% Mizar problem: t10_brouwer,brouwer,673,35 fof(t10_brouwer,conjecture,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_struct_0(C) & m1_pre_topc(C,k2_brouwer(2,B,A)) ) => ~ ( C = k7_toprealb(2,B,A) & r1_borsuk_1(k2_brouwer(2,B,A),C) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_group_1,abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_tex_2,cc11_tex_2,cc12_tex_2,cc13_tex_2,cc14_tex_2,cc15_tex_2,cc16_tex_2,cc17_tex_2,cc18_tex_2,cc19_tex_2,cc1_borsuk_2,cc1_funct_1,cc1_nat_1,cc1_partfun3,cc1_pre_topc,cc1_real_1,cc1_relat_1,cc1_relset_1,cc1_seq_1,cc1_tex_1,cc1_tex_2,cc1_topalg_2,cc1_toprealb,cc1_tops_1,cc1_xreal_0,cc20_tex_2,cc21_tex_2,cc22_tex_2,cc23_tex_2,cc24_tex_2,cc25_tex_2,cc26_tex_2,cc27_tex_2,cc28_tex_2,cc29_tex_2,cc2_borsuk_2,cc2_funct_1,cc2_nat_1,cc2_partfun3,cc2_pscomp_1,cc2_tex_1,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc30_tex_2,cc31_tex_2,cc32_tex_2,cc33_tex_2,cc34_tex_2,cc35_tex_2,cc36_tex_2,cc37_tex_2,cc38_tex_2,cc39_tex_2,cc3_borsuk_2,cc3_nat_1,cc3_tex_1,cc3_tex_2,cc3_topalg_2,cc3_tops_1,cc3_xreal_0,cc40_tex_2,cc41_tex_2,cc42_tex_2,cc43_tex_2,cc44_tex_2,cc45_tex_2,cc46_tex_2,cc47_tex_2,cc48_tex_2,cc49_tex_2,cc4_borsuk_2,cc4_tex_1,cc4_tex_2,cc4_topalg_2,cc4_tops_1,cc4_xreal_0,cc50_tex_2,cc5_tex_1,cc5_tex_2,cc5_tops_1,cc5_xreal_0,cc6_tex_2,cc6_tops_1,cc6_xreal_0,cc7_tex_2,cc7_xreal_0,cc8_tex_2,cc8_xreal_0,cc9_tex_2,commutativity_k2_tarski,d10_xboole_0,d17_borsuk_1,d18_borsuk_1,d19_borsuk_1,d1_binop_1,d1_tarski,d1_topalg_1,d20_borsuk_1,d2_borsuk_2,d2_brouwer,d3_borsuk_1,d3_tarski,d3_topalg_1,d5_eqrel_1,d5_tarski,d7_borsuk_2,dt_g1_group_1,dt_g1_pre_topc,dt_k15_euclid,dt_k1_binop_1,dt_k1_borsuk_1,dt_k1_borsuk_2,dt_k1_funct_1,dt_k1_numbers,dt_k1_tarski,dt_k1_topalg_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_borsuk_1,dt_k23_borsuk_1,dt_k24_borsuk_1,dt_k2_brouwer,dt_k2_funcop_1,dt_k2_tarski,dt_k2_topalg_1,dt_k2_topreal9,dt_k2_zfmisc_1,dt_k3_borsuk_1,dt_k3_pre_topc,dt_k3_topalg_1,dt_k3_topmetr,dt_k3_topreal9,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_topmetr,dt_k6_borsuk_1,dt_k6_eqrel_1,dt_k7_eqrel_1,dt_k7_funct_2,dt_k7_toprealb,dt_k8_borsuk_1,dt_k8_eqrel_1,dt_k8_funct_2,dt_l1_group_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_borsuk_2,dt_m1_eqrel_1,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_group_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_group_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_borsuk_2,existence_m1_eqrel_1,existence_m1_pre_topc,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_partfun3,fc10_pscomp_1,fc10_relat_1,fc10_topalg_5,fc11_partfun3,fc12_relat_1,fc14_topreal9,fc15_topreal9,fc19_toprealb,fc1_borsuk_1,fc1_funct_1,fc1_jordan5a,fc1_pscomp_1,fc1_revrot_1,fc1_seq_1,fc1_struct_0,fc1_subset_1,fc1_tex_2,fc1_topalg_1,fc1_topalg_2,fc20_toprealb,fc21_toprealb,fc22_toprealb,fc25_toprealb,fc2_borsuk_1,fc2_borsuk_2,fc2_pscomp_1,fc2_subset_1,fc2_topalg_1,fc2_topalg_5,fc2_topmetr,fc3_brouwer,fc3_pre_topc,fc3_revrot_1,fc3_subset_1,fc3_topalg_1,fc3_topalg_2,fc3_topalg_5,fc3_topmetr,fc3_topreal9,fc4_borsuk_2,fc4_brouwer,fc4_pre_topc,fc4_relat_1,fc4_subset_1,fc4_topalg_1,fc4_topalg_5,fc4_topreal9,fc5_borsuk_1,fc5_topalg_5,fc6_borsuk_2,fc6_topalg_1,fc6_topreal9,fc7_borsuk_2,fc7_partfun3,fc7_topreal9,fc8_partfun3,fc9_partfun3,fc9_relat_1,fc9_topreal9,free_g1_group_1,free_g1_pre_topc,rc10_pscomp_1,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc11_tex_2,rc12_tex_2,rc13_tex_2,rc14_tex_2,rc15_tex_2,rc16_tex_2,rc17_tex_2,rc18_tex_2,rc19_tex_2,rc1_borsuk_1,rc1_borsuk_2,rc1_funct_1,rc1_jordan5a,rc1_nat_1,rc1_partfun3,rc1_pre_topc,rc1_pscomp_1,rc1_relat_1,rc1_seq_1,rc1_subset_1,rc1_tex_2,rc1_topalg_2,rc1_toprealb,rc1_tops_1,rc1_xreal_0,rc20_tex_2,rc2_borsuk_1,rc2_borsuk_2,rc2_funct_1,rc2_nat_1,rc2_partfun3,rc2_pre_topc,rc2_pscomp_1,rc2_relat_1,rc2_subset_1,rc2_tex_2,rc2_topalg_2,rc2_tops_1,rc2_xreal_0,rc3_borsuk_1,rc3_borsuk_2,rc3_funct_1,rc3_nat_1,rc3_partfun3,rc3_pre_topc,rc3_pscomp_1,rc3_relat_1,rc3_struct_0,rc3_tex_1,rc3_tex_2,rc3_topalg_2,rc3_tops_1,rc3_xreal_0,rc4_borsuk_1,rc4_borsuk_2,rc4_funct_1,rc4_pre_topc,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc4_xreal_0,rc5_funct_1,rc5_pre_topc,rc5_struct_0,rc5_tex_1,rc5_tex_2,rc5_tops_1,rc6_pre_topc,rc6_tex_1,rc6_tex_2,rc7_pre_topc,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_pscomp_1,rc9_tex_1,rc9_tex_2,redefinition_k1_borsuk_1,redefinition_k5_numbers,redefinition_k5_topmetr,redefinition_k7_funct_2,redefinition_k8_borsuk_1,redefinition_k8_eqrel_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_borsuk_6,redefinition_r2_borsuk_2,redefinition_r4_borsuk_2,reflexivity_r1_borsuk_6,reflexivity_r1_tarski,reflexivity_r2_borsuk_2,reflexivity_r4_borsuk_2,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r1_borsuk_6,symmetry_r3_borsuk_2,symmetry_r4_borsuk_2,t13_funcop_1,t17_topreal9,t1_numerals,t1_subset,t1_topalg_2,t21_funct_2,t2_subset,t2_topalg_2,t3_brouwer,t3_subset,t47_topalg_1,t48_topalg_1,t4_subset,t58_tops_2,t5_subset,t6_boole,t6_borsuk_2,t7_boole,t8_boole,t9_toprealb]), [file(brouwer,t10_brouwer)]). fof(abstractness_v1_group_1,axiom,( ! [A] : ( l1_group_1(A) => ( v1_group_1(A) => A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ), file(group_1,v1_group_1), []). 