% Mizar problem: t42_waybel25,waybel25,2455,25 fof(t42_waybel25,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) ) => ( v1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C)))) & v1_funct_2(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),A,B) & m2_relset_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v1_waybel_9,abstractness_v6_waybel_0,antisymmetry_r2_hidden,cc10_membered,cc10_tsp_1,cc10_waybel_0,cc11_membered,cc11_waybel_0,cc12_membered,cc12_waybel_0,cc13_membered,cc13_waybel_0,cc14_membered,cc14_waybel_0,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_3,cc1_funct_1,cc1_funct_2,cc1_lattice3,cc1_membered,cc1_relset_1,cc1_tex_1,cc1_tops_1,cc1_tsp_1,cc1_waybel12,cc1_waybel17,cc1_waybel19,cc1_waybel_2,cc1_waybel_8,cc1_yellow14,cc1_yellow_0,cc20_membered,cc2_funct_1,cc2_lattice3,cc2_membered,cc2_tex_1,cc2_tops_1,cc2_tsp_1,cc2_waybel12,cc2_waybel19,cc2_waybel_2,cc2_waybel_8,cc2_yellow_0,cc3_membered,cc3_tex_1,cc3_tops_1,cc3_tsp_1,cc3_waybel12,cc3_waybel25,cc3_waybel_2,cc3_waybel_8,cc3_yellow14,cc3_yellow_0,cc4_membered,cc4_tex_1,cc4_tops_1,cc4_tsp_1,cc4_waybel12,cc4_waybel25,cc4_waybel_2,cc4_waybel_8,cc4_yellow_0,cc5_funct_2,cc5_tex_1,cc5_tops_1,cc5_tsp_1,cc5_waybel25,cc5_waybel_0,cc5_waybel_2,cc5_yellow_0,cc6_funct_2,cc6_tops_1,cc6_tsp_1,cc6_waybel25,cc6_waybel_2,cc6_yellow_0,cc7_tsp_1,cc7_waybel_2,cc7_yellow_0,cc8_tsp_1,cc8_waybel25,cc8_yellow_0,cc9_tsp_1,cc9_waybel25,cc9_waybel_0,commutativity_k3_xboole_0,commutativity_k5_subset_1,d13_funct_1,d13_pre_topc,d13_yellow_0,d1_funct_2,d1_tarski,d1_tops_2,d1_waybel_2,d1_yellow_2,d2_waybel25,d3_tarski,d3_waybel24,d3_waybel25,d3_xboole_0,d4_tarski,d4_waybel25,d5_funct_1,d5_yellow_2,d7_waybel_0,d8_waybel_0,dt_g1_orders_2,dt_g1_pre_topc,dt_g1_waybel_0,dt_g1_waybel_9,dt_k10_funct_6,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_waybel25,dt_k1_waybel_0,dt_k1_waybel_2,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_waybel25,dt_k2_waybel_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k3_waybel24,dt_k3_waybel_0,dt_k3_xboole_0,dt_k3_yellow_6,dt_k4_relset_1,dt_k5_pre_topc,dt_k5_setfam_1,dt_k5_subset_1,dt_k5_yellow_2,dt_k6_pre_topc,dt_k6_yellow_1,dt_k7_yellow_2,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_subset_1,dt_m1_yellow_0,dt_m2_relset_1,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_subset_1,existence_m1_yellow_0,existence_m2_relset_1,fc10_membered,fc10_waybel24,fc10_waybel_8,fc11_membered,fc11_waybel24,fc11_waybel25,fc11_waybel_8,fc11_yellow_1,fc12_waybel_8,fc12_yellow_1,fc13_waybel25,fc13_yellow_1,fc14_yellow_1,fc15_waybel25,fc15_yellow_1,fc16_yellow_1,fc17_yellow_1,fc18_yellow_1,fc1_borsuk_3,fc1_funct_2,fc1_struct_0,fc1_subset_1,fc1_waybel12,fc1_yellow12,fc1_yellow14,fc1_yellow_0,fc27_membered,fc28_membered,fc29_membered,fc2_borsuk_3,fc2_funct_2,fc2_subset_1,fc2_tops_1,fc2_waybel17,fc2_yellow14,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_waybel25,fc3_yellow14,fc4_subset_1,fc4_waybel25,fc4_waybel_8,fc5_waybel25,fc5_waybel_8,fc5_yellow12,fc6_membered,fc6_waybel24,fc6_waybel25,fc6_waybel_0,fc6_waybel_8,fc6_yellow12,fc7_funcop_1,fc7_membered,fc7_waybel24,fc7_waybel25,fc7_waybel_8,fc8_membered,fc8_waybel24,fc8_waybel25,fc8_waybel_8,fc9_membered,fc9_waybel24,fc9_waybel_8,fraenkel_a_4_0_waybel25,free_g1_orders_2,free_g1_pre_topc,free_g1_waybel_0,free_g1_waybel_9,idempotence_k3_xboole_0,idempotence_k5_subset_1,l30_waybel25,rc10_tex_1,rc10_waybel_0,rc11_tex_1,rc11_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_borsuk_3,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_lattice3,rc1_membered,rc1_pre_topc,rc1_subset_1,rc1_tops_1,rc1_tsp_1,rc1_waybel10,rc1_waybel12,rc1_waybel19,rc1_waybel_0,rc1_yellow14,rc1_yellow_0,rc2_borsuk_1,rc2_funct_1,rc2_lattice3,rc2_pre_topc,rc2_subset_1,rc2_tops_1,rc2_tsp_1,rc2_waybel12,rc2_waybel_0,rc2_yellow_0,rc2_yellow_9,rc3_funct_1,rc3_struct_0,rc3_tex_1,rc3_tops_1,rc3_tsp_1,rc3_waybel12,rc3_waybel25,rc3_yellow14,rc3_yellow_0,rc4_tex_1,rc4_tops_1,rc4_tsp_1,rc4_waybel12,rc4_waybel_0,rc4_yellow14,rc4_yellow_0,rc5_struct_0,rc5_tex_1,rc5_tops_1,rc5_waybel12,rc5_waybel_0,rc5_yellow14,rc6_pre_topc,rc6_tex_1,rc6_waybel12,rc6_yellow14,rc7_pre_topc,rc7_tex_1,rc7_waybel12,rc7_waybel_0,rc8_tex_1,rc8_waybel_0,rc9_tex_1,rc9_waybel_0,redefinition_k1_struct_0,redefinition_k1_waybel_0,redefinition_k3_yellow_6,redefinition_k4_relset_1,redefinition_k5_pre_topc,redefinition_k5_setfam_1,redefinition_k5_subset_1,redefinition_k7_yellow_2,redefinition_k8_yellow_2,redefinition_m2_relset_1,redefinition_r3_orders_2,redefinition_r4_nattra_1,reflexivity_r1_tarski,reflexivity_r3_orders_2,reflexivity_r4_nattra_1,symmetry_r1_xboole_0,symmetry_r4_nattra_1,t18_waybel_2,t19_waybel24,t1_subset,t21_waybel24,t26_tops_2,t26_waybel25,t2_boole,t2_subset,t2_tarski,t31_waybel25,t36_yellow12,t3_subset,t3_xboole_0,t40_waybel25,t41_waybel25,t46_funct_2,t4_subset,t4_xboole_0,t55_tops_2,t5_subset,t6_boole,t7_boole,t86_funct_6,t8_boole]), [file(waybel25,t42_waybel25)]). 