% Mizar problem: t105_jordan,jordan,5685,5 fof(t105_jordan,conjecture,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & v1_jordan21(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( v6_compts_1(C,k15_euclid(2)) & v1_jordan21(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_topreal1(k15_euclid(2),k23_euclid(k1_real_1(1),0),k23_euclid(1,0),B) & r1_topreal1(k15_euclid(2),k23_euclid(k1_real_1(1),0),k23_euclid(1,0),C) & A = k4_subset_1(u1_struct_0(k15_euclid(2)),B,C) & k5_subset_1(u1_struct_0(k15_euclid(2)),B,C) = k2_struct_0(k15_euclid(2),k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(k1_jordan21(A),B) & r2_hidden(k2_jordan21(A),C) & k18_pscomp_1(A) = k18_pscomp_1(B) & k20_pscomp_1(A) = k20_pscomp_1(B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k1_connsp_1(k3_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),k2_connsp_3(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A),k18_euclid(k6_real_1(1,2),2,k17_euclid(2,k1_jordan21(k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k2_jordan21(B),k23_euclid(0,k1_real_1(3))),C)),k2_jordan21(B))))) => ( r1_jordan2c(2,A,D) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan2c(2,A,E) => E = D ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_metric_1,abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_isomichi,cc10_membered,cc10_topreal6,cc10_yellow13,cc11_isomichi,cc11_membered,cc11_topreal6,cc11_yellow13,cc12_isomichi,cc12_membered,cc13_isomichi,cc13_membered,cc14_isomichi,cc14_membered,cc15_isomichi,cc15_membered,cc16_isomichi,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_2,cc1_borsuk_4,cc1_funct_1,cc1_funct_2,cc1_isomichi,cc1_jordan,cc1_jordan21,cc1_jordan2c,cc1_membered,cc1_nat_1,cc1_pre_topc,cc1_realset1,cc1_relset_1,cc1_seq_1,cc1_sprect_4,cc1_tex_4,cc1_topreal6,cc1_topreala,cc1_tops_1,cc1_xreal_0,cc1_yellow13,cc20_membered,cc2_borsuk_2,cc2_funct_1,cc2_funct_2,cc2_isomichi,cc2_jordan,cc2_jordan21,cc2_membered,cc2_nat_1,cc2_pscomp_1,cc2_tex_4,cc2_topgrp_1,cc2_topreal6,cc2_topreala,cc2_tops_1,cc2_xreal_0,cc2_yellow13,cc3_borsuk_2,cc3_funct_2,cc3_isomichi,cc3_jordan,cc3_membered,cc3_nat_1,cc3_pscomp_1,cc3_tex_4,cc3_topreal6,cc3_topreala,cc3_tops_1,cc3_xreal_0,cc3_yellow13,cc4_borsuk_2,cc4_isomichi,cc4_jordan,cc4_membered,cc4_tex_4,cc4_topgrp_1,cc4_topreal6,cc4_topreala,cc4_tops_1,cc4_xreal_0,cc4_yellow13,cc5_funct_2,cc5_isomichi,cc5_jordan,cc5_tex_4,cc5_topreal6,cc5_tops_1,cc5_xreal_0,cc5_yellow13,cc6_funct_2,cc6_isomichi,cc6_membered,cc6_tex_4,cc6_topreal6,cc6_tops_1,cc6_xreal_0,cc6_yellow13,cc7_isomichi,cc7_tex_4,cc7_topreal6,cc7_waybel_3,cc7_xreal_0,cc7_yellow13,cc8_isomichi,cc8_tex_4,cc8_topreal6,cc8_xreal_0,cc8_yellow13,cc9_isomichi,cc9_membered,cc9_topreal6,cc9_yellow13,commutativity_k17_euclid,commutativity_k1_gobrd14,commutativity_k2_struct_0,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_topreal1,commutativity_k3_xboole_0,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_subset_1,commutativity_k5_subset_1,connectedness_r1_xreal_0,d13_pre_topc,d16_euclid,d1_borsuk_2,d1_euclid,d1_funct_2,d1_jordan1,d1_jordan24,d1_jordan5c,d1_tarski,d20_pscomp_1,d21_pscomp_1,d26_pscomp_1,d2_borsuk_2,d2_jgraph_6,d2_jordan21,d2_sppol_1,d2_tarski,d2_tops_1,d2_xboole_0,d30_pscomp_1,d32_pscomp_1,d3_borsuk_2,d3_jordan21,d3_jordan2c,d3_sppol_1,d3_tarski,d3_topreal4,d3_xboole_0,d4_xboole_0,d5_connsp_1,d5_funct_1,d5_real_1,d6_connsp_1,d7_euclid,d8_euclid,dt_g1_metric_1,dt_g1_pre_topc,dt_k10_finseq_1,dt_k12_pscomp_1,dt_k13_euclid,dt_k13_pscomp_1,dt_k14_euclid,dt_k15_euclid,dt_k15_pscomp_1,dt_k16_pscomp_1,dt_k17_euclid,dt_k17_pscomp_1,dt_k18_euclid,dt_k18_pscomp_1,dt_k1_borsuk_2,dt_k1_connsp_1,dt_k1_euclid,dt_k1_funct_1,dt_k1_gobrd14,dt_k1_jordan21,dt_k1_jordan5c,dt_k1_numbers,dt_k1_pre_topc,dt_k1_pscomp_1,dt_k1_real_1,dt_k1_relat_1,dt_k1_sppol_2,dt_k1_struct_0,dt_k1_tarski,dt_k1_topreal1,dt_k1_topreal9,dt_k1_topreala,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_pscomp_1,dt_k21_euclid,dt_k22_borsuk_1,dt_k22_euclid,dt_k23_euclid,dt_k2_borsuk_2,dt_k2_connsp_3,dt_k2_funct_2,dt_k2_jgraph_6,dt_k2_jordan21,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_seq_4,dt_k2_struct_0,dt_k2_tarski,dt_k2_tops_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_pre_topc,dt_k3_pscomp_1,dt_k3_real_1,dt_k3_seq_4,dt_k3_subset_1,dt_k3_topmetr,dt_k3_topreal1,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k4_finseq_2,dt_k4_pre_topc,dt_k4_pscomp_1,dt_k4_real_1,dt_k4_relset_1,dt_k4_subset_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_jordan6,dt_k5_numbers,dt_k5_ordinal2,dt_k5_pcomps_1,dt_k5_subset_1,dt_k5_topmetr,dt_k6_connsp_3,dt_k6_jordan6,dt_k6_pre_topc,dt_k6_real_1,dt_k6_subset_1,dt_k7_relat_1,dt_k7_xcmplx_0,dt_k8_funct_2,dt_k9_relat_1,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_borsuk_2,dt_m1_finseq_2,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_metric_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_borsuk_2,existence_m1_finseq_2,existence_m1_pre_topc,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc10_pscomp_1,fc10_xreal_0,fc11_isomichi,fc11_jordan,fc11_membered,fc11_pscomp_1,fc11_sppol_2,fc11_tops_1,fc11_xreal_0,fc12_jordan,fc12_membered,fc12_pscomp_1,fc12_sppol_2,fc12_tops_1,fc12_xreal_0,fc13_membered,fc13_tops_1,fc13_xreal_0,fc14_membered,fc14_xreal_0,fc15_jordan,fc15_membered,fc16_membered,fc17_topreala,fc1_borsuk_4,fc1_euclid,fc1_jgraph_8,fc1_jordan2c,fc1_jordan5a,fc1_nat_1,fc1_partfun3,fc1_pre_topc,fc1_pscomp_1,fc1_seq_1,fc1_struct_0,fc1_subset_1,fc1_tex_4,fc1_topreal6,fc1_topreal9,fc1_tops_1,fc1_waybel_2,fc1_xreal_0,fc1_yellow13,fc21_xreal_0,fc22_membered,fc22_xreal_0,fc23_membered,fc23_xreal_0,fc24_membered,fc24_xreal_0,fc25_membered,fc26_membered,fc27_membered,fc27_xreal_0,fc28_membered,fc28_xreal_0,fc29_membered,fc29_xreal_0,fc2_euclid,fc2_isomichi,fc2_jgraph_8,fc2_jordan,fc2_jordan2c,fc2_membered,fc2_nat_1,fc2_partfun3,fc2_pre_topc,fc2_pscomp_1,fc2_seq_1,fc2_subset_1,fc2_tex_4,fc2_topalg_5,fc2_topmetr,fc2_topreal6,fc2_topreal9,fc2_tops_1,fc2_yellow13,fc30_membered,fc30_xreal_0,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_isomichi,fc3_nat_1,fc3_pre_topc,fc3_pscomp_1,fc3_realset1,fc3_subset_1,fc3_tex_4,fc3_topalg_5,fc3_topgen_3,fc3_topmetr,fc3_tops_1,fc3_xreal_0,fc3_yellow13,fc40_membered,fc41_membered,fc4_funct_1,fc4_isomichi,fc4_nat_1,fc4_pre_topc,fc4_subset_1,fc4_tex_4,fc4_topalg_5,fc4_topgen_3,fc4_tops_1,fc4_xreal_0,fc5_borsuk_1,fc5_isomichi,fc5_membered,fc5_pre_topc,fc5_topalg_5,fc5_topreal9,fc6_membered,fc6_xreal_0,fc7_borsuk_2,fc7_membered,fc7_topreal6,fc7_tops_1,fc7_xreal_0,fc8_isomichi,fc8_membered,fc8_topgen_3,fc8_topreal9,fc8_tops_1,fc8_xreal_0,fc9_membered,fc9_pscomp_1,fc9_tops_1,fc9_xreal_0,fraenkel_a_4_3_jgraph_6,free_g1_metric_1,free_g1_pre_topc,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,involutiveness_k1_real_1,involutiveness_k3_subset_1,involutiveness_k4_xcmplx_0,irreflexivity_r1_subset_1,irreflexivity_r2_subset_1,l105_jordan,l106_jordan,l109_jordan,l110_jordan,l111_jordan,l112_jordan,l113_jordan,l114_jordan,l115_jordan,l116_jordan,l117_jordan,l118_jordan,l119_jordan,l120_jordan,l127_jordan,l131_jordan,l134_jordan,l135_jordan,l140_jordan,l141_jordan,l142_jordan,l143_jordan,l146_jordan,l147_jordan,l148_jordan,l149_jordan,l151_jordan,l152_jordan,l158_jordan,l161_jordan,l163_jordan,l166_jordan,l168_jordan,l169_jordan,l170_jordan,l174_jordan,l175_jordan,l176_jordan,l177_jordan,l178_jordan,l179_jordan,l180_jordan,l181_jordan,l182_jordan,l189_jordan,l1_jordan,l204_jordan,l2_jordan,l3_jordan,l61_jordan,l63_jordan,rc10_pscomp_1,rc1_borsuk_2,rc1_borsuk_4,rc1_funct_1,rc1_funct_2,rc1_isomichi,rc1_jordan,rc1_jordan1a,rc1_jordan21,rc1_jordan2c,rc1_jordan5a,rc1_membered,rc1_metric_1,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_realset1,rc1_seq_1,rc1_subset_1,rc1_tex_4,rc1_topgen_3,rc1_topgrp_1,rc1_topreal6,rc1_topreala,rc1_tops_1,rc1_xreal_0,rc2_borsuk_1,rc2_borsuk_2,rc2_borsuk_4,rc2_funct_1,rc2_funct_2,rc2_isomichi,rc2_jordan,rc2_jordan1a,rc2_metric_1,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_realset1,rc2_subset_1,rc2_tex_4,rc2_topgrp_1,rc2_topreal6,rc2_tops_1,rc2_xreal_0,rc3_borsuk_1,rc3_borsuk_2,rc3_borsuk_4,rc3_funct_1,rc3_isomichi,rc3_jordan,rc3_jordan1a,rc3_metric_1,rc3_nat_1,rc3_pre_topc,rc3_pscomp_1,rc3_struct_0,rc3_tops_1,rc3_xreal_0,rc4_borsuk_1,rc4_isomichi,rc4_pre_topc,rc4_pscomp_1,rc4_rcomp_3,rc4_topgrp_1,rc4_tops_1,rc4_waybel