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(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v1_realset1(B) ) => ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ), file(tex_2,cc10_tex_2), []). fof(cc11_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ) ) ), file(tex_2,cc11_tex_2), []). fof(cc12_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_realset2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_struct_0(B) => ( ~ v3_struct_0(B) & ~ v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc12_tex_2), []). fof(cc13_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_realset2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v3_realset2(B) ) ) ) ) ), file(tex_2,cc13_tex_2), []). fof(cc14_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc14_tex_2), []). fof(cc15_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_tex_2(B,A) ) => ( ~ v3_struct_0(B) & ~ v3_realset2(B) ) ) ) ) ), file(tex_2,cc15_tex_2), []). fof(cc16_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tdlat_3(B) => v2_pre_topc(B) ) ) ) ), file(tex_2,cc16_tex_2), []). fof(cc17_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tdlat_3(B) => v2_pre_topc(B) ) ) ) ), file(tex_2,cc17_tex_2), []). fof(cc18_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_pre_topc(B) => ~ v1_tdlat_3(B) ) ) ) ), file(tex_2,cc18_tex_2), []). fof(cc19_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_pre_topc(B) => ~ v2_tdlat_3(B) ) ) ) ), file(tex_2,cc19_tex_2), []). fof(cc1_borsuk_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( v1_xreal_0(A) & v1_xcmplx_0(A) ) ) ), file(borsuk_2,cc1_borsuk_2), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_partfun3(A) ) => ( v1_relat_1(A) & v2_relat_1(A) & v4_partfun3(A) ) ) ), file(partfun3,cc1_partfun3), []). fof(cc1_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_pre_topc(B) ) ) ), file(pre_topc,cc1_pre_topc), []). fof(cc1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ( v1_xreal_0(A) & v1_xcmplx_0(A) ) ) ), file(real_1,cc1_real_1), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_seq_1,axiom,( ! [A,B] : ( v2_membered(B) => ! [C] : ( m1_relset_1(C,A,B) => ( v1_funct_1(C) => ( v1_funct_1(C) & v1_seq_1(C) ) ) ) ) ), file(seq_1,cc1_seq_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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_tex_2(B,k1_zfmisc_1(A)) => ~ v1_xboole_0(B) ) ) ) ), file(tex_2,cc1_tex_2), []). fof(cc1_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_pre_topc(B,k15_euclid(A)) => ( ( ~ v3_struct_0(B) & v1_topalg_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_borsuk_2(B) & v1_connsp_1(B) ) ) ) ) ), file(topalg_2,cc1_topalg_2), []). fof(cc1_toprealb,axiom,( ! [A] : ( m1_pre_topc(A,k15_euclid(2)) => ( v1_toprealb(A) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v10_pscomp_1(A) & v1_borsuk_2(A) & v1_monoid_0(A) & v2_monoid_0(A) ) ) ) ), file(toprealb,cc1_toprealb), []). 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_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tdlat_3(B) => v3_tdlat_3(B) ) ) ) ), file(tex_2,cc20_tex_2), []). fof(cc21_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_tdlat_3(B) => ~ v1_tdlat_3(B) ) ) ) ), file(tex_2,cc21_tex_2), []). fof(cc22_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tdlat_3(B) => v3_tdlat_3(B) ) ) ) ), file(tex_2,cc22_tex_2), []). fof(cc23_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_tdlat_3(B) => ~ v2_tdlat_3(B) ) ) ) ), file(tex_2,cc23_tex_2), []). fof(cc24_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_tdlat_3(B) & v2_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v3_realset2(B) ) ) ) ) ), file(tex_2,cc24_tex_2), []). fof(cc25_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tdlat_3(B) & ~ v3_realset2(B) ) => ( ~ v3_struct_0(B) & ~ v1_tdlat_3(B) ) ) ) ) ), file(tex_2,cc25_tex_2), []). fof(cc26_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_tdlat_3(B) & ~ v3_realset2(B) ) => ( ~ v3_struct_0(B) & ~ v2_tdlat_3(B) ) ) ) ) ), file(tex_2,cc26_tex_2), []). fof(cc27_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) ) ) ) ) ), file(tex_2,cc27_tex_2), []). fof(cc28_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_tex_2(B,A) => ( v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) ) ) ) ) ), file(tex_2,cc28_tex_2), []). fof(cc29_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tsep_1(B,A) => ( v2_pre_topc(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc29_tex_2), []). fof(cc2_borsuk_2,axiom,( ! [A,B,C] : ( ( v1_borsuk_2(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( v1_relat_1(D) & v5_pre_topc(D,k5_topmetr,A) ) ) ) ), file(borsuk_2,cc2_borsuk_2), []). 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_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_partfun3(A) ) => ( v1_relat_1(A) & v2_relat_1(A) & v3_partfun3(A) ) ) ), file(partfun3,cc2_partfun3), []). fof(cc2_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v10_pscomp_1(A) ) ) ) ), file(pscomp_1,cc2_pscomp_1), []). 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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ), file(tex_2,cc2_tex_2), []). 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_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc30_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_borsuk_1(B,A) => ( v2_pre_topc(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc30_tex_2), []). fof(cc31_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) ) ) ) ) ), file(tex_2,cc31_tex_2), []). fof(cc32_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & ~ v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v3_realset2(B) ) ) ) ) ), file(tex_2,cc32_tex_2), []). fof(cc33_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) ) ) ) ) ), file(tex_2,cc33_tex_2), []). fof(cc34_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v3_realset2(B) ) ) ) ) ), file(tex_2,cc34_tex_2), []). fof(cc35_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_tsep_1(B,A) & ~ v1_borsuk_1(B,A) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc35_tex_2), []). fof(cc36_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc36_tex_2), []). fof(cc37_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v5_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) ) ) ) ) ), file(tex_2,cc37_tex_2), []). fof(cc38_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v1_tdlat_3(B) ) => ( ~ v3_struct_0(B) & ~ v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc38_tex_2), []). fof(cc39_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v5_tex_2(B,A) => ( v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & ~ v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc39_tex_2), []). fof(cc3_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(A) ) ) ) ), file(borsuk_2,cc3_borsuk_2), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_tex_2(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc3_tex_2), []). fof(cc3_topalg_2,axiom,( ! [A] : ( m1_pre_topc(A,k3_topmetr) => ( v2_pre_topc(A) & v1_borsuk_6(A) ) ) ), file(topalg_2,cc3_topalg_2), []). 