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(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_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). 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_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_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). 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_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). 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_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). 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(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_borsuk_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v3_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v2_compts_1(A) ) ) ) ), file(borsuk_3,cc1_borsuk_3), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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_tex_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) & v2_pre_topc(A) ) => ( ~ v3_struct_0(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) ) ) ) ), file(tex_1,cc1_tex_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_waybel12,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) & v1_finset_1(B) ) ) ) ), file(waybel12,cc1_waybel12), []). 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_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_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel_2,cc1_waybel_2), []). fof(cc1_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ) ) ), file(waybel_8,cc1_waybel_8), []). fof(cc1_yellow14,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_waybel_0(B,A) => v1_yellow14(B,A) ) ) ), file(yellow14,cc1_yellow14), []). 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(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_tex_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) ) => ( ~ v3_struct_0(A) & v3_realset2(A) & v2_pre_topc(A) ) ) ) ), file(tex_1,cc2_tex_1), []). 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_waybel12,axiom,( ! [A] : ( v1_finset_1(A) => v1_card_4(A) ) ), file(waybel12,cc2_waybel12), []). 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_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ), file(waybel_2,cc2_waybel_2), []). fof(cc2_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_8(A) ) ) ) ), file(waybel_8,cc2_waybel_8), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_tex_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) ) ) ) ), file(tex_1,cc3_tex_1), []). 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_waybel12,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_waybel_6(B,A) & v12_waybel_0(B,A) ) => v2_waybel_0(B,A) ) ) ) ), file(waybel12,cc3_waybel12), []). 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_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & v1_waybel_8(A) & v2_waybel_8(A) ) ) ) ), file(waybel_8,cc3_waybel_8), []). fof(cc3_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_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_tex_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) ) ) ) ), file(tex_1,cc4_tex_1), []). 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_waybel12,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) => v1_waybel_6(B,A) ) ) ) ), file(waybel12,cc4_waybel12), []). fof(cc4_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) => ( v3_pre_topc(B,k1_waybel25(A)) => v13_waybel_0(B,k1_waybel25(A)) ) ) ) ), file(waybel25,cc4_waybel25), []). fof(cc4_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc4_waybel_2), []). fof(cc4_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) ) ) ) ), file(waybel_8,cc4_waybel_8), []). fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_tex_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_tdlat_3(A) ) ) ) ), file(tex_1,cc5_tex_1), []). 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_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] : ( l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) => ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) ) => ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & v1_yellow14(C,k3_waybel24(A,k1_waybel25(B))) ) ) ) ) ), file(waybel25,cc5_waybel25), []). 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_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_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). 