_3,rc4_xreal_0,rc4_yellow13,rc5_pre_topc,rc5_rcomp_3,rc5_struct_0,rc5_topgrp_1,rc5_tops_1,rc6_pre_topc,rc6_topgrp_1,rc7_isomichi,rc7_pre_topc,rc7_pscomp_1,rc8_pscomp_1,rc9_pscomp_1,redefinition_k1_pscomp_1,redefinition_k1_real_1,redefinition_k1_struct_0,redefinition_k2_funct_2,redefinition_k2_struct_0,redefinition_k3_pscomp_1,redefinition_k3_real_1,redefinition_k3_topreal1,redefinition_k4_pre_topc,redefinition_k4_pscomp_1,redefinition_k4_real_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_subset_1,redefinition_k5_topmetr,redefinition_k6_real_1,redefinition_k6_subset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_borsuk_6,redefinition_r1_subset_1,redefinition_r2_subset_1,reflexivity_r1_borsuk_6,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc10_boole,spc10_numerals,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,symmetry_r1_borsuk_6,symmetry_r1_subset_1,symmetry_r1_xboole_0,symmetry_r2_subset_1,t100_jordan,t101_jordan,t103_jordan,t114_xboole_1,t11_jgraph_6,t11_jordan6,t11_topreal3,t12_jordan6,t12_pre_topc,t146_relat_1,t14_weierstr,t16_compts_1,t16_jordan2c,t17_jordan2c,t17_sprect_1,t17_xboole_1,t18_sprect_3,t1_arithm,t1_boole,t1_jordan,t1_jordan1,t1_numerals,t1_real,t1_subset,t1_topalg_2,t1_xboole_1,t1_xreal_1,t20_compts_1,t20_jordan20,t23_connsp_1,t24_connsp_1,t24_jordan,t26_connsp_3,t27_connsp_3,t2_arithm,t2_boole,t2_jordan,t2_jordan1e,t2_real,t2_subset,t2_tarski,t2_xreal_1,t30_topreal4,t33_jordan,t33_jordan21,t34_connsp_1,t34_jordan6,t35_jordan21,t35_tops_1,t36_sppol_1,t37_connsp_1,t37_sppol_1,t37_zfmisc_1,t38_connsp_1,t38_jordan,t39_jordan,t3_arithm,t3_boole,t3_jordan,t3_real,t3_subset,t3_topreal4,t3_xboole_0,t41_jordan,t41_jordan21,t42_jordan21,t43_connsp_1,t43_jordan21,t43_subset_1,t44_jordan21,t45_xboole_1,t49_jordan,t4_boole,t4_goboard9,t4_jordan,t4_jordan1e,t4_real,t4_subset,t4_topreal1,t50_subset_1,t51_jordan,t52_jordan,t53_jordan,t53_topreala,t55_zfmisc_1,t56_euclid,t56_zfmisc_1,t57_euclid,t57_zfmisc_1,t5_arithm,t5_jordan15,t5_jordan16,t5_jordan1h,t5_real,t5_subset,t61_jordan,t62_sprect_1,t63_xboole_1,t64_zfmisc_1,t65_sprect_1,t66_jordan,t6_arithm,t6_boole,t6_jgraph_8,t6_jordan15,t6_real,t6_topreal1,t70_xboole_1,t78_jordan,t79_jordan,t7_boole,t7_goboard7,t7_real,t7_topreal3,t7_xboole_1,t81_jordan,t85_jordan,t86_jordan,t8_boole,t8_goboard7,t8_real,t8_xboole_1,t93_jordan,t94_jordan,t99_jordan,t9_jgraph_6,t9_topreal3]), [file(jordan,t105_jordan)]). fof(abstractness_v1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v1_metric_1(A) => A = g1_metric_1(u1_struct_0(A),u1_metric_1(A)) ) ) ), file(metric_1,v1_metric_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_isomichi,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) & v4_tops_1(B,A) ) => ( v4_pre_topc(B,A) & v5_tops_1(B,A) ) ) ) ) ), file(isomichi,cc10_isomichi), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc10_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => v2_connsp_1(A,k15_euclid(2)) ) ) ), file(topreal6,cc10_topreal6), []). fof(cc10_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v3_compts_1(A) ) => ( v2_pre_topc(A) & v1_urysohn1(A) ) ) ) ), file(yellow13,cc10_yellow13), []). fof(cc11_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_isomichi(B,A) => ( ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc11_isomichi), []). 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_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_finset_1(A) => ( v1_membered(A) & v2_membered(A) & v1_rcomp_1(A) ) ) ) ), file(topreal6,cc11_topreal6), []). fof(cc11_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_urysohn1(A) ) => ( v2_pre_topc(A) & v2_t_0topsp(A) ) ) ) ), file(yellow13,cc11_yellow13), []). fof(cc12_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_isomichi(B,A) => ( ~ v3_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc12_isomichi), []). 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(cc13_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_isomichi(B,A) => ( ~ v3_isomichi(B,A) & ~ v4_isomichi(B,A) ) ) ) ) ), file(isomichi,cc13_isomichi), []). 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(cc14_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_isomichi(B,A) => ( v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc14_isomichi), []). 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(cc15_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => ( v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc15_isomichi), []). 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_isomichi,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(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))) ) => ( ~ v3_isomichi(B,A) & v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc16_isomichi), []). 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_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_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_xboole_0(A) & ~ v1_realset1(A) & v1_topreal2(A) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) ) ) ) ), file(borsuk_4,cc1_borsuk_4), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) => ( v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) ), file(isomichi,cc1_isomichi), []). fof(cc1_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & v2_sppol_1(A) ) => ( ~ v1_xboole_0(A) & v1_jordan21(A) ) ) ) ), file(jordan,cc1_jordan), []). fof(cc1_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_jordan21(A) => ~ v1_xboole_0(A) ) ) ), file(jordan21,cc1_jordan21), []). fof(cc1_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v6_compts_1(B,k15_euclid(A)) => v1_jordan2c(B,A) ) ) ) ), file(jordan2c,cc1_jordan2c), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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_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_realset1,axiom,( ! [A] : ( ~ v1_realset1(A) => ~ v1_xboole_0(A) ) ), file(realset1,cc1_realset1), []). 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_sprect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_compts_1(B,A) => v4_pre_topc(B,A) ) ) ) ), file(sprect_4,cc1_sprect_4), []). fof(cc1_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_4(B,A) => ( v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) ) ) ) ) ), file(tex_4,cc1_tex_4), []). fof(cc1_topreal6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_connsp_1(B,A) ) ) ) ), file(topreal6,cc1_topreal6), []). fof(cc1_topreala,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_monoid_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_pre_topc(B) & v1_monoid_0(B) & v2_monoid_0(B) ) ) ) ), file(topreala,cc1_topreala), []). 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(cc1_yellow13,axiom,( ! [A] : ( v1_realset1(A) => v1_finset_1(A) ) ), file(yellow13,cc1_yellow13), []). 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_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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). fof(cc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_isomichi(B,A) & v2_isomichi(B,A) ) => v4_tops_1(B,A) ) ) ) ), file(isomichi,cc2_isomichi), []). fof(cc2_jordan,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_jordan2c(B,A) ) ) ) ), file(jordan,cc2_jordan), []). fof(cc2_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & ~ v1_realset1(A) & v1_topreal2(A) & v1_jordan21(A) ) ) ) ), file(jordan21,cc2_jordan21), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). 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_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_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_tdlat_3(B) => ~ v4_tex_4(B,A) ) ) ) ), file(tex_4,cc2_tex_4), []). fof(cc2_topgrp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & l1_pre_topc(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)) & v3_tops_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_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)) & v1_t_0topsp(C,A,B) ) ) ) ) ), file(topgrp_1,cc2_topgrp_1), []). fof(cc2_topreal6,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v6_compts_1(B,A) ) ) ) ), file(topreal6,cc2_topreal6), []). fof(cc2_topreala,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v3_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) ) ) ) ), file(topreala,cc2_topreala), []). 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(cc2_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_realset2(A) => v6_group_1(A) ) ) ), file(yellow13,cc2_yellow13), []). 