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_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc40_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tex_2(B,A) => ( v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & ~ v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc40_tex_2), []). fof(cc41_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_tex_2(B,A) => ( v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc41_tex_2), []). fof(cc42_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v5_tex_2(B,A) => ( v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc42_tex_2), []). fof(cc43_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v5_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) ) ) ) ) ), file(tex_2,cc43_tex_2), []). fof(cc44_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc44_tex_2), []). fof(cc45_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc45_tex_2), []). fof(cc46_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v5_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v3_realset2(B) & ~ v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc46_tex_2), []). fof(cc47_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v5_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v2_tex_2(B,A) ) ) ) ) ), file(tex_2,cc47_tex_2), []). fof(cc48_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc48_tex_2), []). fof(cc49_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v5_tex_2(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v3_realset2(B) ) ) ) ) ), file(tex_2,cc49_tex_2), []). 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_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_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_xboole_0(B) => ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc4_tex_2), []). fof(cc4_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( v1_xboole_0(A) => v2_topalg_2(A) ) ) ), file(topalg_2,cc4_topalg_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_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc50_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v3_realset2(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & ~ v5_tex_2(B,A) ) ) ) ) ), file(tex_2,cc50_tex_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_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc5_tex_2), []). 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_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & v1_realset1(B) ) => ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc6_tex_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_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ) ) ), file(tex_2,cc7_tex_2), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_realset2(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v1_xboole_0(B) => ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ), file(tex_2,cc8_tex_2), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_realset2(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(B) & v1_realset1(B) ) ) ) ) ), file(tex_2,cc9_tex_2), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d17_borsuk_1,axiom,( k23_borsuk_1 = 0 ), file(borsuk_1,d17_borsuk_1), []). fof(d18_borsuk_1,axiom,( k24_borsuk_1 = 1 ), file(borsuk_1,d18_borsuk_1), []). fof(d19_borsuk_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ! [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)) ) => ( v3_borsuk_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,u1_struct_0(B)) => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = D ) ) ) ) ) ) ), file(borsuk_1,d19_borsuk_1), []). fof(d1_binop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ), file(binop_1,d1_binop_1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_topalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( C = k1_topalg_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> m1_borsuk_2(D,A,B,B) ) ) ) ) ), file(topalg_1,d1_topalg_1), []). fof(d20_borsuk_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ( r1_borsuk_1(A,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)) & v3_borsuk_1(C,A,B) ) ) ) ) ), file(borsuk_1,d20_borsuk_1), []). fof(d2_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_2(A,B,C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) ) => ( m1_borsuk_2(D,A,B,C) <=> ( v5_pre_topc(D,k5_topmetr,A) & k1_funct_1(D,0) = B & k1_funct_1(D,1) = C ) ) ) ) ) ) ) ), file(borsuk_2,d2_borsuk_2), []). fof(d2_brouwer,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k2_brouwer(A,B,C) = k3_pre_topc(k15_euclid(A),k2_topreal9(A,B,C)) ) ) ) ), file(brouwer,d2_brouwer), []). fof(d3_borsuk_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_borsuk_1(A,B,C) = k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C) ) ) ) ), file(borsuk_1,d3_borsuk_1), []). 