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_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v1_waybel_2(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc6_waybel_2), []). fof(cc6_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v2_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc6_yellow_0), []). fof(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_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_waybel_1(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ) ) ), file(waybel_2,cc7_waybel_2), []). fof(cc7_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v3_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc7_yellow_0), []). fof(cc8_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_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( l1_waybel_0(B,k1_waybel25(A)) => ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & v10_waybel_0(B,k1_waybel25(A)) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & v10_waybel_0(B,k1_waybel25(A)) & v3_yellow_6(B,k1_waybel25(A)) ) ) ) ) ), file(waybel25,cc8_waybel25), []). fof(cc8_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc8_yellow_0), []). fof(cc9_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(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(d13_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k10_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ), file(funct_1,d13_funct_1), []). fof(d13_pre_topc,axiom,( ! [A] : ( l1_pre_topc(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 = k6_pre_topc(A,B) <=> ! [D] : ( r2_hidden(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(E,A) & r2_hidden(D,E) & r1_xboole_0(B,E) ) ) ) ) ) ) ) ) ), file(pre_topc,d13_pre_topc), []). fof(d13_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( m1_yellow_0(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & r1_tarski(u1_orders_2(B),u1_orders_2(A)) ) ) ) ) ), file(yellow_0,d13_yellow_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_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tops_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v3_pre_topc(C,A) ) ) ) ) ) ), file(tops_2,d1_tops_2), []). fof(d1_waybel_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => k1_waybel_2(A,B) = k5_yellow_2(A,u1_waybel_0(A,B)) ) ) ), file(waybel_2,d1_waybel_2), []). 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_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_waybel_9(B) & l1_waybel_9(B) ) => ( B = k1_waybel25(A) <=> ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & E = k1_tarski(D) & r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ) ) ), file(waybel25,d2_waybel25), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_waybel24,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k3_waybel24(A,B) <=> ( v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & ! [D] : ( r2_hidden(D,u1_struct_0(C)) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) & D = E & v5_pre_topc(E,A,B) ) ) ) ) ) ) ) ), file(waybel24,d3_waybel24), []). fof(d3_waybel25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,C) ) => ! [E] : ( m1_subset_1(E,A) => ( r1_tarski(u1_struct_0(C),u1_struct_0(k6_yellow_1(A,B))) => ! [F] : ( ( ~ v3_struct_0(F) & v3_orders_2(F) & v6_waybel_0(F,B) & v7_waybel_0(F) & l1_waybel_0(F,B) ) => ( F = k2_waybel25(A,B,C,D,E) <=> ( g1_orders_2(u1_struct_0(F),u1_orders_2(F)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) & u1_waybel_0(B,F) = k1_funct_1(k10_funct_6(u1_waybel_0(C,D)),E) ) ) ) ) ) ) ) ) ) ), file(waybel25,d3_waybel25), []). 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(d4_tarski,axiom,( ! [A,B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) ), file(tarski,d4_tarski), []). fof(d4_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_waybel25(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_waybel25(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) ) => ( r1_yellow_0(k1_waybel25(A),B) & ! [C] : ( ( v3_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(k1_yellow_0(k1_waybel25(A),B),C) & r1_xboole_0(B,C) ) ) ) ) ) ) ), file(waybel25,d4_waybel25), []). 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_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( v1_relat_1(B) => k5_yellow_2(A,B) = k1_yellow_0(A,k2_relat_1(B)) ) ) ), file(yellow_2,d5_yellow_2), []). fof(d7_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => k2_waybel_0(A,B) = u1_waybel_0(A,B) ) ) ), file(waybel_0,d7_waybel_0), []). 