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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_2), []). fof(cc3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => v1_decomp_1(B,A) ) ) ) ), file(isomichi,cc3_isomichi), []). fof(cc3_jordan,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ~ v1_jordan2c(B,A) => ~ v1_xboole_0(B) ) ) ) ), file(jordan,cc3_jordan), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). 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_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v10_pscomp_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) ) => ( ~ v1_xboole_0(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_seq_1(B) & v3_seq_2(B) & v1_partfun1(B,u1_struct_0(A),k1_numbers) & v7_pscomp_1(B,u1_struct_0(A)) & v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) ), file(pscomp_1,cc3_pscomp_1), []). fof(cc3_tex_4,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_tsep_1(B,A) & v2_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc3_tex_4), []). fof(cc3_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( ~ v1_xboole_0(A) & v1_jordan1(A,2) ) => v2_connsp_1(A,k15_euclid(2)) ) ) ), file(topreal6,cc3_topreal6), []). fof(cc3_topreala,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(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)) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) ) ) ) ) ), file(topreala,cc3_topreala), []). 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(cc3_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v3_realset2(A) => ~ v3_struct_0(A) ) ) ), file(yellow13,cc3_yellow13), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_decomp_1(B,A) => v2_isomichi(B,A) ) ) ) ), file(isomichi,cc4_isomichi), []). fof(cc4_jordan,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_jordan2c(B,A) => v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) ) ), file(jordan,cc4_jordan), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_tex_4,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_tsep_1(B,A) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & ~ v3_realset2(B) & v2_pre_topc(B) & ~ v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc4_tex_4), []). fof(cc4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v1_topgrp_1(A) ) ) ) ), file(topgrp_1,cc4_topgrp_1), []). fof(cc4_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_sppol_1(A) => ~ v1_xboole_0(A) ) ) ), file(topreal6,cc4_topreal6), []). fof(cc4_topreala,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) ) ) ) ) ), file(topreala,cc4_topreala), []). 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(cc4_yellow13,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v4_pre_topc(B,A) ) ) ) ), file(yellow13,cc4_yellow13), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tops_1(B,A) => v3_pre_topc(B,A) ) ) ) ), file(isomichi,cc5_isomichi), []). fof(cc5_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_struct_0(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_compts_1(B) ) ) ) ) ), file(jordan,cc5_jordan), []). fof(cc5_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_tsep_1(B,A) & v2_tex_2(B,A) ) ) ) ) ), file(tex_4,cc5_tex_4), []). fof(cc5_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v2_sppol_1(A) => ~ v1_xboole_0(A) ) ) ), file(topreal6,cc5_topreal6), []). 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(cc5_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & v6_group_1(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) ) ) ) ), file(yellow13,cc5_yellow13), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_tops_1(B,A) => v4_pre_topc(B,A) ) ) ) ), file(isomichi,cc6_isomichi), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_tex_4,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_borsuk_1(B,A) & v2_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc6_tex_4), []). fof(cc6_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v2_topreal4(A,k15_euclid(2)) => ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) ) ) ), file(topreal6,cc6_topreal6), []). 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(cc6_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v6_group_1(A) ) => ( v2_pre_topc(A) & v2_compts_1(A) ) ) ) ), file(yellow13,cc6_yellow13), []). fof(cc7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tops_1(B,A) => ( v3_pre_topc(B,A) & v4_tops_1(B,A) & v1_decomp_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) ), file(isomichi,cc7_isomichi), []). fof(cc7_tex_4,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_borsuk_1(B,A) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & ~ v3_realset2(B) & v2_pre_topc(B) & ~ v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc7_tex_4), []). fof(cc7_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) => v2_topreal4(A,k15_euclid(2)) ) ) ), file(topreal6,cc7_topreal6), []). fof(cc7_waybel_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v3_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v4_compts_1(A) & v5_compts_1(A) & v6_waybel_3(A) ) ) ) ), file(waybel_3,cc7_waybel_3), []). 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(cc7_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) => ( v2_pre_topc(A) & v1_urysohn1(A) & v3_compts_1(A) & v4_compts_1(A) & v5_compts_1(A) ) ) ) ), file(yellow13,cc7_yellow13), []). fof(cc8_isomichi,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_tops_1(B,A) ) => ( v3_pre_topc(B,A) & v6_tops_1(B,A) ) ) ) ) ), file(isomichi,cc8_isomichi), []). fof(cc8_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_borsuk_1(B,A) & v2_tex_2(B,A) ) ) ) ) ), file(tex_4,cc8_tex_4), []). fof(cc8_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v1_sppol_1(A) ) ) ), file(topreal6,cc8_topreal6), []). 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(cc8_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & v5_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v4_compts_1(A) ) ) ) ), file(yellow13,cc8_yellow13), []). fof(cc9_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_tops_1(B,A) => ( v4_pre_topc(B,A) & v4_tops_1(B,A) & v1_decomp_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) ), file(isomichi,cc9_isomichi), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(cc9_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v2_sppol_1(A) ) ) ), file(topreal6,cc9_topreal6), []). fof(cc9_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_urysohn1(A) & v4_compts_1(A) ) => ( v2_pre_topc(A) & v3_compts_1(A) ) ) ) ), file(yellow13,cc9_yellow13), []). fof(commutativity_k17_euclid,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k17_euclid(A,B,C) = k17_euclid(A,C,B) ) ), file(euclid,k17_euclid), []). fof(commutativity_k1_gobrd14,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k1_gobrd14(A,B,C) = k1_gobrd14(A,C,B) ) ), file(gobrd14,k1_gobrd14), []). fof(commutativity_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_struct_0(A,B,C) = k2_struct_0(A,C,B) ) ), file(struct_0,k2_struct_0), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k3_topreal1(A,B,C) = k3_topreal1(A,C,B) ) ), file(topreal1,k3_topreal1), []). 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_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). 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(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). 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(d16_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k23_euclid(A,B) = k10_finseq_1(A,B) ) ) ), file(euclid,d16_euclid), []). fof(d1_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)) & v5_pre_topc(D,k5_topmetr,A) & k1_funct_1(D,0) = B & k1_funct_1(D,1) = C ) ) ) ) ) ), file(borsuk_2,d1_borsuk_2), []). fof(d1_euclid,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k1_euclid(A) = k4_finseq_2(A,k1_numbers) ) ), file(euclid,d1_euclid), []). 