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_topalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_group_1(C) & l1_group_1(C) ) => ( C = k3_topalg_1(A,B) <=> ( u1_struct_0(C) = k8_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_borsuk_2(F,A,B,B) & ? [G] : ( m1_borsuk_2(G,A,B,B) & D = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),F) & E = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),G) & k1_binop_1(u1_group_1(C),D,E) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),k1_borsuk_2(A,B,B,B,F,G)) ) ) ) ) ) ) ) ) ) ), file(topalg_1,d3_topalg_1), []). fof(d5_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k7_eqrel_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,A) & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ), file(eqrel_1,d5_eqrel_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d7_borsuk_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ( r3_borsuk_2(A,B,C,D,E) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) & m2_relset_1(F,u1_struct_0(k6_borsuk_1(k5_topmetr,k5_topmetr)),u1_struct_0(A)) & v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),A) & ! [G] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ( k1_binop_1(F,G,0) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),D,G) & k1_binop_1(F,G,1) = k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),E,G) & ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ( k1_binop_1(F,0,H) = B & k1_binop_1(F,1,H) = C ) ) ) ) ) ) ) ) ) ) ) ), file(borsuk_2,d7_borsuk_2), []). fof(dt_g1_group_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) ) => ( v1_group_1(g1_group_1(A,B)) & l1_group_1(g1_group_1(A,B)) ) ) ), file(group_1,g1_group_1), []). 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_k15_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & l1_pre_topc(k15_euclid(A)) ) ) ), file(euclid,k15_euclid), []). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), []). fof(dt_k1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => ( v1_funct_1(k1_borsuk_1(A,B,C)) & v1_funct_2(k1_borsuk_1(A,B,C),B,A) & m2_relset_1(k1_borsuk_1(A,B,C),B,A) ) ) ), file(borsuk_1,k1_borsuk_1), []). fof(dt_k1_borsuk_2,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_borsuk_2(E,A,B,C) & m1_borsuk_2(F,A,C,D) ) => m1_borsuk_2(k1_borsuk_2(A,B,C,D,E,F),A,B,D) ) ), file(borsuk_2,k1_borsuk_2), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_topalg_1,axiom,( $true ), file(topalg_1,k1_topalg_1), []). 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_k22_borsuk_1,axiom,( l1_pre_topc(k22_borsuk_1) ), file(borsuk_1,k22_borsuk_1), []). fof(dt_k23_borsuk_1,axiom,( m1_subset_1(k23_borsuk_1,u1_struct_0(k22_borsuk_1)) ), file(borsuk_1,k23_borsuk_1), []). fof(dt_k24_borsuk_1,axiom,( m1_subset_1(k24_borsuk_1,u1_struct_0(k22_borsuk_1)) ), file(borsuk_1,k24_borsuk_1), []). fof(dt_k2_brouwer,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_pre_topc(k2_brouwer(A,B,C),k15_euclid(A)) ) ), file(brouwer,k2_brouwer), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_topalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => m2_relset_1(k2_topalg_1(A,B),k1_topalg_1(A,B),k1_topalg_1(A,B)) ) ), file(topalg_1,k2_topalg_1), []). fof(dt_k2_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_subset_1(k2_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal9,k2_topreal9), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_borsuk_1,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( v1_funct_1(k3_borsuk_1(A,B,C)) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ), file(borsuk_1,k3_borsuk_1), []). fof(dt_k3_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & m1_pre_topc(k3_pre_topc(A,B),A) ) ) ), file(pre_topc,k3_pre_topc), []). fof(dt_k3_topalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_group_1(k3_topalg_1(A,B)) & l1_group_1(k3_topalg_1(A,B)) ) ) ), file(topalg_1,k3_topalg_1), []). fof(dt_k3_topmetr,axiom, ( v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) & l1_pre_topc(k3_topmetr) ), file(topmetr,k3_topmetr), []). fof(dt_k3_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_subset_1(k3_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal9,k3_topreal9), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). 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_topmetr,axiom, ( v1_pre_topc(k5_topmetr) & m1_pre_topc(k5_topmetr,k3_topmetr) ), file(topmetr,k5_topmetr), []). fof(dt_k6_borsuk_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & l1_pre_topc(k6_borsuk_1(A,B)) ) ) ), file(borsuk_1,k6_borsuk_1), []). fof(dt_k6_eqrel_1,axiom,( ! [A,B,C] : ( ( v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)) ) ), file(eqrel_1,k6_eqrel_1), []). fof(dt_k7_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,k7_eqrel_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_toprealb,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_pre_topc(k7_toprealb(A,B,C),k15_euclid(A)) ) ), file(toprealb,k7_toprealb), []). fof(dt_k8_borsuk_1,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) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))) ) ), file(borsuk_1,k8_borsuk_1), []). fof(dt_k8_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_eqrel_1(k8_eqrel_1(A,B),A) ) ), file(eqrel_1,k8_eqrel_1), []). 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_l1_group_1,axiom,( ! [A] : ( l1_group_1(A) => l1_struct_0(A) ) ), file(group_1,l1_group_1), []). 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_m1_borsuk_2,axiom,( ! [A,B,C] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(k5_topmetr),u1_struct_0(A)) ) ) ) ), file(borsuk_2,m1_borsuk_2), []). fof(dt_m1_eqrel_1,axiom,( ! [A,B] : ( m1_eqrel_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,m1_eqrel_1), []). fof(dt_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => l1_pre_topc(B) ) ) ), file(pre_topc,m1_pre_topc), []). 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_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_group_1,axiom,( ! [A] : ( l1_group_1(A) => ( v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(group_1,u1_group_1), []). 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_group_1,axiom,( ? [A] : l1_group_1(A) ), file(group_1,l1_group_1), []). 