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(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_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_k10_relat_1,axiom,( $true ), file(relat_1,k10_relat_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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_waybel_9(k1_waybel25(A)) & l1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,k1_waybel25), []). fof(dt_k1_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_waybel_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & l1_waybel_0(B,A) ) => m1_subset_1(k1_waybel_2(A,B),u1_struct_0(A)) ) ), file(waybel_2,k1_waybel_2), []). 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_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_waybel25,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(B) & ~ v3_struct_0(C) & l1_orders_2(C) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,C) & m1_subset_1(E,A) ) => ( ~ v3_struct_0(k2_waybel25(A,B,C,D,E)) & v3_orders_2(k2_waybel25(A,B,C,D,E)) & v6_waybel_0(k2_waybel25(A,B,C,D,E),B) & v7_waybel_0(k2_waybel25(A,B,C,D,E)) & l1_waybel_0(k2_waybel25(A,B,C,D,E),B) ) ) ), file(waybel25,k2_waybel25), []). fof(dt_k2_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ( v1_funct_1(k2_waybel_0(A,B)) & v1_funct_2(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(waybel_0,k2_waybel_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). 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_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_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_k5_pre_topc,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & 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(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k5_pre_topc), []). fof(dt_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k5_setfam_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_yellow_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v1_relat_1(B) ) => m1_subset_1(k5_yellow_2(A,B),u1_struct_0(A)) ) ), file(yellow_2,k5_yellow_2), []). fof(dt_k6_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k6_pre_topc), []). fof(dt_k6_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_orders_2(k6_yellow_1(A,B)) & l1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,k6_yellow_1), []). fof(dt_k7_yellow_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_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_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) ), file(yellow_0,m1_yellow_0), []). fof(dt_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(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_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) ), file(yellow_0,m1_yellow_0), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). 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_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc10_waybel_8), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). 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_waybel25,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(k1_waybel25(A))) ) => ( ~ v1_xboole_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B))) & v4_pre_topc(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A)) & v1_waybel_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A)) & v12_waybel_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A)) ) ) ), file(waybel25,fc11_waybel25), []). fof(fc11_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc11_waybel_8), []). fof(fc11_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc11_yellow_1), []). fof(fc12_waybel_8,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc12_waybel_8), []). fof(fc12_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v2_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc12_yellow_1), []). fof(fc13_waybel25,axiom,( ! [A,B,C,D] : ( ( ~ 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(C) & v3_orders_2(C) & v7_waybel_0(C) & v10_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) & m1_subset_1(D,u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) & v3_orders_2(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) & v6_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) & v7_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) & v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) ) ) ), file(waybel25,fc13_waybel25), []). 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_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_3,axiom,( ! [A,B] : ( v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(borsuk_3,fc1_borsuk_3), []). fof(fc1_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_2), []). 