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_jordan1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_jordan1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r1_tarski(k3_topreal1(A,C,D),B) ) ) ) ) ) ) ), file(jordan1,d1_jordan1), []). fof(d1_jordan24,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r1_jordan24(A,B,C,D) <=> ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(E,B) & r2_hidden(F,B) ) => r1_xreal_0(k1_gobrd14(A,E,F),k1_gobrd14(A,C,D)) ) ) ) ) ) ) ) ) ) ), file(jordan24,d1_jordan24), []). fof(d1_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( v4_pre_topc(k5_subset_1(u1_struct_0(k15_euclid(2)),A,B),k15_euclid(2)) & r1_topreal1(k15_euclid(2),C,D,A) ) => ( r1_xboole_0(A,B) | ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( E = k1_jordan5c(A,B,C,D) <=> ( r2_hidden(E,k5_subset_1(u1_struct_0(k15_euclid(2)),A,B)) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(2),A))) & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(2),A))) ) => ! [G] : ( m1_subset_1(G,k1_numbers) => ( ( v3_tops_2(F,k5_topmetr,k3_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,0) = C & k1_funct_1(F,1) = D & k1_funct_1(F,G) = E & r1_xreal_0(0,G) & r1_xreal_0(G,1) ) => ! [H] : ( m1_subset_1(H,k1_numbers) => ~ ( r1_xreal_0(0,H) & ~ r1_xreal_0(G,H) & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(jordan5c,d1_jordan5c), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d20_pscomp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => k12_pscomp_1(A,B) = k4_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) ), file(pscomp_1,d20_pscomp_1), []). fof(d21_pscomp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => k13_pscomp_1(A,B) = k3_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) ), file(pscomp_1,d21_pscomp_1), []). fof(d26_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & m2_relset_1(C,u1_struct_0(A),k1_numbers) ) => k15_pscomp_1(A,B,C) = k7_relat_1(C,B) ) ) ) ), file(pscomp_1,d26_pscomp_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_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k2_jgraph_6(A,B,C,D) = a_4_3_jgraph_6(A,B,C,D) ) ) ) ) ), file(jgraph_6,d2_jgraph_6), []). fof(d2_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k1_jordan21(A) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),2),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),2)))))) ) ), file(jordan21,d2_jordan21), []). fof(d2_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_sppol_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => k22_euclid(B) = k22_euclid(C) ) ) ) ) ) ), file(sppol_1,d2_sppol_1), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). fof(d2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) ), file(tops_1,d2_tops_1), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d30_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k18_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(2),A),k15_pscomp_1(k15_euclid(2),A,k16_pscomp_1)) ) ), file(pscomp_1,d30_pscomp_1), []). fof(d32_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k20_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(2),A),k15_pscomp_1(k15_euclid(2),A,k16_pscomp_1)) ) ), file(pscomp_1,d32_pscomp_1), []). fof(d3_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_borsuk_2(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) ) ) ) ) ), file(borsuk_2,d3_borsuk_2), []). fof(d3_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k2_jordan21(A) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),2),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),2)))))) ) ), file(jordan21,d3_jordan21), []). fof(d3_jordan2c,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r1_jordan2c(A,B,C) <=> ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C) & v1_jordan2c(C,A) ) ) ) ) ) ), file(jordan2c,d3_jordan2c), []). fof(d3_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v2_sppol_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => k21_euclid(B) = k21_euclid(C) ) ) ) ) ) ), file(sppol_1,d3_sppol_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_topreal4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_topreal4(B,A) <=> ( v3_pre_topc(B,A) & v2_connsp_1(B,A) ) ) ) ) ), file(topreal4,d3_topreal4), []). 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_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(d5_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r3_connsp_1(A,B) <=> ( v2_connsp_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_connsp_1(C,A) & r1_tarski(B,C) ) => B = C ) ) ) ) ) ) ), file(connsp_1,d5_connsp_1), []). 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_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d6_connsp_1,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))) => ( r4_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) & D = C & r3_connsp_1(k3_pre_topc(A,B),D) ) ) ) ) ) ), file(connsp_1,d6_connsp_1), []). fof(d7_euclid,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k14_euclid(A) = g1_metric_1(k1_euclid(A),k13_euclid(A)) ) ), file(euclid,d7_euclid), []). fof(d8_euclid,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k15_euclid(A) = k5_pcomps_1(k14_euclid(A)) ) ), file(euclid,d8_euclid), []). fof(dt_g1_metric_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) ) => ( v1_metric_1(g1_metric_1(A,B)) & l1_metric_1(g1_metric_1(A,B)) ) ) ), file(metric_1,g1_metric_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_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k12_pscomp_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => m1_subset_1(k12_pscomp_1(A,B),k1_numbers) ) ), file(pscomp_1,k12_pscomp_1), []). fof(dt_k13_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_funct_1(k13_euclid(A)) & v1_funct_2(k13_euclid(A),k2_zfmisc_1(k1_euclid(A),k1_euclid(A)),k1_numbers) & m2_relset_1(k13_euclid(A),k2_zfmisc_1(k1_euclid(A),k1_euclid(A)),k1_numbers) ) ) ), file(euclid,k13_euclid), []). fof(dt_k13_pscomp_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => m1_subset_1(k13_pscomp_1(A,B),k1_numbers) ) ), file(pscomp_1,k13_pscomp_1), []). fof(dt_k14_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_metric_1(k14_euclid(A)) & v6_metric_1(k14_euclid(A)) & v7_metric_1(k14_euclid(A)) & v8_metric_1(k14_euclid(A)) & v9_metric_1(k14_euclid(A)) & l1_metric_1(k14_euclid(A)) ) ) ), file(euclid,k14_euclid), []). 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_k15_pscomp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k15_pscomp_1(A,B,C)) & v1_funct_2(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) & m2_relset_1(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) ) ) ), file(pscomp_1,k15_pscomp_1), []). fof(dt_k16_pscomp_1,axiom, ( v1_funct_1(k16_pscomp_1) & v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) & m2_relset_1(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) ), file(pscomp_1,k16_pscomp_1), []). fof(dt_k17_euclid,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k17_euclid(A,B,C),u1_struct_0(k15_euclid(A))) ) ), file(euclid,k17_euclid), []). fof(dt_k17_pscomp_1,axiom, ( v1_funct_1(k17_pscomp_1) & v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) & m2_relset_1(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) ), file(pscomp_1,k17_pscomp_1), []). fof(dt_k18_euclid,axiom,( ! [A,B,C] : ( ( v1_xreal_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) ) => m1_subset_1(k18_euclid(A,B,C),u1_struct_0(k15_euclid(B))) ) ), file(euclid,k18_euclid), []). fof(dt_k18_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k18_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k18_pscomp_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_connsp_1,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_connsp_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(connsp_1,k1_connsp_1), []). fof(dt_k1_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k1_euclid(A)) & m1_finseq_2(k1_euclid(A),k1_numbers) ) ) ), file(euclid,k1_euclid), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_gobrd14,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k1_gobrd14(A,B,C),k1_numbers) ) ), file(gobrd14,k1_gobrd14), []). fof(dt_k1_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k1_jordan21(A),u1_struct_0(k15_euclid(2))) ) ), file(jordan21,k1_jordan21), []). fof(dt_k1_jordan5c,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) & m1_subset_1(D,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(k1_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(2))) ) ), file(jordan5c,k1_jordan5c), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k1_pre_topc), []). fof(dt_k1_pscomp_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k1_pscomp_1(A,B,C),k1_zfmisc_1(B)) ) ), file(pscomp_1,k1_pscomp_1), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_sppol_2,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => m1_subset_1(k1_sppol_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(sppol_2,k1_sppol_2), []). 