25,fc7_waybel_3,fc8_waybel18,fc8_waybel24,fc8_waybel25,fc8_waybel_3,fc9_waybel18,fc9_waybel24,fc9_waybel_3,fc9_yellow_6,free_g1_orders_2,free_g1_pre_topc,free_g1_waybel_9,irreflexivity_r2_orders_2,rc10_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_borsuk_2,rc1_finset_1,rc1_funct_1,rc1_lattice3,rc1_monoid_0,rc1_pre_topc,rc1_subset_1,rc1_tops_1,rc1_tsp_1,rc1_waybel10,rc1_waybel18,rc1_waybel25,rc1_waybel26,rc1_waybel_0,rc1_waybel_3,rc1_xboole_0,rc1_yellow14,rc1_yellow16,rc1_yellow_0,rc1_yellow_1,rc1_yellow_6,rc2_borsuk_1,rc2_funct_1,rc2_lattice3,rc2_pre_topc,rc2_subset_1,rc2_tops_1,rc2_tsp_1,rc2_waybel10,rc2_waybel18,rc2_waybel_0,rc2_waybel_3,rc2_xboole_0,rc2_yellow16,rc2_yellow_0,rc2_yellow_6,rc2_yellow_9,rc3_finset_1,rc3_funct_1,rc3_struct_0,rc3_tops_1,rc3_tsp_1,rc3_waybel25,rc3_waybel_3,rc3_yellow14,rc3_yellow16,rc3_yellow_6,rc3_yellow_9,rc4_finset_1,rc4_tops_1,rc4_tsp_1,rc4_yellow_9,rc5_funct_1,rc5_struct_0,rc5_tops_1,rc5_yellow_6,rc6_pre_topc,rc7_pre_topc,redefinition_k2_pre_circ,redefinition_k2_yellow16,redefinition_k3_waybel_3,redefinition_k4_relset_1,redefinition_k4_waybel18,redefinition_k4_waybel_3,redefinition_k5_waybel18,redefinition_k6_waybel_3,redefinition_k7_funct_2,redefinition_k7_waybel_3,redefinition_k7_yellow_2,redefinition_k8_funct_2,redefinition_k8_yellow_2,redefinition_m2_relset_1,redefinition_r3_orders_2,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r3_orders_2,reflexivity_r6_pboole,s5_pboole__e1_46__waybel26,s5_pboole__e6_46__waybel26,symmetry_r6_pboole,t113_funct_2,t11_grcat_1,t13_funcop_1,t14_waybel25,t17_yellow16,t1_subset,t1_waybel26,t1_yellow_0,t20_card_3,t21_funct_2,t28_waybel_3,t28_yellow_1,t2_subset,t2_waybel26,t31_waybel26,t32_waybel26,t33_waybel26,t34_waybel26,t3_subset,t3_waybel26,t4_funct_2,t4_subset,t5_subset,t63_funct_5,t6_boole,t7_boole,t86_funct_6,t87_funct_6,t8_boole]), [file(waybel26,t35_waybel26)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(abstractness_v1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(A) => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ), file(pre_topc,v1_pre_topc), []). fof(abstractness_v1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( v1_waybel_9(A) => A = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) ), file(waybel_9,v1_waybel_9), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_tdlat_3(A) & ~ v3_tdlat_3(A) ) ) ) ), file(tsp_1,cc10_tsp_1), []). fof(cc10_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc10_waybel25), []). fof(cc10_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_0,cc10_waybel_0), []). fof(cc11_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_yellow_0(A) ) ) ) ), file(waybel_0,cc11_waybel_0), []). fof(cc12_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(waybel_0,cc12_waybel_0), []). fof(cc13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) ) ) ) ), file(waybel_0,cc13_waybel_0), []). fof(cc14_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc14_waybel_0), []). fof(cc1_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_monoid_0,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(monoid_0,cc1_monoid_0), []). fof(cc1_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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc1_tsp_1), []). fof(cc1_waybel10,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) ) => ( v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(B) & v5_orders_3(B,A,A) ) ) ) ) ), file(waybel10,cc1_waybel10), []). fof(cc1_waybel17,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(C,A,B) ) => ( ~ v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(waybel17,cc1_waybel17), []). fof(cc1_waybel18,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel18(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) ), file(waybel18,cc1_waybel18), []). fof(cc1_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_seqm_3(C) ) => ( ~ v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(waybel24,cc1_waybel24), []). fof(cc1_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel_2,cc1_waybel_2), []). fof(cc1_waybel_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_yellow16,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_yellow16(A) ) => ( v1_relat_1(A) & v1_yellow_1(A) & v5_waybel_3(A) ) ) ), file(yellow16,cc1_yellow16), []). fof(cc1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(yellow_0,cc1_yellow_0), []). fof(cc1_yellow_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_yellow_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) ), file(yellow_1,cc1_yellow_1), []). fof(cc1_yellow_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(yellow_2,cc1_yellow_2), []). fof(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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & ~ v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) ) ) ) ), file(tsp_1,cc2_tsp_1), []). fof(cc2_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ), file(waybel_2,cc2_waybel_2), []). fof(cc2_waybel_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_yellow14,axiom,( ! [A,B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(yellow14,cc2_yellow14), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc3_tsp_1), []). fof(cc3_waybel25,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) & v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B)) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) & v1_partfun1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) & v5_orders_3(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) ), file(waybel25,cc3_waybel25), []). fof(cc3_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc3_waybel_2), []). fof(cc3_waybel_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_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_struct_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow14,cc3_yellow14), []). fof(cc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow_0,cc3_yellow_0), []). fof(cc4_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( v3_struct_0(A) => v2_t_0topsp(A) ) ) ), file(borsuk_2,cc4_borsuk_2), []). 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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) ) ) ) ), file(tsp_1,cc4_tsp_1), []). fof(cc4_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) => ( v3_pre_topc(B,k1_waybel25(A)) => v13_waybel_0(B,k1_waybel25(A)) ) ) ) ), file(waybel25,cc4_waybel25), []). fof(cc4_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc4_waybel_2), []). fof(cc4_waybel_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_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & v2_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc5_tsp_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_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc5_waybel_2), []). fof(cc5_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_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) ), file(yellow_0,cc5_yellow_0), []). fof(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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & v3_realset2(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc6_tsp_1), []). fof(cc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc6_waybel25), []). fof(cc6_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B) ) ) ) ) ), file(waybel_0,cc6_waybel_0), []). fof(cc6_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v1_waybel_2(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc6_waybel_2), []). fof(cc6_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(cc7_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) ) ) ) ), file(tsp_1,cc7_tsp_1), []). fof(cc7_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) ) ) ) ) ), file(waybel_0,cc7_waybel_0), []). fof(cc7_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_waybel_1(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ) ) ), file(waybel_2,cc7_waybel_2), []). fof(cc8_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc8_tsp_1), []). fof(cc8_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) ) ) ), file(waybel_0,cc8_waybel_0), []). fof(cc9_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v3_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc9_tsp_1), []). fof(cc9_waybel25,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) & v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B)) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) & v1_partfun1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) & v22_waybel_0(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) ), file(waybel25,cc9_waybel25), []). 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(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => k1_waybel26(A,B) = k3_waybel24(A,k1_waybel25(B)) ) ) ), file(waybel26,d1_waybel26), []). fof(d1_yellow_2,axiom,( ! [A,B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m2_relset_1(C,A,u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(B)) & m2_relset_1(D,A,u1_struct_0(B)) ) => ( r1_yellow_2(A,B,C,D) <=> ! [E] : ~ ( r2_hidden(E,A) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( F = k1_funct_1(C,E) & G = k1_funct_1(D,E) & r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ), file(yellow_2,d1_yellow_2), []). fof(d2_funct_2,axiom,( ! [A,B,C] : ( C = k1_funct_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & D = E & k1_relat_1(E) = A & r1_tarski(k2_relat_1(E),B) ) ) ) ), file(funct_2,d2_funct_2), []). fof(d2_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v5_orders_3(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_orders_2(A,D,E) => r1_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) ) ), file(waybel_1,d2_waybel_1), []). fof(d3_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), []). 