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_m1_borsuk_2,axiom,( ! [A,B,C] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ? [D] : m1_borsuk_2(D,A,B,C) ) ), file(borsuk_2,m1_borsuk_2), []). fof(existence_m1_eqrel_1,axiom,( ! [A] : ? [B] : m1_eqrel_1(B,A) ), file(eqrel_1,m1_eqrel_1), []). fof(existence_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_pre_topc(B,A) ) ), file(pre_topc,m1_pre_topc), []). 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_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v4_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc10_partfun3), []). fof(fc10_pscomp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & v6_compts_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)) & v2_compts_1(k3_pre_topc(A,B)) ) ) ), file(pscomp_1,fc10_pscomp_1), []). fof(fc10_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). fof(fc10_topalg_5,axiom,( ! [A,B] : ( ( v1_toprealb(A) & m1_pre_topc(A,k15_euclid(2)) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k3_topalg_1(A,B)) & v1_group_1(k3_topalg_1(A,B)) & v2_group_1(k3_topalg_1(A,B)) & v3_group_1(k3_topalg_1(A,B)) & v4_group_1(k3_topalg_1(A,B)) & ~ v6_group_1(k3_topalg_1(A,B)) ) ) ), file(topalg_5,fc10_topalg_5), []). fof(fc11_partfun3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k2_funcop_1(A,0)) & ~ v2_relat_1(k2_funcop_1(A,0)) & v1_funct_1(k2_funcop_1(A,0)) & v3_partfun3(k2_funcop_1(A,0)) & v4_partfun3(k2_funcop_1(A,0)) ) ) ), file(partfun3,fc11_partfun3), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc14_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & v3_xreal_0(C) ) => ( v1_xboole_0(k3_topreal9(A,B,C)) & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ), file(topreal9,fc14_topreal9), []). fof(fc15_topreal9,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ( ~ v1_xboole_0(k3_topreal9(A,B,C)) & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ), file(topreal9,fc15_topreal9), []). fof(fc19_toprealb,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k3_topreal9(2,B,A)) & v4_pre_topc(k3_topreal9(2,B,A),k15_euclid(2)) & v1_jordan2c(k3_topreal9(2,B,A),2) & v2_connsp_1(k3_topreal9(2,B,A),k15_euclid(2)) & v6_compts_1(k3_topreal9(2,B,A),k15_euclid(2)) & v1_topreal2(k3_topreal9(2,B,A)) ) ) ), file(toprealb,fc19_toprealb), []). fof(fc1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( ~ v1_xboole_0(k3_borsuk_1(A,B,C)) & v1_relat_1(k3_borsuk_1(A,B,C)) & v1_funct_1(k3_borsuk_1(A,B,C)) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k3_borsuk_1(A,B,C),A,B) & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ), file(borsuk_1,fc1_borsuk_1), []). fof(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & v3_compts_1(k15_euclid(A)) & v1_borsuk_2(k15_euclid(A)) ) ) ), file(jordan5a,fc1_jordan5a), []). fof(fc1_pscomp_1,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) & ~ v1_setfam_1(k1_numbers) ), file(pscomp_1,fc1_pscomp_1), []). fof(fc1_revrot_1,axiom,( ! [A] : ( ( ~ v3_realset2(A) & l1_struct_0(A) ) => ( ~ v1_xboole_0(u1_struct_0(A)) & ~ v1_realset1(u1_struct_0(A)) ) ) ), file(revrot_1,fc1_revrot_1), []). fof(fc1_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_xcmplx_0(k1_funct_1(A,B)) & v1_xreal_0(k1_funct_1(A,B)) ) ) ), file(seq_1,fc1_seq_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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(tex_2,fc1_tex_2), []). fof(fc1_topalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v1_xboole_0(k1_topalg_1(A,B)) ) ), file(topalg_1,fc1_topalg_1), []). fof(fc1_topalg_2,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & ~ v3_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) & m1_subset_1(C,u1_struct_0(B)) ) => ( ~ v3_struct_0(k3_topalg_1(B,C)) & v1_group_1(k3_topalg_1(B,C)) & v2_group_1(k3_topalg_1(B,C)) & v3_group_1(k3_topalg_1(B,C)) & v4_group_1(k3_topalg_1(B,C)) & v3_realset2(k3_topalg_1(B,C)) ) ) ), file(topalg_2,fc1_topalg_2), []). fof(fc20_toprealb,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ( ~ v3_struct_0(k7_toprealb(A,B,C)) & v1_pre_topc(k7_toprealb(A,B,C)) & v2_pre_topc(k7_toprealb(A,B,C)) & v1_monoid_0(k7_toprealb(A,B,C)) & v2_monoid_0(k7_toprealb(A,B,C)) ) ) ), file(toprealb,fc20_toprealb), []). fof(fc21_toprealb,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xboole_0(C) & v1_xreal_0(C) ) => ( v2_pre_topc(k7_toprealb(A,B,C)) & v3_realset2(k7_toprealb(A,B,C)) & v1_monoid_0(k7_toprealb(A,B,C)) & v2_monoid_0(k7_toprealb(A,B,C)) ) ) ), file(toprealb,fc21_toprealb), []). fof(fc22_toprealb,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) & v2_xreal_0(B) ) => ( ~ v3_struct_0(k7_toprealb(2,A,B)) & v1_pre_topc(k7_toprealb(2,A,B)) & v2_pre_topc(k7_toprealb(2,A,B)) & v2_compts_1(k7_toprealb(2,A,B)) & v10_pscomp_1(k7_toprealb(2,A,B)) & v1_borsuk_2(k7_toprealb(2,A,B)) & v1_monoid_0(k7_toprealb(2,A,B)) & v2_monoid_0(k7_toprealb(2,A,B)) & v1_toprealb(k7_toprealb(2,A,B)) ) ) ), file(toprealb,fc22_toprealb), []). fof(fc25_toprealb,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v3_struct_0(k7_toprealb(2,A,B)) & v1_pre_topc(k7_toprealb(2,A,B)) & v2_pre_topc(k7_toprealb(2,A,B)) & v1_borsuk_2(k7_toprealb(2,A,B)) & v1_monoid_0(k7_toprealb(2,A,B)) & v2_monoid_0(k7_toprealb(2,A,B)) ) ) ), file(toprealb,fc25_toprealb), []). fof(fc2_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) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) ) ) ), file(borsuk_1,fc2_borsuk_1), []). fof(fc2_borsuk_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & v5_seqm_3(C) & m1_borsuk_2(C,A,B,B) ) => ( ~ v1_xboole_0(k1_borsuk_2(A,B,B,B,C,C)) & v1_relat_1(k1_borsuk_2(A,B,B,B,C,C)) & v1_funct_1(k1_borsuk_2(A,B,B,B,C,C)) & v1_funct_2(k1_borsuk_2(A,B,B,B,C,C),u1_struct_0(k5_topmetr),u1_struct_0(A)) & v1_partfun1(k1_borsuk_2(A,B,B,B,C,C),u1_struct_0(k5_topmetr),u1_struct_0(A)) & v5_seqm_3(k1_borsuk_2(A,B,B,B,C,C)) ) ) ), file(borsuk_2,fc2_borsuk_2), []). fof(fc2_pscomp_1,axiom, ( ~ v1_xboole_0(k5_ordinal2) & v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) & ~ v1_setfam_1(k5_ordinal2) ), file(pscomp_1,fc2_pscomp_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_topalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_relat_1(k2_topalg_1(A,B)) & ~ v1_xboole_0(k2_topalg_1(A,B)) & v1_relat_2(k2_topalg_1(A,B)) & v3_relat_2(k2_topalg_1(A,B)) & v8_relat_2(k2_topalg_1(A,B)) & v1_partfun1(k2_topalg_1(A,B),k1_topalg_1(A,B),k1_topalg_1(A,B)) ) ) ), file(topalg_1,fc2_topalg_1), []). fof(fc2_topalg_5,axiom,( ! [A] : ( ( ~ v6_group_1(A) & l1_struct_0(A) ) => ~ v1_finset_1(u1_struct_0(A)) ) ), file(topalg_5,fc2_topalg_5), []). fof(fc2_topmetr,axiom, ( ~ v3_struct_0(k3_topmetr) & v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) ), file(topmetr,fc2_topmetr), []). fof(fc3_brouwer,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ( ~ v3_struct_0(k2_brouwer(A,B,C)) & v2_pre_topc(k2_brouwer(A,B,C)) ) ) ), file(brouwer,fc3_brouwer), []). fof(fc3_pre_topc,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)) ) ) ), file(pre_topc,fc3_pre_topc), []). fof(fc3_revrot_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & ~ v3_realset2(k15_euclid(A)) ) ) ), file(revrot_1,fc3_revrot_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_topalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k3_topalg_1(A,B)) & v1_group_1(k3_topalg_1(A,B)) ) ) ), file(topalg_1,fc3_topalg_1), []). fof(fc3_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( ~ v3_struct_0(k3_topalg_1(k5_topmetr,A)) & v1_group_1(k3_topalg_1(k5_topmetr,A)) & v2_group_1(k3_topalg_1(k5_topmetr,A)) & v3_group_1(k3_topalg_1(k5_topmetr,A)) & v4_group_1(k3_topalg_1(k5_topmetr,A)) & v3_realset2(k3_topalg_1(k5_topmetr,A)) ) ) ), file(topalg_2,fc3_topalg_2), []). fof(fc3_topalg_5,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)) & v1_tsep_1(k3_pre_topc(A,B),A) ) ) ), file(topalg_5,fc3_topalg_5), []). fof(fc3_topmetr,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & m1_relset_1(B,A,u1_struct_0(k3_topmetr)) ) => ( v1_xcmplx_0(k1_funct_1(B,C)) & v1_xreal_0(k1_funct_1(B,C)) ) ) ), file(topmetr,fc3_topmetr), []). fof(fc3_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & v3_xreal_0(C) ) => v1_xboole_0(k2_topreal9(A,B,C)) ) ), file(topreal9,fc3_topreal9), []). fof(fc4_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v2_t_0topsp(k6_borsuk_1(A,B)) ) ) ), file(borsuk_2,fc4_borsuk_2), []). fof(fc4_brouwer,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v2_pre_topc(k2_brouwer(A,B,C)) & v1_topalg_2(k2_brouwer(A,B,C),A) ) ) ), file(brouwer,fc4_brouwer), []). fof(fc4_pre_topc,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)) ) ) ), file(pre_topc,fc4_pre_topc), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_topalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k3_topalg_1(A,B)) & v1_group_1(k3_topalg_1(A,B)) & v2_group_1(k3_topalg_1(A,B)) & v3_group_1(k3_topalg_1(A,B)) & v4_group_1(k3_topalg_1(A,B)) ) ) ), file(topalg_1,fc4_topalg_1), []). fof(fc4_topalg_5,axiom, ( ~ v3_struct_0(k22_borsuk_1) & v1_pre_topc(k22_borsuk_1) & v2_pre_topc(k22_borsuk_1) & v2_t_0topsp(k22_borsuk_1) & v2_compts_1(k22_borsuk_1) & v3_compts_1(k22_borsuk_1) & v1_connsp_2(k22_borsuk_1) & v3_yellow_8(k22_borsuk_1) ), file(topalg_5,fc4_topalg_5), []). fof(fc4_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ~ v1_xboole_0(k2_topreal9(A,B,C)) ) ), file(topreal9,fc4_topreal9), []). fof(fc5_borsuk_1,axiom, ( ~ v3_struct_0(k22_borsuk_1) & v1_pre_topc(k22_borsuk_1) & v2_pre_topc(k22_borsuk_1) ), file(borsuk_1,fc5_borsuk_1), []). fof(fc5_topalg_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_pre_topc(A,k5_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) => ( ~ v3_struct_0(k3_pre_topc(k5_topmetr,A)) & v1_pre_topc(k3_pre_topc(k5_topmetr,A)) & v2_pre_topc(k3_pre_topc(k5_topmetr,A)) & v1_connsp_2(k3_pre_topc(k5_topmetr,A)) & v1_tsep_1(k3_pre_topc(k5_topmetr,A),k5_topmetr) ) ) ), file(topalg_5,fc5_topalg_5), []). fof(fc6_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v3_compts_1(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v2_t_0topsp(k6_borsuk_1(A,B)) & v3_compts_1(k6_borsuk_1(A,B)) & v3_yellow_8(k6_borsuk_1(A,B)) ) ) ), file(borsuk_2,fc6_borsuk_2), []). fof(fc6_topalg_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) ) => ( ~ v3_struct_0(k3_topalg_1(k15_euclid(A),B)) & v1_group_1(k3_topalg_1(k15_euclid(A),B)) & v2_group_1(k3_topalg_1(k15_euclid(A),B)) & v3_group_1(k3_topalg_1(k15_euclid(A),B)) & v4_group_1(k3_topalg_1(k15_euclid(A),B)) & v3_realset2(k3_topalg_1(k15_euclid(A),B)) ) ) ), file(topalg_1,fc6_topalg_1), []). fof(fc6_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k2_topreal9(A,B,C),A) ) ) ), file(topreal9,fc6_topreal9), []). fof(fc7_borsuk_2,axiom, ( ~ v3_struct_0(k22_borsuk_1) & v1_pre_topc(k22_borsuk_1) & v2_pre_topc(k22_borsuk_1) & v2_t_0topsp(k22_borsuk_1) & v2_compts_1(k22_borsuk_1) & v3_compts_1(k22_borsuk_1) & v3_yellow_8(k22_borsuk_1) ), file(borsuk_2,fc7_borsuk_2), []). fof(fc7_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & v2_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc7_partfun3), []). fof(fc7_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ), file(topreal9,fc7_topreal9), []). fof(fc8_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & v3_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc8_partfun3), []). fof(fc9_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v3_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc9_partfun3), []). fof(fc9_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fc9_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k2_topreal9(A,B,C),A) & v1_jordan1(k2_topreal9(A,B,C),A) ) ) ), file(topreal9,fc9_topreal9), []). fof(free_g1_group_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) ) => ! [C,D] : ( g1_group_1(A,B) = g1_group_1(C,D) => ( A = C & B = D ) ) ) ), file(group_1,g1_group_1), []). 