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_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k1_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k1_topreal1), []). fof(dt_k1_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(k1_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal9,k1_topreal9), []). fof(dt_k1_topreala,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => m1_pre_topc(k1_topreala(A,B,C,D),k15_euclid(2)) ) ), file(topreala,k1_topreala), []). 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_k20_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k20_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k20_pscomp_1), []). fof(dt_k21_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k21_euclid(A),k1_numbers) ) ), file(euclid,k21_euclid), []). fof(dt_k22_borsuk_1,axiom,( l1_pre_topc(k22_borsuk_1) ), file(borsuk_1,k22_borsuk_1), []). fof(dt_k22_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k22_euclid(A),k1_numbers) ) ), file(euclid,k22_euclid), []). fof(dt_k23_euclid,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k23_euclid(A,B),u1_struct_0(k15_euclid(2))) ) ), file(euclid,k23_euclid), []). fof(dt_k2_borsuk_2,axiom,( ! [A,B,C,D] : ( ( ~ 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_borsuk_2(D,A,B,C) ) => m1_borsuk_2(k2_borsuk_2(A,B,C,D),A,C,B) ) ), file(borsuk_2,k2_borsuk_2), []). fof(dt_k2_connsp_3,axiom,( ! [A,B,C] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_connsp_3(A,B,C),u1_struct_0(k3_pre_topc(A,B))) ) ), file(connsp_3,k2_connsp_3), []). fof(dt_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ), file(funct_2,k2_funct_2), []). fof(dt_k2_jgraph_6,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => m1_subset_1(k2_jgraph_6(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jgraph_6,k2_jgraph_6), []). fof(dt_k2_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k2_jordan21(A),u1_struct_0(k15_euclid(2))) ) ), file(jordan21,k2_jordan21), []). fof(dt_k2_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k2_pre_topc), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_seq_4,axiom,( ! [A] : ( v2_membered(A) => v1_xreal_0(k2_seq_4(A)) ) ), file(seq_4,k2_seq_4), []). fof(dt_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k2_struct_0), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_tops_1,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(tops_1,k2_tops_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_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_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k3_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k3_pscomp_1), []). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k3_seq_4,axiom,( ! [A] : ( v2_membered(A) => v1_xreal_0(k3_seq_4(A)) ) ), file(seq_4,k3_seq_4), []). fof(dt_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ), file(subset_1,k3_subset_1), []). fof(dt_k3_topmetr,axiom, ( v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) & l1_pre_topc(k3_topmetr) ), file(topmetr,k3_topmetr), []). fof(dt_k3_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k3_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k3_topreal1), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_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(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ), file(pre_topc,k4_pre_topc), []). fof(dt_k4_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k4_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k4_pscomp_1), []). fof(dt_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_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(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_jordan6,axiom,( ! [A,B,C,D,E] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) & m1_subset_1(D,u1_struct_0(k15_euclid(2))) & m1_subset_1(E,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(k5_jordan6(A,B,C,D,E),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan6,k5_jordan6), []). 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_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => l1_pre_topc(k5_pcomps_1(A)) ) ), file(pcomps_1,k5_pcomps_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_topmetr,axiom, ( v1_pre_topc(k5_topmetr) & m1_pre_topc(k5_topmetr,k3_topmetr) ), file(topmetr,k5_topmetr), []). fof(dt_k6_connsp_3,axiom,( ! [A,B,C] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k6_connsp_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(connsp_3,k6_connsp_3), []). fof(dt_k6_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k6_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan6,k6_jordan6), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ), file(real_1,k6_real_1), []). fof(dt_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_1), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). 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_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_l1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => l1_struct_0(A) ) ), file(metric_1,l1_metric_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_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). 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_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v1_funct_1(u1_metric_1(A)) & v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) ) ) ), file(metric_1,u1_metric_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_metric_1,axiom,( ? [A] : l1_metric_1(A) ), file(metric_1,l1_metric_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_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). 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_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_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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_isomichi,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_isomichi(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v3_isomichi(k3_subset_1(u1_struct_0(A),B),A) & ~ v4_isomichi(k3_subset_1(u1_struct_0(A),B),A) & ~ v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ), file(isomichi,fc11_isomichi), []). fof(fc11_jordan,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_jordan2c(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( v4_pre_topc(k6_pre_topc(k15_euclid(A),B),k15_euclid(A)) & v1_jordan2c(k6_pre_topc(k15_euclid(A),B),A) ) ) ), file(jordan,fc11_jordan), []). 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_pscomp_1,axiom, ( ~ v1_xboole_0(k16_pscomp_1) & v1_relat_1(k16_pscomp_1) & v1_funct_1(k16_pscomp_1) & v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) & v1_seq_1(k16_pscomp_1) & v1_partfun1(k16_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) & v9_pscomp_1(k16_pscomp_1,k15_euclid(2)) ), file(pscomp_1,fc11_pscomp_1), []). fof(fc11_sppol_2,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => ( ~ v1_xboole_0(k1_topreal1(A,B,C)) & v6_compts_1(k1_topreal1(A,B,C),k15_euclid(A)) ) ) ), file(sppol_2,fc11_sppol_2), []). fof(fc11_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ), file(tops_1,fc11_tops_1), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_jordan,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_jordan2c(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( v4_pre_topc(k2_tops_1(k15_euclid(A),B),k15_euclid(A)) & v1_jordan2c(k2_tops_1(k15_euclid(A),B),A) ) ) ), file(jordan,fc12_jordan), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_pscomp_1,axiom, ( ~ v1_xboole_0(k17_pscomp_1) & v1_relat_1(k17_pscomp_1) & v1_funct_1(k17_pscomp_1) & v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) & v1_seq_1(k17_pscomp_1) & v1_partfun1(k17_pscomp_1,u1_struct_0(k15_euclid(2)),k1_numbers) & v9_pscomp_1(k17_pscomp_1,k15_euclid(2)) ), file(pscomp_1,fc12_pscomp_1), []). fof(fc12_sppol_2,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( ~ v1_xboole_0(k1_sppol_2(A,B,C,D)) & v6_compts_1(k1_sppol_2(A,B,C,D),k15_euclid(2)) ) ) ), file(sppol_2,fc12_sppol_2), []). fof(fc12_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A) ) ) ), file(tops_1,fc12_tops_1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc13_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A) ) ) ), file(tops_1,fc13_tops_1), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). fof(fc15_jordan,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( v4_pre_topc(k2_jgraph_6(A,B,C,D),k15_euclid(2)) & v1_jordan1(k2_jgraph_6(A,B,C,D),2) ) ) ), file(jordan,fc15_jordan), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc17_topreala,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) & v1_xreal_0(C) & ~ v3_xreal_0(C) & v1_xreal_0(D) & ~ v3_xreal_0(D) ) => ( ~ v3_struct_0(k1_topreala(A,C,B,D)) & v2_pre_topc(k1_topreala(A,C,B,D)) & v1_monoid_0(k1_topreala(A,C,B,D)) & v2_monoid_0(k1_topreala(A,C,B,D)) ) ) ), file(topreala,fc17_topreala), []). fof(fc1_borsuk_4,axiom, ( ~ v1_xboole_0(u1_struct_0(k5_topmetr)) & v1_membered(u1_struct_0(k5_topmetr)) & v2_membered(u1_struct_0(k5_topmetr)) ), file(borsuk_4,fc1_borsuk_4), []). fof(fc1_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v3_struct_0(k14_euclid(A)) & v1_metric_1(k14_euclid(A)) & v6_metric_1(k14_euclid(A)) & v7_metric_1(k14_euclid(A)) & v8_metric_1(k14_euclid(A)) & v9_metric_1(k14_euclid(A)) ) ) ), file(euclid,fc1_euclid), []). fof(fc1_jgraph_8,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => v1_jordan1(k2_jgraph_6(A,B,C,D),2) ) ), file(jgraph_8,fc1_jgraph_8), []). fof(fc1_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k2_pre_topc(k15_euclid(A))) & v4_pre_topc(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) & v2_connsp_1(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) ) ) ), file(jordan2c,fc1_jordan2c), []). 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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k7_xcmplx_0(A,A)) & v1_xreal_0(k7_xcmplx_0(A,A)) & ~ v3_xreal_0(k7_xcmplx_0(A,A)) ) ) ), file(partfun3,fc1_partfun3), []). fof(fc1_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) ) ) ), file(pre_topc,fc1_pre_topc), []). 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_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_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A) ) ) ), file(tex_4,fc1_tex_4), []). fof(fc1_topreal6,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & v6_group_1(k3_pre_topc(A,B)) ) ) ), file(topreal6,fc1_topreal6), []). fof(fc1_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) & ~ v2_xreal_0(C) ) => v1_xboole_0(k1_topreal9(A,B,C)) ) ), file(topreal9,fc1_topreal9), []). fof(fc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_xboole_0(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) ) ) ), file(tops_1,fc1_tops_1), []). fof(fc1_waybel_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ~ v1_xboole_0(k9_relat_1(C,D)) ) ), file(waybel_2,fc1_waybel_2), []). fof(fc1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). fof(fc1_yellow13,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) ), file(yellow13,fc1_yellow13), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc27_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc28_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), []). 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(fc29_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), []). fof(fc2_euclid,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)) ) ) ), file(euclid,fc2_euclid), []). fof(fc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A) & v1_tops_1(k2_pre_topc(A),A) & v5_tops_1(k2_pre_topc(A),A) & v6_tops_1(k2_pre_topc(A),A) ) ) ), file(isomichi,fc2_isomichi), []). fof(fc2_jgraph_8,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( v2_pre_topc(k1_topreala(A,B,C,D)) & v1_topalg_2(k1_topreala(A,B,C,D),2) ) ) ), file(jgraph_8,fc2_jgraph_8), []). fof(fc2_jordan,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => ( v1_xreal_0(k1_gobrd14(A,B,C)) & ~ v3_xreal_0(k1_gobrd14(A,B,C)) & v1_xcmplx_0(k1_gobrd14(A,B,C)) ) ) ), file(jordan,fc2_jordan), []). fof(fc2_jordan2c,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k1_topreal1(2,A,B)) & v2_tops_1(k1_topreal1(2,A,B),k15_euclid(2)) ) ) ), file(jordan2c,fc2_jordan2c), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(nat_1,fc2_nat_1), []). fof(fc2_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k3_xcmplx_0(A,A)) & v1_xreal_0(k3_xcmplx_0(A,A)) & ~ v3_xreal_0(k3_xcmplx_0(A,A)) ) ) ), file(partfun3,fc2_partfun3), []). fof(fc2_pre_topc,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k2_pre_topc(A)) ) ), file(pre_topc,fc2_pre_topc), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) ) ) ), file(seq_1,fc2_seq_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_tex_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_xboole_0(k6_pre_topc(A,B)) & v3_pre_topc(k6_pre_topc(A,B),A) & v4_pre_topc(k6_pre_topc(A,B),A) & v2_tops_1(k6_pre_topc(A,B),A) & v3_tops_1(k6_pre_topc(A,B),A) & v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) & v1_membered(k6_pre_topc(A,B)) & v2_membered(k6_pre_topc(A,B)) & v3_membered(k6_pre_topc(A,B)) & v4_membered(k6_pre_topc(A,B)) & v5_membered(k6_pre_topc(A,B)) ) ) ), file(tex_4,fc2_tex_4), []). 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(fc2_topreal6,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k1_topreal1(2,A,B)) & v2_connsp_1(k1_topreal1(2,A,B),k15_euclid(2)) & v1_jordan1(k1_topreal1(2,A,B),2) & v2_tops_1(k1_topreal1(2,A,B),k15_euclid(2)) ) ) ), file(topreal6,fc2_topreal6), []). fof(fc2_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) & v2_xreal_0(C) ) => ~ v1_xboole_0(k1_topreal9(A,B,C)) ) ), file(topreal9,fc2_topreal9), []). 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_yellow13,axiom,( ! [A] : ( ( v3_realset2(A) & l1_struct_0(A) ) => v1_realset1(u1_struct_0(A)) ) ), file(yellow13,fc2_yellow13), []). 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(fc30_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), []). 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(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). fof(fc3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_xboole_0(k1_pre_topc(A)) & v3_pre_topc(k1_pre_topc(A),A) & v4_pre_topc(k1_pre_topc(A),A) & v2_tops_1(k1_pre_topc(A),A) & v3_tops_1(k1_pre_topc(A),A) & v5_tops_1(k1_pre_topc(A),A) & v6_tops_1(k1_pre_topc(A),A) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) ) ) ), file(isomichi,fc3_isomichi), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). 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_pscomp_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ~ v1_xboole_0(k9_relat_1(C,A)) ) ), file(pscomp_1,fc3_pscomp_1), []). fof(fc3_realset1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ), file(realset1,fc3_realset1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_tex_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A) & ~ v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(tex_4,fc3_tex_4), []). 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_topgen_3,axiom, ( ~ v1_xboole_0(k1_numbers) & ~ v1_finset_1(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(topgen_3,fc3_topgen_3), []). 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_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ), file(tops_1,fc3_tops_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc3_yellow13,axiom,( ! [A] : ( ( v2_compts_1(A) & l1_pre_topc(A) ) => ( v1_tops_1(k2_pre_topc(A),A) & v6_compts_1(k2_pre_topc(A),A) ) ) ), file(yellow13,fc3_yellow13), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_isomichi,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v6_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ), file(isomichi,fc4_isomichi), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). 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_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_tex_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & ~ v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(k6_pre_topc(A,B)) & ~ v1_realset1(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A) ) ) ), file(tex_4,fc4_tex_4), []). 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_topgen_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_xboole_0(k1_zfmisc_1(A)) & ~ v1_finset_1(k1_zfmisc_1(A)) ) ) ), file(topgen_3,fc4_topgen_3), []). fof(fc4_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ), file(tops_1,fc4_tops_1), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). 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_isomichi,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v5_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v6_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ), file(isomichi,fc5_isomichi), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v4_pre_topc(k2_pre_topc(A),A) ) ), file(pre_topc,fc5_pre_topc), []). 