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_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ! [C] : ( ( v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = k3_waybel18(A,B) <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B)) & m2_cantor_1(k2_waybel18(A,B),C) ) ) ) ) ), file(waybel18,d3_waybel18), []). 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_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)) ) ), file(yellow_1,d5_yellow_1), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(pre_topc,g1_pre_topc), []). fof(dt_g1_waybel_9,axiom,( ! [A,B,C] : ( ( m1_relset_1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( v1_waybel_9(g1_waybel_9(A,B,C)) & l1_waybel_9(g1_waybel_9(A,B,C)) ) ) ), file(waybel_9,g1_waybel_9), []). fof(dt_k10_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k10_funct_6(A)) & v1_funct_1(k10_funct_6(A)) & v1_funcop_1(k10_funct_6(A)) ) ) ), file(funct_6,k10_funct_6), []). fof(dt_k12_pralg_1,axiom,( ! [A,B] : ( ( v2_pralg_1(B) & m1_pboole(B,A) ) => m1_pboole(k12_pralg_1(A,B),A) ) ), file(pralg_1,k12_pralg_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_waybel_9(k1_waybel25(A)) & l1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,k1_waybel25), []). fof(dt_k1_waybel26,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k1_waybel26(A,B)) & v1_orders_2(k1_waybel26(A,B)) & l1_orders_2(k1_waybel26(A,B)) ) ) ), file(waybel26,k1_waybel26), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_waybel18,axiom,( ! [A,B] : ( ( v1_waybel18(B) & m1_pboole(B,A) ) => m1_subset_1(k2_waybel18(A,B),k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) ) ), file(waybel18,k2_waybel18), []). fof(dt_k2_yellow16,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_yellow16(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k2_yellow16(A,B,C)) & v2_orders_2(k2_yellow16(A,B,C)) & v3_orders_2(k2_yellow16(A,B,C)) & v4_orders_2(k2_yellow16(A,B,C)) & l1_orders_2(k2_yellow16(A,B,C)) ) ) ), file(yellow16,k2_yellow16), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ( v1_pre_topc(k3_waybel18(A,B)) & v2_pre_topc(k3_waybel18(A,B)) & l1_pre_topc(k3_waybel18(A,B)) ) ) ), file(waybel18,k3_waybel18), []). fof(dt_k3_waybel24,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & ~ v3_struct_0(B) & l1_waybel_9(B) ) => ( v1_orders_2(k3_waybel24(A,B)) & l1_orders_2(k3_waybel24(A,B)) ) ) ), file(waybel24,k3_waybel24), []). fof(dt_k3_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k3_waybel_3(A,B,C)) & l1_orders_2(k3_waybel_3(A,B,C)) ) ) ), file(waybel_3,k3_waybel_3), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). 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_waybel18,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k4_waybel18(A,B,C)) & l1_pre_topc(k4_waybel18(A,B,C)) ) ) ), file(waybel18,k4_waybel18), []). fof(dt_k4_waybel_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => m1_subset_1(k4_waybel_3(A,B,C,D),u1_struct_0(k3_waybel_3(A,B,D))) ) ), file(waybel_3,k4_waybel_3), []). 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_waybel18,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k3_waybel18(A,B))) & m1_subset_1(D,A) ) => m1_subset_1(k5_waybel18(A,B,C,D),u1_struct_0(k4_waybel18(A,B,D))) ) ), file(waybel18,k5_waybel18), []). fof(dt_k5_yellow_1,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & m1_pboole(B,A) ) => ( v1_orders_2(k5_yellow_1(A,B)) & l1_orders_2(k5_yellow_1(A,B)) ) ) ), file(yellow_1,k5_yellow_1), []). fof(dt_k6_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k6_waybel_3(A,B,C)) & v2_orders_2(k6_waybel_3(A,B,C)) & l1_orders_2(k6_waybel_3(A,B,C)) ) ) ), file(waybel_3,k6_waybel_3), []). fof(dt_k6_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_orders_2(k6_yellow_1(A,B)) & l1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,k6_yellow_1), []). fof(dt_k7_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_grcat_1,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(grcat_1,k7_grcat_1), []). fof(dt_k7_waybel_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => m1_subset_1(k7_waybel_3(A,B,C,D),u1_struct_0(k6_waybel_3(A,B,D))) ) ), file(waybel_3,k7_waybel_3), []). 