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(rc10_pscomp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v10_pscomp_1(A) ) ), file(pscomp_1,rc10_pscomp_1), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(tex_2,rc10_tex_2), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & ~ v2_tex_2(B,A) ) ) ), file(tex_2,rc11_tex_2), []). fof(rc12_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v3_realset2(B) ) ) ), file(tex_2,rc12_tex_2), []). fof(rc13_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v3_realset2(B) & v2_tex_2(B,A) ) ) ), file(tex_2,rc13_tex_2), []). fof(rc14_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) ) ) ), file(tex_2,rc14_tex_2), []). fof(rc15_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) ) ) ), file(tex_2,rc15_tex_2), []). fof(rc16_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) ) ) ), file(tex_2,rc16_tex_2), []). fof(rc17_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v2_tex_2(B,A) ) ) ), file(tex_2,rc17_tex_2), []). fof(rc18_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & ~ v1_tsep_1(B,A) & ~ v1_borsuk_1(B,A) & v2_tdlat_3(B) & v3_tdlat_3(B) & v2_tex_2(B,A) ) ) ), file(tex_2,rc18_tex_2), []). fof(rc19_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v2_tex_2(B,A) ) ) ), file(tex_2,rc19_tex_2), []). fof(rc1_borsuk_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_eqrel_1(B,A) & ~ v1_xboole_0(B) & v1_setfam_1(B) ) ) ), file(borsuk_1,rc1_borsuk_1), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_pre_topc(B,k15_euclid(A)) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v2_compts_1(B) & v3_compts_1(B) ) ) ), file(jordan5a,rc1_jordan5a), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_partfun3,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k1_numbers) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v1_seq_1(B) & v2_partfun3(B) & v3_partfun3(B) ) ), file(partfun3,rc1_partfun3), []). fof(rc1_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) ), file(pre_topc,rc1_pre_topc), []). fof(rc1_pscomp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(pscomp_1,rc1_pscomp_1), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_seq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(seq_1,rc1_seq_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_tex_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(tex_2,rc1_tex_2), []). fof(rc1_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(B) & v1_jordan1(B,A) ) ) ), file(topalg_2,rc1_topalg_2), []). fof(rc1_toprealb,axiom,( ? [A] : ( m1_pre_topc(A,k15_euclid(2)) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_compts_1(A) & v10_pscomp_1(A) & v1_borsuk_2(A) & v1_monoid_0(A) & v2_monoid_0(A) & v1_toprealb(A) ) ), file(toprealb,rc1_toprealb), []). 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_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc20_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v5_tex_2(B,A) ) ) ), file(tex_2,rc20_tex_2), []). 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_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_borsuk_2(C,A,B,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) & v5_pre_topc(C,k5_topmetr,A) & v1_partfun1(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) ) ) ), file(borsuk_2,rc2_borsuk_2), []). 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_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_partfun3,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k1_numbers) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v1_seq_1(B) & v1_partfun3(B) & v4_partfun3(B) ) ), file(partfun3,rc2_partfun3), []). 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_pscomp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) ), file(pscomp_1,rc2_pscomp_1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_tex_2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ), file(tex_2,rc2_tex_2), []). fof(rc2_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_pre_topc(B,k15_euclid(A)) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_2(B) & v1_connsp_1(B) & v1_topalg_2(B,A) ) ) ), file(topalg_2,rc2_topalg_2), []). 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_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) ) ) ), file(borsuk_1,rc3_borsuk_1), []). fof(rc3_borsuk_2,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) ) ), file(borsuk_2,rc3_borsuk_2), []). 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_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_partfun3,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(partfun3,rc3_partfun3), []). fof(rc3_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) ) ) ), file(pre_topc,rc3_pre_topc), []). fof(rc3_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v1_setfam_1(A) ) ), file(pscomp_1,rc3_pscomp_1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc3_tex_2), []). fof(rc3_topalg_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & ~ v1_xboole_0(A) & v2_topalg_2(A) ) ), file(topalg_2,rc3_topalg_2), []). 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_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_borsuk_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) ) ) ), file(borsuk_1,rc4_borsuk_1), []). fof(rc4_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_borsuk_2(C,A,B,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) & v1_partfun1(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) & v5_seqm_3(C) ) ) ), file(borsuk_2,rc4_borsuk_2), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_pre_topc,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) ) ) ), file(pre_topc,rc4_pre_topc), []). fof(rc4_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & ~ v1_setfam_1(A) ) ), file(pscomp_1,rc4_pscomp_1), []). 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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc4_tex_2), []). 