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_waybel12,axiom,( ! [A] : ( ( v3_struct_0(A) & l1_struct_0(A) ) => ( v1_xboole_0(u1_struct_0(A)) & v1_finset_1(u1_struct_0(A)) ) ) ), file(waybel12,fc1_waybel12), []). fof(fc1_yellow12,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k3_tarski(A)) & v1_membered(k3_tarski(A)) & v2_membered(k3_tarski(A)) & v3_membered(k3_tarski(A)) & v4_membered(k3_tarski(A)) & v5_membered(k3_tarski(A)) ) ) ), file(yellow12,fc1_yellow12), []). fof(fc1_yellow14,axiom,( ! [A,B] : ( ( v1_monoid_0(A) & l1_struct_0(A) & v1_yellow14(B,A) & l1_waybel_0(B,A) ) => ( 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)) & v1_funcop_1(u1_waybel_0(A,B)) ) ) ), file(yellow14,fc1_yellow14), []). fof(fc1_yellow_0,axiom,( ! [A,B] : ( m1_relset_1(B,k1_tarski(A),k1_tarski(A)) => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ), file(yellow_0,fc1_yellow_0), []). fof(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). fof(fc2_borsuk_3,axiom,( ! [A,B] : ( v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(borsuk_3,fc2_borsuk_3), []). fof(fc2_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v4_pre_topc(k6_pre_topc(A,B),A) ) ), file(tops_1,fc2_tops_1), []). fof(fc2_waybel17,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( v1_orders_2(k6_yellow_1(A,B)) & v3_lattice3(k6_yellow_1(A,B)) ) ) ), file(waybel17,fc2_waybel17), []). fof(fc2_yellow14,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ~ v1_xboole_0(k2_relat_1(u1_waybel_0(A,B))) ) ), file(yellow14,fc2_yellow14), []). fof(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). 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_yellow14,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ~ v1_xboole_0(k2_relat_1(k2_waybel_0(A,B))) ) ), file(yellow14,fc3_yellow14), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc4_waybel25), []). fof(fc4_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc4_waybel_8), []). fof(fc5_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_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc5_waybel_8), []). fof(fc5_yellow12,axiom,( ! [A] : ( ( ~ v3_struct_0(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))) ) ) ), file(yellow12,fc5_yellow12), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). 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_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_waybel_8,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc6_waybel_8), []). fof(fc6_yellow12,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_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))) ) ) ), file(yellow12,fc6_yellow12), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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_8,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc7_waybel_8), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( ~ v3_struct_0(k3_waybel24(A,B)) & v1_orders_2(k3_waybel24(A,B)) & v2_orders_2(k3_waybel24(A,B)) & ~ v1_yellow_3(k3_waybel24(A,B)) & v1_monoid_0(k3_waybel24(A,B)) ) ) ), file(waybel24,fc8_waybel24), []). fof(fc8_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k1_waybel25(A)) & v2_pre_topc(k1_waybel25(A)) & v2_orders_2(k1_waybel25(A)) & v3_orders_2(k1_waybel25(A)) & v4_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) ), file(waybel25,fc8_waybel25), []). fof(fc8_waybel_8,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc8_waybel_8), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). 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_8,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc9_waybel_8), []). fof(fraenkel_a_4_0_waybel25,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v3_struct_0(C) & v2_pre_topc(C) & v2_t_0topsp(C) & v1_waybel25(C) & l1_pre_topc(C) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,k3_waybel24(B,k1_waybel25(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_4_0_waybel25(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & A = F & ? [G] : ( m1_subset_1(G,u1_struct_0(D)) & ? [H] : ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(B),u1_struct_0(k1_waybel25(C))) & m2_relset_1(H,u1_struct_0(B),u1_struct_0(k1_waybel25(C))) & H = k3_waybel_0(k3_waybel24(B,k1_waybel25(C)),D,G) & F = k5_pre_topc(B,k1_waybel25(C),H,E) ) ) ) ) ) ), file(waybel25,a_4_0_waybel25), []). 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(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(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(l30_waybel25,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] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => r2_hidden(u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C),k1_funct_2(u1_struct_0(C),k1_funct_2(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ), file(waybel25,l30_waybel25), []). fof(rc10_tex_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_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) ) ), file(tex_1,rc10_tex_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_tex_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_tdlat_3(A) & ~ v3_tdlat_3(A) ) ), file(tex_1,rc11_tex_1), []). 