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_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_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_k9_waybel18,axiom, ( v1_pre_topc(k9_waybel18) & l1_pre_topc(k9_waybel18) ), file(waybel18,k9_waybel18), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( l1_pre_topc(A) & l1_orders_2(A) ) ) ), file(waybel_9,l1_waybel_9), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_cantor_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(cantor_1,m2_cantor_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pre_topc,u1_pre_topc), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) ), file(waybel_9,l1_waybel_9), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m2_cantor_1(B,A) ) ), file(cantor_1,m2_cantor_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_waybel18,axiom,( ! [A,B] : ( ( v2_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc10_waybel18), []). fof(fc10_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v4_orders_2(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc10_waybel24), []). fof(fc10_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v1_lattice3(k1_waybel25(A)) & v2_lattice3(k1_waybel25(A)) & v3_lattice3(k1_waybel25(A)) & v1_yellow_0(k1_waybel25(A)) & v2_yellow_0(k1_waybel25(A)) & v3_yellow_0(k1_waybel25(A)) & v24_waybel_0(k1_waybel25(A)) & v25_waybel_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) & v3_waybel_3(k1_waybel25(A)) ) ) ), file(waybel25,fc10_waybel25), []). fof(fc10_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) ) ) ), file(yellow_1,fc10_yellow_1), []). fof(fc11_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc11_waybel18), []). fof(fc11_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v1_monoid_0(k6_yellow_1(A,B)) ) ) ), file(waybel24,fc11_waybel24), []). fof(fc11_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc11_yellow_1), []). fof(fc12_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc12_waybel18), []). fof(fc12_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v2_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc12_yellow_1), []). fof(fc13_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc13_waybel18), []). fof(fc13_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ), file(yellow_1,fc13_yellow_1), []). fof(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(fc14_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v2_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_orders_2(k6_yellow_1(k1_xboole_0,A)) & v4_orders_2(k6_yellow_1(k1_xboole_0,A)) & v1_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v2_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v3_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_lattice3(k6_yellow_1(k1_xboole_0,A)) & v2_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ), file(yellow_1,fc14_yellow_1), []). fof(fc15_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v24_waybel_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc15_waybel25), []). fof(fc15_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v3_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc15_yellow_1), []). fof(fc16_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc16_yellow_1), []). fof(fc17_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v2_lattice3(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc17_yellow_1), []). fof(fc18_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v1_lattice3(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc18_yellow_1), []). fof(fc1_borsuk_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ( ~ v1_xboole_0(k7_grcat_1(A)) & v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(k7_grcat_1(A),A,A) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_t_0topsp(k7_grcat_1(A),A,A) ) ) ), file(borsuk_2,fc1_borsuk_2), []). 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_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_waybel10,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v4_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(waybel10,fc1_waybel10), []). fof(fc1_waybel17,axiom,( ! [A,B] : ( ( v2_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) ) ) ), file(waybel17,fc1_waybel17), []). fof(fc1_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k3_waybel18(A,B)) & v1_pre_topc(k3_waybel18(A,B)) & v2_pre_topc(k3_waybel18(A,B)) ) ) ), file(waybel18,fc1_waybel18), []). fof(fc1_waybel25,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) & ~ v1_urysohn1(k9_waybel18) & v2_waybel18(k9_waybel18) ), file(waybel25,fc1_waybel25), []). fof(fc1_waybel26,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(waybel26,fc1_waybel26), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc1_yellow16,axiom,( ! [A,B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow16(k2_funcop_1(A,B)) ) ) ), file(yellow16,fc1_yellow16), []). fof(fc2_waybel17,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( v1_orders_2(k6_yellow_1(A,B)) & v3_lattice3(k6_yellow_1(A,B)) ) ) ), file(waybel17,fc2_waybel17), []). fof(fc2_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k3_waybel18(A,B)) & v1_pre_topc(k3_waybel18(A,B)) & v2_pre_topc(k3_waybel18(A,B)) & v1_monoid_0(k3_waybel18(A,B)) ) ) ), file(waybel18,fc2_waybel18), []). fof(fc2_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v2_waybel18(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ), file(waybel25,fc2_waybel25), []). fof(fc2_waybel26,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k1_waybel26(A,B)) & v1_orders_2(k1_waybel26(A,B)) & v2_orders_2(k1_waybel26(A,B)) & v3_orders_2(k1_waybel26(A,