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_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). 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_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) ) ) ), file(pre_topc,rc5_pre_topc), []). 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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) ) ) ), file(tex_2,rc5_tex_2), []). 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(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_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc6_tex_2), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc7_tex_2), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(tex_2,rc8_tex_2), []). fof(rc9_pscomp_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) & v6_compts_1(B,A) ) ) ), file(pscomp_1,rc9_pscomp_1), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & ~ v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(tex_2,rc9_tex_2), []). fof(redefinition_k1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k1_borsuk_1(A,B,C) = k2_funcop_1(B,C) ) ), file(borsuk_1,k1_borsuk_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_topmetr,axiom,( k5_topmetr = k22_borsuk_1 ), file(topmetr,k5_topmetr), []). 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_k8_borsuk_1,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) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => k8_borsuk_1(A,B,C,D) = k4_tarski(C,D) ) ), file(borsuk_1,k8_borsuk_1), []). fof(redefinition_k8_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => k8_eqrel_1(A,B) = k7_eqrel_1(A,B) ) ), file(eqrel_1,k8_eqrel_1), []). 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_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_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r1_borsuk_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r1_borsuk_6(A,B,C) <=> r1_borsuk_2(A,B,C) ) ) ), file(borsuk_6,r1_borsuk_6), []). fof(redefinition_r2_borsuk_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r2_borsuk_2(A,B,C) <=> r1_borsuk_2(A,B,C) ) ) ), file(borsuk_2,r2_borsuk_2), []). fof(redefinition_r4_borsuk_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_borsuk_2(D,A,B,C) & m1_borsuk_2(E,A,B,C) ) => ( r4_borsuk_2(A,B,C,D,E) <=> r3_borsuk_2(A,B,C,D,E) ) ) ), file(borsuk_2,r4_borsuk_2), []). fof(reflexivity_r1_borsuk_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r1_borsuk_6(A,B,B) ) ), file(borsuk_6,r1_borsuk_6), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r2_borsuk_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r2_borsuk_2(A,B,B) ) ), file(borsuk_2,r2_borsuk_2), []). fof(reflexivity_r4_borsuk_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_borsuk_2(D,A,B,C) & m1_borsuk_2(E,A,B,C) ) => r4_borsuk_2(A,B,C,D,D) ) ), file(borsuk_2,r4_borsuk_2), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(symmetry_r1_borsuk_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r1_borsuk_6(A,B,C) => r1_borsuk_6(A,C,B) ) ) ), file(borsuk_6,r1_borsuk_6), []). fof(symmetry_r3_borsuk_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_borsuk_2(D,A,B,C) & m1_borsuk_2(E,A,B,C) ) => ( r3_borsuk_2(A,B,C,D,E) => r3_borsuk_2(A,B,C,E,D) ) ) ), file(borsuk_2,r3_borsuk_2), []). fof(symmetry_r4_borsuk_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_borsuk_2(D,A,B,C) & m1_borsuk_2(E,A,B,C) ) => ( r4_borsuk_2(A,B,C,D,E) => r4_borsuk_2(A,B,C,E,D) ) ) ), file(borsuk_2,r4_borsuk_2), []). 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(t17_topreal9,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_tarski(k3_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) ), file(topreal9,t17_topreal9), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_topalg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ! [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)) => ! [G] : ( m1_borsuk_2(G,B,E,F) => ( ( C = E & D = F & r1_borsuk_6(B,E,F) ) => m1_borsuk_2(G,A,C,D) ) ) ) ) ) ) ) ) ), file(topalg_2,t1_topalg_2), []). 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(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_topalg_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_borsuk_2(E,B,C,D) => ! [F] : ( m1_borsuk_2(F,B,C,D) => r4_borsuk_2(B,C,D,E,F) ) ) ) ) ) ) ), file(topalg_2,t2_topalg_2), []). fof(t3_brouwer,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => u1_struct_0(k2_brouwer(A,C,B)) = k2_topreal9(A,C,B) ) ) ) ), file(brouwer,t3_brouwer), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t47_topalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_borsuk_2(C,A,B,B) => ! [D] : ( m1_borsuk_2(D,A,B,B) => ( k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),C) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),D) <=> r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) ), file(topalg_1,t47_topalg_1), []). fof(t48_topalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(C,u1_struct_0(k3_topalg_1(A,B))) <=> ? [D] : ( m1_borsuk_2(D,A,B,B) & C = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),D) ) ) ) ) ), file(topalg_1,t48_topalg_1), []). 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(t58_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( ~ v3_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) ) => ( ( v5_pre_topc(D,A,C) & v5_pre_topc(E,C,B) ) => v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(B),D,E),A,B) ) ) ) ) ) ) ), file(tops_2,t58_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(t6_borsuk_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v5_seqm_3(C) & m1_borsuk_2(C,A,B,B) ) => C = k3_borsuk_1(k5_topmetr,A,B) ) ) ) ), file(borsuk_2,t6_borsuk_2), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_toprealb,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => u1_struct_0(k7_toprealb(A,C,B)) = k3_topreal9(A,C,B) ) ) ) ), file(toprealb,t9_toprealb), []).