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_borsuk_3,axiom,( ? [A] : ( l1_pre_topc(A) & v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) ) ), file(borsuk_3,rc1_borsuk_3), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). 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_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). 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_waybel12,axiom,( ? [A] : ( l1_struct_0(A) & v3_struct_0(A) ) ), file(waybel12,rc1_waybel12), []). fof(rc1_waybel19,axiom,( ? [A] : ( l1_waybel_9(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) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v2_pre_topc(A) & v2_waybel_3(A) & v3_waybel_3(A) & ~ v1_yellow_3(A) & v1_waybel_9(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) & v1_waybel19(A) ) ), file(waybel19,rc1_waybel19), []). 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_yellow14,axiom,( ? [A] : ( l1_orders_2(A) & v3_struct_0(A) & v1_orders_2(A) ) ), file(yellow14,rc1_yellow14), []). 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(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_waybel12,axiom,( ? [A] : ( v1_xboole_0(A) & v1_finset_1(A) & v1_card_4(A) ) ), file(waybel12,rc2_waybel12), []). 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_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_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_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_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v3_realset2(A) & v1_pre_topc(A) ) ), file(tex_1,rc3_tex_1), []). 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_waybel12,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_finset_1(B) & v1_card_4(B) ) ) ), file(waybel12,rc3_waybel12), []). 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_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_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc3_yellow_0), []). fof(rc4_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_pre_topc(A) ) ), file(tex_1,rc4_tex_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_waybel12,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_card_4(A) ) ), file(waybel12,rc4_waybel12), []). 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_yellow14,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) & v1_yellow14(B,A) ) ) ), file(yellow14,rc4_yellow14), []). fof(rc4_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc4_yellow_0), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc5_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) ) ), file(tex_1,rc5_tex_1), []). 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_waybel12,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) & v1_finset_1(B) & v1_card_4(B) ) ) ), file(waybel12,rc5_waybel12), []). 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(rc5_yellow14,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_monoid_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v6_waybel_0(B,A) & v1_yellow14(B,A) ) ) ), file(yellow14,rc5_yellow14), []). 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(rc6_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) ) ), file(tex_1,rc6_tex_1), []). fof(rc6_waybel12,axiom,( ? [A] : ( ~ v1_finset_1(A) & v1_card_4(A) ) ), file(waybel12,rc6_waybel12), []). fof(rc6_yellow14,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_monoid_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v3_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v1_yellow14(B,A) ) ) ), file(yellow14,rc6_yellow14), []). 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(rc7_tex_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_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) ) ), file(tex_1,rc7_tex_1), []). fof(rc7_waybel12,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) & v1_card_4(B) ) ) ), file(waybel12,rc7_waybel12), []). 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(rc8_tex_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_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) ) ), file(tex_1,rc8_tex_1), []). 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_tex_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_tdlat_3(A) ) ), file(tex_1,rc9_tex_1), []). 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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). 