B)) & v1_monoid_0(k1_waybel26(A,B)) ) ) ), file(waybel26,fc2_waybel26), []). fof(fc2_yellow16,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_yellow16(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v2_orders_2(k5_yellow_1(A,B)) & v3_orders_2(k5_yellow_1(A,B)) & v4_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(yellow16,fc2_yellow16), []). fof(fc3_waybel10,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(waybel10,fc3_waybel10), []). fof(fc3_waybel25,axiom,( ! [A] : ( ( v3_struct_0(A) & l1_pre_topc(A) ) => ( v3_struct_0(k1_waybel25(A)) & v1_yellow_0(k1_waybel25(A)) & v2_yellow_0(k1_waybel25(A)) & v3_yellow_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc3_waybel25), []). fof(fc3_waybel26,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k1_waybel26(A,B)) & v1_orders_2(k1_waybel26(A,B)) & v2_orders_2(k1_waybel26(A,B)) & v3_orders_2(k1_waybel26(A,B)) & v4_orders_2(k1_waybel26(A,B)) & v1_monoid_0(k1_waybel26(A,B)) ) ) ), file(waybel26,fc3_waybel26), []). fof(fc3_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v5_seqm_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(yellow_6,fc3_yellow_6), []). 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_waybel10,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & ~ v1_xboole_0(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A),A,A) & v17_waybel_0(k7_grcat_1(A),A,A) & v18_waybel_0(k7_grcat_1(A),A,A) & v19_waybel_0(k7_grcat_1(A),A,A) & v20_waybel_0(k7_grcat_1(A),A,A) & v21_waybel_0(k7_grcat_1(A),A,A) & v22_waybel_0(k7_grcat_1(A),A,A) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) & v8_waybel_1(k7_grcat_1(A),A) ) ) ), file(waybel10,fc4_waybel10), []). fof(fc4_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc4_waybel25), []). fof(fc4_yellow_6,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & m1_pboole(B,A) ) => v1_fraenkel(u1_struct_0(k5_yellow_1(A,B))) ) ), file(yellow_6,fc4_yellow_6), []). fof(fc5_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) ), file(waybel18,fc5_waybel18), []). fof(fc5_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_pre_topc(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc5_waybel25), []). fof(fc5_waybel26,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) & ~ v2_tdlat_3(k9_waybel18) & ~ v1_urysohn1(k9_waybel18) & ~ v3_realset2(k9_waybel18) & v2_waybel18(k9_waybel18) & v1_waybel25(k9_waybel18) ), file(waybel26,fc5_waybel26), []). fof(fc5_yellow14,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k3_waybel18(A,k2_pre_circ(A,B))) & v1_pre_topc(k3_waybel18(A,k2_pre_circ(A,B))) & v2_pre_topc(k3_waybel18(A,k2_pre_circ(A,B))) & v2_t_0topsp(k3_waybel18(A,k2_pre_circ(A,B))) & v1_monoid_0(k3_waybel18(A,k2_pre_circ(A,B))) ) ) ), file(yellow14,fc5_yellow14), []). fof(fc5_yellow16,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) ) => ( ~ v3_struct_0(k6_yellow_1(B,A)) & v1_orders_2(k6_yellow_1(B,A)) & v2_orders_2(k6_yellow_1(B,A)) & v3_orders_2(k6_yellow_1(B,A)) & v4_orders_2(k6_yellow_1(B,A)) & v24_waybel_0(k6_yellow_1(B,A)) ) ) ), file(yellow16,fc5_yellow16), []). fof(fc5_yellow_6,axiom,( ! [A,B] : ( ( v2_pralg_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( v1_relat_1(k12_pralg_1(A,B)) & v2_relat_1(k12_pralg_1(A,B)) & v1_funct_1(k12_pralg_1(A,B)) ) ) ), file(yellow_6,fc5_yellow_6), []). fof(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc6_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) ), file(waybel18,fc6_waybel18), []). fof(fc6_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) ) ) ), file(waybel24,fc6_waybel24), []). fof(fc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc6_waybel25), []). fof(fc6_yellow14,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v1_urysohn1(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k3_waybel18(A,k2_pre_circ(A,B))) & v1_pre_topc(k3_waybel18(A,k2_pre_circ(A,B))) & v2_pre_topc(k3_waybel18(A,k2_pre_circ(A,B))) & v1_urysohn1(k3_waybel18(A,k2_pre_circ(A,B))) & v1_monoid_0(k3_waybel18(A,k2_pre_circ(A,B))) ) ) ), file(yellow14,fc6_yellow14), []). fof(fc6_yellow16,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(u1_pre_topc(A)) ) ), file(yellow16,fc6_yellow16), []). fof(fc7_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) & v2_waybel18(k9_waybel18) ), file(waybel18,fc7_waybel18), []). fof(fc7_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc7_waybel24), []). fof(fc7_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc7_waybel25), []). fof(fc7_waybel_3,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) ) ) ), file(waybel_3,fc7_waybel_3), []). fof(fc8_waybel18,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v4_waybel_3(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc8_waybel18), []). fof(fc8_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v2_orders_2(k3_waybel24(A,B)) & ~ v1_yellow_3(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc8_waybel24), []). fof(fc8_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc8_waybel25), []). fof(fc8_waybel_3,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(waybel_3,fc8_waybel_3), []). fof(fc9_waybel18,axiom,( ! [A,B] : ( l1_pre_topc(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_waybel18(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc9_waybel18), []). fof(fc9_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v3_orders_2(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc9_waybel24), []). fof(fc9_waybel_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v2_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(waybel_3,fc9_waybel_3), []). fof(fc9_yellow_6,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) ) ) ), file(yellow_6,fc9_yellow_6), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). fof(free_g1_waybel_9,axiom,( ! [A,B,C] : ( ( m1_relset_1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [D,E,F] : ( g1_waybel_9(A,B,C) = g1_waybel_9(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(waybel_9,g1_waybel_9), []). fof(irreflexivity_r2_orders_2,axiom,( ! [A,B,C] : ( ( l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ~ r2_orders_2(A,B,B) ) ), file(orders_2,r2_orders_2), []). 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(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_borsuk_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(B,A,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ), file(borsuk_2,rc1_borsuk_2), []). 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_monoid_0,axiom,( ? [A] : ( l1_struct_0(A) & v1_monoid_0(A) ) ), file(monoid_0,rc1_monoid_0), []). fof(rc1_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) ), file(pre_topc,rc1_pre_topc), []). 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_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) ) ), file(tsp_1,rc1_tsp_1), []). fof(rc1_waybel10,axiom,( ! [A,B] : ( ( l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) ), file(waybel10,rc1_waybel10), []). fof(rc1_waybel18,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_waybel18(B) ) ), file(waybel18,rc1_waybel18), []). fof(rc1_waybel25,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) ) ), file(waybel25,rc1_waybel25), []). fof(rc1_waybel26,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & ~ v2_tdlat_3(A) & ~ v3_realset2(A) & v2_waybel18(A) & v1_waybel25(A) ) ), file(waybel26,rc1_waybel26), []). 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_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_yellow14,axiom,( ? [A] : ( l1_orders_2(A) & v3_struct_0(A) & v1_orders_2(A) ) ), file(yellow14,rc1_yellow14), []). fof(rc1_yellow16,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v22_waybel_0(C,A,B) ) ) ), file(yellow16,rc1_yellow16), []). fof(rc1_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) ), file(yellow_0,rc1_yellow_0), []). fof(rc1_yellow_1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_yellow_1(B) ) ), file(yellow_1,rc1_yellow_1), []). fof(rc1_yellow_6,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) ), file(yellow_6,rc1_yellow_6), []). fof(rc2_borsuk_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ), file(borsuk_1,rc2_borsuk_1), []). 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_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) ), file(pre_topc,rc2_pre_topc), []). 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_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v2_t_0topsp(A) ) ), file(tsp_1,rc2_tsp_1), []). fof(rc2_waybel10,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) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(B) & v5_orders_3(B,A,A) & v17_waybel_0(B,A,A) & v18_waybel_0(B,A,A) & v19_waybel_0(B,A,A) & v20_waybel_0(B,A,A) & v21_waybel_0(B,A,A) & v22_waybel_0(B,A,A) & v6_waybel_1(B,A) & v7_waybel_1(B,A) & v8_waybel_1(B,A) ) ) ), file(waybel10,rc2_waybel10), []). fof(rc2_waybel18,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v4_waybel_3(B) & v2_pralg_1(B) & v1_waybel18(B) ) ), file(waybel18,rc2_waybel18), []). 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_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc2_yellow16,axiom,( ! [A] : ( l1_struct_0(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)) & v11_quantal1(B) ) ) ), file(yellow16,rc2_yellow16), []). fof(rc2_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ), file(yellow_0,rc2_yellow_0), []). fof(rc2_yellow_6,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) & v2_pralg_1(A) ) ), file(yellow_6,rc2_yellow_6), []). fof(rc2_yellow_9,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) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_waybel_9(A) & v1_tdlat_3(A) & v2_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) ), file(yellow_9,rc2_yellow_9), []). 