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_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_pre_topc,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & 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)) ) => k5_pre_topc(A,B,C,D) = k10_relat_1(C,D) ) ), file(pre_topc,k5_pre_topc), []). fof(redefinition_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A,B) = k3_tarski(B) ) ), file(setfam_1,k5_setfam_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_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_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_r4_nattra_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) ) => ( r4_nattra_1(A,B,C,D,E,F) <=> E = F ) ) ), file(nattra_1,r4_nattra_1), []). 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_r4_nattra_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) ) => r4_nattra_1(A,B,C,D,E,E) ) ), file(nattra_1,r4_nattra_1), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(symmetry_r4_nattra_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) ) => ( r4_nattra_1(A,B,C,D,E,F) => r4_nattra_1(A,B,C,D,F,E) ) ) ), file(nattra_1,r4_nattra_1), []). fof(t18_waybel_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ( v10_waybel_0(B,A) => v1_waybel_0(k8_yellow_2(u1_struct_0(B),A,k2_waybel_0(A,B)),A) ) ) ) ), file(waybel_2,t18_waybel_2), []). fof(t19_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B))) <=> ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m2_relset_1(C,A,u1_struct_0(B)) ) ) ) ), file(waybel24,t19_waybel24), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t21_waybel24,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ! [C] : ( ( 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)) ) <=> m1_subset_1(C,u1_struct_0(k3_waybel24(A,B))) ) ) ) ), file(waybel24,t21_waybel24), []). fof(t26_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tops_2(B,A) => v3_pre_topc(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ), file(tops_2,t26_tops_2), []). fof(t26_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_waybel_9(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) ) => r1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) ) ) ) ) ), file(waybel25,t26_waybel25), []). 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(t31_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & v10_waybel_0(B,k1_waybel25(A)) & l1_waybel_0(B,k1_waybel25(A)) ) => r1_waybel_9(k1_waybel25(A),B) ) ) ), file(waybel25,t31_waybel25), []). fof(t36_yellow12,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(D)) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) ) => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) & E = F & v5_pre_topc(E,A,C) ) => v5_pre_topc(F,B,D) ) ) ) ) ) ) ) ), file(yellow12,t36_yellow12), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_xboole_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), []). fof(t40_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k1_waybel25(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))) ) => ( ( D = k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) & r1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) & r2_hidden(E,k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) ) => r1_yellow_2(u1_struct_0(A),k1_waybel25(B),E,D) ) ) ) ) ) ) ), file(waybel25,t40_waybel25), []). fof(t41_waybel25,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [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] : ( m1_subset_1(F,u1_struct_0(A)) => v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,F),k1_waybel25(B)) ) & E = k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) ) => k3_yellow_6(u1_struct_0(A),k1_waybel25(B),E,D) = k1_waybel_2(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) ) ) ) ) ) ) ), file(waybel25,t41_waybel25), []). fof(t46_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( B != k1_xboole_0 => ! [E] : ( r2_hidden(E,k10_relat_1(D,C)) <=> ( r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ), file(funct_2,t46_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(t4_xboole_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) ) & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B)) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t4_xboole_0), []). fof(t55_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_pre_topc(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_pre_topc(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( v3_pre_topc(D,B) => v3_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ), file(tops_2,t55_tops_2), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(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(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).