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_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_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) & v2_t_0topsp(A) ) ), file(tsp_1,rc3_tsp_1), []). fof(rc3_waybel25,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v3_realset2(A) & v1_waybel25(A) ) ), file(waybel25,rc3_waybel25), []). fof(rc3_waybel_3,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_yellow_1(B) & v2_pralg_1(B) & v4_waybel_3(B) & v5_waybel_3(B) ) ), file(waybel_3,rc3_waybel_3), []). fof(rc3_yellow14,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v1_monoid_0(A) ) ), file(yellow14,rc3_yellow14), []). fof(rc3_yellow16,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & v2_pralg_1(B) & v1_yellow16(B) ) ), file(yellow16,rc3_yellow16), []). fof(rc3_yellow_6,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v4_waybel_3(B) ) ), file(yellow_6,rc3_yellow_6), []). fof(rc3_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ), file(yellow_9,rc3_yellow_9), []). 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_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_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_t_0topsp(A) ) ), file(tsp_1,rc4_tsp_1), []). fof(rc4_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ), file(yellow_9,rc4_yellow_9), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). 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_yellow_6,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_yellow_1(B) & v4_waybel_3(B) ) ), file(yellow_6,rc5_yellow_6), []). fof(rc6_pre_topc,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) ) ) ), file(pre_topc,rc6_pre_topc), []). fof(rc7_pre_topc,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) & v4_pre_topc(B,A) ) ) ), file(pre_topc,rc7_pre_topc), []). fof(redefinition_k2_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). fof(redefinition_k2_yellow16,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_yellow16(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k2_yellow16(A,B,C) = k1_funct_1(B,C) ) ), file(yellow16,k2_yellow16), []). fof(redefinition_k3_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k3_waybel_3(A,B,C) = k1_funct_1(B,C) ) ), file(waybel_3,k3_waybel_3), []). 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_k4_waybel18,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k4_waybel18(A,B,C) = k1_funct_1(B,C) ) ), file(waybel18,k4_waybel18), []). fof(redefinition_k4_waybel_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => k4_waybel_3(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_3,k4_waybel_3), []). fof(redefinition_k5_waybel18,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k3_waybel18(A,B))) & m1_subset_1(D,A) ) => k5_waybel18(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel18,k5_waybel18), []). fof(redefinition_k6_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k6_waybel_3(A,B,C) = k1_funct_1(B,C) ) ), file(waybel_3,k6_waybel_3), []). 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_waybel_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => k7_waybel_3(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_3,k7_waybel_3), []). 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_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_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(redefinition_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). 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(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(s5_pboole__e1_46__waybel26,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_pboole(C,u1_struct_0(k1_waybel26(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18))))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k1_waybel26(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18))))) => k1_funct_1(C,D) = k10_funct_6(D) ) ) ) ), file(waybel26,s5_pboole__e1_46__waybel26), []). fof(s5_pboole__e6_46__waybel26,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_pboole(C,u1_struct_0(k5_yellow_1(B,k2_pre_circ(B,k1_waybel26(A,k9_waybel18))))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k5_yellow_1(B,k2_pre_circ(B,k1_waybel26(A,k9_waybel18))))) => k1_funct_1(C,D) = k10_funct_6(D) ) ) ) ), file(waybel26,s5_pboole__e6_46__waybel26), []). fof(symmetry_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(t113_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( ! [E] : ( m1_subset_1(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => C = D ) ) ) ), file(funct_2,t113_funct_2), []). fof(t11_grcat_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B ) ) ), file(grcat_1,t11_grcat_1), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t14_waybel25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => g1_orders_2(u1_struct_0(k1_waybel25(k3_waybel18(A,k2_pre_circ(A,B)))),u1_orders_2(k1_waybel25(k3_waybel18(A,k2_pre_circ(A,B))))) = g1_orders_2(u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k1_waybel25(B)))),u1_orders_2(k5_yellow_1(A,k2_pre_circ(A,k1_waybel25(B))))) ) ) ), file(waybel25,t14_waybel25), []). fof(t17_yellow16,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v23_waybel_0(C,A,B) <=> ( v5_orders_3(C,A,B) & ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v5_orders_3(D,B,A) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C) = k7_grcat_1(B) & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A) ) ) ) ) ) ) ), file(yellow16,t17_yellow16), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_waybel26(A,B))) <=> ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) & v5_pre_topc(C,A,k1_waybel25(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) ) ) ) ) ), file(waybel26,t1_waybel26), []). fof(t1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => ( ( r1_orders_2(A,C,D) => r1_orders_2(B,E,F) ) & ( r2_orders_2(A,C,D) => r2_orders_2(B,E,F) ) ) ) ) ) ) ) ) ) ) ), file(yellow_0,t1_yellow_0), []). fof(t20_card_3,axiom,( ! [A,B] : k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B)) ), file(card_3,t20_card_3), []). fof(t21_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ), file(funct_2,t21_funct_2), []). fof(t28_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_yellow_1(A,B))) => ( r1_orders_2(k5_yellow_1(A,B),C,D) <=> ! [E] : ( m1_subset_1(E,A) => r1_orders_2(k3_waybel_3(A,B,E),k4_waybel_3(A,B,C,E),k4_waybel_3(A,B,D,E)) ) ) ) ) ) ) ), file(waybel_3,t28_waybel_3), []). fof(t28_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => k1_funct_2(A,u1_struct_0(B)) = u1_struct_0(k6_yellow_1(A,B)) ) ), file(yellow_1,t28_yellow_1), []). 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_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_waybel26(A,B))) <=> ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(waybel26,t2_waybel26), []). fof(t31_waybel26,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : r6_pboole(B,k12_pralg_1(B,k2_pre_circ(B,A)),k2_pre_circ(B,u1_struct_0(A))) ) ), file(waybel26,t31_waybel26), []). fof(t32_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_waybel18(C,k2_pre_circ(C,B)))) & v5_pre_topc(D,A,k3_waybel18(C,k2_pre_circ(C,B))) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_waybel18(C,k2_pre_circ(C,B)))) ) => ( v1_funct_1(k10_funct_6(D)) & v1_funct_2(k10_funct_6(D),C,u1_struct_0(k1_waybel26(A,B))) & m2_relset_1(k10_funct_6(D),C,u1_struct_0(k1_waybel26(A,B))) ) ) ) ) ) ), file(waybel26,t32_waybel26), []). fof(t33_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => r1_tarski(u1_struct_0(k1_waybel26(A,B)),k1_funct_2(u1_struct_0(A),u1_struct_0(B))) ) ) ), file(waybel26,t33_waybel26), []). fof(t34_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,u1_struct_0(k1_waybel26(A,B))) & m2_relset_1(D,C,u1_struct_0(k1_waybel26(A,B))) ) => ( v1_funct_1(k10_funct_6(D)) & v1_funct_2(k10_funct_6(D),u1_struct_0(A),u1_struct_0(k3_waybel18(C,k2_pre_circ(C,B)))) & v5_pre_topc(k10_funct_6(D),A,k3_waybel18(C,k2_pre_circ(C,B))) & m2_relset_1(k10_funct_6(D),u1_struct_0(A),u1_struct_0(k3_waybel18(C,k2_pre_circ(C,B)))) ) ) ) ) ) ), file(waybel26,t34_waybel26), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_waybel26,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_waybel26(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_waybel26(A,B))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) & m2_relset_1(F,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) ) => ( ( C = E & D = F ) => ( r3_orders_2(k1_waybel26(A,B),C,D) <=> r1_yellow_2(u1_struct_0(A),k1_waybel25(B),E,F) ) ) ) ) ) ) ) ) ), file(waybel26,t3_waybel26), []). fof(t4_funct_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k2_relat_1(B),A) => ( v1_funct_1(B) & v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ), file(funct_2,t4_funct_2), []). 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(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(t63_funct_5,axiom,( ! [A,B,C] : ( r1_tarski(A,B) => r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)) ) ), file(funct_5,t63_funct_5), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t86_funct_6,axiom,( ! [A,B,C,D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) => ( A = k1_xboole_0 | B = k1_xboole_0 | ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G,H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) & k1_funct_1(D,G) = E & k1_funct_1(k10_funct_6(D),H) = F ) => ( k1_funct_1(F,G) = k1_funct_1(E,H) & k1_relat_1(F) = A & k1_relat_1(E) = B & r1_tarski(k2_relat_1(F),C) & r1_tarski(k2_relat_1(E),C) ) ) ) ) ) ) ) ), file(funct_6,t86_funct_6), []). fof(t87_funct_6,axiom,( ! [A,B,C,D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) => ( A = k1_xboole_0 | B = k1_xboole_0 | k10_funct_6(k10_funct_6(D)) = D ) ) ) ), file(funct_6,t87_funct_6), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).