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(fc5_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_pre_topc(k1_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k1_topreal9(A,B,C),A) ) ) ), file(topreal9,fc5_topreal9), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), []). 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_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_topreal6,axiom, ( ~ v3_struct_0(k3_topmetr) & v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) & v3_compts_1(k3_topmetr) ), file(topreal6,fc7_topreal6), []). fof(fc7_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_xboole_0(k1_pre_topc(A)) & v3_pre_topc(k1_pre_topc(A),A) & v4_pre_topc(k1_pre_topc(A),A) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) ) ) ), file(tops_1,fc7_tops_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_isomichi,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(k2_tops_1(A,B),A) ) ), file(isomichi,fc8_isomichi), []). 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_topgen_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_tex_2(B,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ~ v1_xboole_0(k3_subset_1(A,B)) ) ), file(topgen_3,fc8_topgen_3), []). fof(fc8_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_pre_topc(k1_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k1_topreal9(A,B,C),A) & v1_jordan1(k1_topreal9(A,B,C),A) ) ) ), file(topreal9,fc8_topreal9), []). fof(fc8_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A) ) ) ), file(tops_1,fc8_tops_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). 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_pscomp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_relat_1(k15_pscomp_1(A,C,B)) & v1_funct_1(k15_pscomp_1(A,C,B)) & v1_funct_2(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers) & v1_seq_1(k15_pscomp_1(A,C,B)) & v1_partfun1(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers) & v9_pscomp_1(k15_pscomp_1(A,C,B),k3_pre_topc(A,C)) ) ) ), file(pscomp_1,fc9_pscomp_1), []). fof(fc9_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A),A) ) ), file(tops_1,fc9_tops_1), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_4_3_jgraph_6,axiom,( ! [A,B,C,D,E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_3_jgraph_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_xreal_0(B,k21_euclid(F)) & r1_xreal_0(k21_euclid(F),C) & r1_xreal_0(D,k22_euclid(F)) & r1_xreal_0(k22_euclid(F),E) ) ) ) ), file(jgraph_6,a_4_3_jgraph_6), []). fof(free_g1_metric_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) ) => ! [C,D] : ( g1_metric_1(A,B) = g1_metric_1(C,D) => ( A = C & B = D ) ) ) ), file(metric_1,g1_metric_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(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,k3_subset_1(A,B)) = B ) ), file(subset_1,k3_subset_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(irreflexivity_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r1_subset_1(A,A) ) ), file(subset_1,r1_subset_1), []). fof(irreflexivity_r2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r2_subset_1(A,A) ) ), file(subset_1,r2_subset_1), []). fof(l105_jordan,axiom,( k21_euclid(k23_euclid(k1_real_1(1),0)) = k1_real_1(1) ), file(jordan,l105_jordan), []). fof(l106_jordan,axiom,( k21_euclid(k23_euclid(1,0)) = 1 ), file(jordan,l106_jordan), []). fof(l109_jordan,axiom,( k21_euclid(k23_euclid(0,3)) = 0 ), file(jordan,l109_jordan), []). fof(l110_jordan,axiom,( k22_euclid(k23_euclid(0,3)) = 3 ), file(jordan,l110_jordan), []). fof(l111_jordan,axiom,( k21_euclid(k23_euclid(0,k1_real_1(3))) = 0 ), file(jordan,l111_jordan), []). fof(l112_jordan,axiom,( k22_euclid(k23_euclid(0,k1_real_1(3))) = k1_real_1(3) ), file(jordan,l112_jordan), []). fof(l113_jordan,axiom,( k21_euclid(k23_euclid(k1_real_1(1),3)) = k1_real_1(1) ), file(jordan,l113_jordan), []). fof(l114_jordan,axiom,( k22_euclid(k23_euclid(k1_real_1(1),3)) = 3 ), file(jordan,l114_jordan), []). fof(l115_jordan,axiom,( k21_euclid(k23_euclid(k1_real_1(1),k1_real_1(3))) = k1_real_1(1) ), file(jordan,l115_jordan), []). fof(l116_jordan,axiom,( k22_euclid(k23_euclid(k1_real_1(1),k1_real_1(3))) = k1_real_1(3) ), file(jordan,l116_jordan), []). fof(l117_jordan,axiom,( k21_euclid(k23_euclid(1,3)) = 1 ), file(jordan,l117_jordan), []). fof(l118_jordan,axiom,( k22_euclid(k23_euclid(1,3)) = 3 ), file(jordan,l118_jordan), []). fof(l119_jordan,axiom,( k21_euclid(k23_euclid(1,k1_real_1(3))) = 1 ), file(jordan,l119_jordan), []). fof(l120_jordan,axiom,( k22_euclid(k23_euclid(1,k1_real_1(3))) = k1_real_1(3) ), file(jordan,l120_jordan), []). fof(l127_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(k1_real_1(1),3)),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l127_jordan), []). fof(l131_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(1,3),k23_euclid(1,k1_real_1(3))),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l131_jordan), []). fof(l134_jordan,axiom,( v2_sppol_1(k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(k1_real_1(1),3))) ), file(jordan,l134_jordan), []). fof(l135_jordan,axiom,( v2_sppol_1(k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(1,3))) ), file(jordan,l135_jordan), []). fof(l140_jordan,axiom,( v1_sppol_1(k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(0,k1_real_1(3)))) ), file(jordan,l140_jordan), []). fof(l141_jordan,axiom,( v1_sppol_1(k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(0,k1_real_1(3)))) ), file(jordan,l141_jordan), []). fof(l142_jordan,axiom,( v1_sppol_1(k3_topreal1(2,k23_euclid(k1_real_1(1),3),k23_euclid(0,3))) ), file(jordan,l142_jordan), []). fof(l143_jordan,axiom,( v1_sppol_1(k3_topreal1(2,k23_euclid(1,3),k23_euclid(0,3))) ), file(jordan,l143_jordan), []). fof(l146_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(k1_real_1(1),0),k23_euclid(k1_real_1(1),3)),k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(k1_real_1(1),3))) ), file(jordan,l146_jordan), []). fof(l147_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(k1_real_1(1),0),k23_euclid(k1_real_1(1),k1_real_1(3))),k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(k1_real_1(1),3))) ), file(jordan,l147_jordan), []). fof(l148_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,3)),k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(1,3))) ), file(jordan,l148_jordan), []). fof(l149_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,k1_real_1(3))),k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(1,3))) ), file(jordan,l149_jordan), []). fof(l151_jordan,axiom,( r2_hidden(k23_euclid(0,3),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l151_jordan), []). fof(l152_jordan,axiom,( r2_hidden(k23_euclid(0,k1_real_1(3)),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l152_jordan), []). fof(l158_jordan,axiom,( r1_tarski(k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3),k2_jgraph_6(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l158_jordan), []). fof(l161_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(k1_real_1(1),3),k23_euclid(0,3)),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l161_jordan), []). fof(l163_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(1,3),k23_euclid(0,3)),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l163_jordan), []). fof(l166_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(0,k1_real_1(3))),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l166_jordan), []). fof(l168_jordan,axiom,( r1_tarski(k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(0,k1_real_1(3))),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) ), file(jordan,l168_jordan), []). fof(l169_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ ( r1_xreal_0(0,k22_euclid(A)) & r2_hidden(A,k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(k1_real_1(1),0),k23_euclid(k1_real_1(1),3))) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(k1_real_1(1),3),k23_euclid(0,3))) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(0,3),k23_euclid(1,3))) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(1,3),k23_euclid(1,0))) ) ) ), file(jordan,l169_jordan), []). fof(l170_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ ( r1_xreal_0(k22_euclid(A),0) & r2_hidden(A,k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(k1_real_1(1),0),k23_euclid(k1_real_1(1),k1_real_1(3)))) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(0,k1_real_1(3)))) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(0,k1_real_1(3)),k23_euclid(1,k1_real_1(3)))) & ~ r2_hidden(A,k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(1,0))) ) ) ), file(jordan,l170_jordan), []). fof(l174_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => r1_subset_1(k3_topreal1(2,k23_euclid(k1_real_1(1),3),k23_euclid(0,3)),A) ) ) ), file(jordan,l174_jordan), []). fof(l175_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => r1_subset_1(k3_topreal1(2,k23_euclid(1,3),k23_euclid(0,3)),A) ) ) ), file(jordan,l175_jordan), []). fof(l176_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => r1_subset_1(k3_topreal1(2,k23_euclid(k1_real_1(1),k1_real_1(3)),k23_euclid(0,k1_real_1(3))),A) ) ) ), file(jordan,l176_jordan), []). fof(l177_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => r1_subset_1(k3_topreal1(2,k23_euclid(1,k1_real_1(3)),k23_euclid(0,k1_real_1(3))),A) ) ) ), file(jordan,l177_jordan), []). fof(l178_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_jordan24(2,B,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(A,k3_subset_1(u1_struct_0(k15_euclid(2)),B)) & r2_hidden(A,k3_topreal1(2,k23_euclid(k1_real_1(1),0),k23_euclid(k1_real_1(1),3))) ) => r1_subset_1(k3_topreal1(2,A,k23_euclid(k1_real_1(1),3)),B) ) ) ) ), file(jordan,l178_jordan), []). fof(l179_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_jordan24(2,B,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(A,k3_subset_1(u1_struct_0(k15_euclid(2)),B)) & r2_hidden(A,k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,3))) ) => r1_subset_1(k3_topreal1(2,A,k23_euclid(1,3)),B) ) ) ) ), file(jordan,l179_jordan), []). fof(l180_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_jordan24(2,B,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(A,k3_subset_1(u1_struct_0(k15_euclid(2)),B)) & r2_hidden(A,k3_topreal1(2,k23_euclid(k1_real_1(1),0),k23_euclid(k1_real_1(1),k1_real_1(3)))) ) => r1_subset_1(k3_topreal1(2,A,k23_euclid(k1_real_1(1),k1_real_1(3))),B) ) ) ) ), file(jordan,l180_jordan), []). fof(l181_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_jordan24(2,B,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(A,k3_subset_1(u1_struct_0(k15_euclid(2)),B)) & r2_hidden(A,k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,k1_real_1(3)))) ) => r1_subset_1(k3_topreal1(2,A,k23_euclid(1,k1_real_1(3))),B) ) ) ) ), file(jordan,l181_jordan), []). fof(l182_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(k23_euclid(0,A),k1_sppol_2(k1_real_1(1),1,k1_real_1(3),3)) & A != k1_real_1(3) & A != 3 ) ) ), file(jordan,l182_jordan), []). fof(l189_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => k21_euclid(k23_euclid(0,3)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),2) ) ) ), file(jordan,l189_jordan), []). fof(l1_jordan,axiom,( ! [A,B,C,D] : ( ( r1_tarski(A,D) & r1_tarski(B,D) & r1_tarski(C,D) ) => r1_tarski(k2_xboole_0(k2_xboole_0(A,B),C),D) ) ), file(jordan,l1_jordan), []). fof(l204_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,k2_jgraph_6(k1_real_1(1),1,k1_real_1(3),3)) => r1_tarski(k2_jgraph_6(k1_real_1(1),1,k1_real_1(3),3),k1_topreal9(2,A,10)) ) ) ), file(jordan,l204_jordan), []). fof(l2_jordan,axiom,( ! [A,B,C,D,E] : ( ( r1_tarski(A,E) & r1_tarski(B,E) & r1_tarski(C,E) & r1_tarski(D,E) ) => r1_tarski(k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D),E) ) ), file(jordan,l2_jordan), []). fof(l3_jordan,axiom,( ! [A,B,C,D,E] : ( ( r1_xboole_0(A,E) & r1_xboole_0(B,E) & r1_xboole_0(C,E) & r1_xboole_0(D,E) ) => r1_xboole_0(k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D),E) ) ), file(jordan,l3_jordan), []). fof(l61_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(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_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( m1_borsuk_2(J,A,E,F) => k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),H)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),I)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),J)) ) ) ) ) ) ) ) ) ) ) ), file(jordan,l61_jordan), []). fof(l63_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(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_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_borsuk_2(H,A,B,C) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,D,E) => ! [K] : ( m1_borsuk_2(K,A,E,F) => ! [L] : ( m1_borsuk_2(L,A,F,G) => k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,F,G,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,H,I),J),K),L)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),H),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),I)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),J)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),K)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),L)) ) ) ) ) ) ) ) ) ) ) ) ) ), file(jordan,l63_jordan), []). 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(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_borsuk_4,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) & v2_connsp_1(B,A) & v6_compts_1(B,A) ) ) ), file(borsuk_4,rc1_borsuk_4), []). 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_isomichi,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) ) ), file(isomichi,rc1_isomichi), []). fof(rc1_jordan,axiom,( ! [A] : ( ( ~ v1_xboole_0(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) & v3_pre_topc(B,k15_euclid(A)) & v4_pre_topc(B,k15_euclid(A)) & ~ v1_jordan2c(B,A) & v1_jordan1(B,A) ) ) ), file(jordan,rc1_jordan), []). fof(rc1_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v1_jordan2c(A,2) & v1_topreal2(A) ) ), file(jordan1a,rc1_jordan1a), []). fof(rc1_jordan21,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & ~ v1_realset1(A) & v1_topreal2(A) & v1_jordan21(A) ) ), file(jordan21,rc1_jordan21), []). fof(rc1_jordan2c,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v6_tbsp_1(B,A) ) ) ), file(jordan2c,rc1_jordan2c), []). 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_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_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & v1_metric_1(A) ) ), file(metric_1,rc1_metric_1), []). 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_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_realset1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(realset1,rc1_realset1), []). 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_4,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) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) ) ) ), file(tex_4,rc1_tex_4), []). fof(rc1_topgen_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_finset_1(B) ) ) ), file(topgen_3,rc1_topgen_3), []). fof(rc1_topgrp_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(topgrp_1,rc1_topgrp_1), []). fof(rc1_topreal6,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_compts_1(A) & v6_group_1(A) & v10_pscomp_1(A) ) ), file(topreal6,rc1_topreal6), []). fof(rc1_topreala,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_monoid_0(A) & v2_monoid_0(A) ) ), file(topreala,rc1_topreala), []). 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(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_borsuk_4,axiom,( ! [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) ) ) ), file(borsuk_4,rc2_borsuk_4), []). 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_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). fof(rc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_tops_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ), file(isomichi,rc2_isomichi), []). fof(rc2_jordan,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) & v4_pre_topc(B,k15_euclid(A)) & v1_jordan2c(B,A) & v1_jordan1(B,A) ) ) ), file(jordan,rc2_jordan), []). fof(rc2_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & v1_sppol_1(A) & v1_jordan2c(A,2) ) ), file(jordan1a,rc2_jordan1a), []). fof(rc2_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & ~ v3_struct_0(A) & v1_metric_1(A) ) ), file(metric_1,rc2_metric_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_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_realset1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ), file(realset1,rc2_realset1), []). 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_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & ~ v2_tex_2(B,A) ) ) ), file(tex_4,rc2_tex_4), []). fof(rc2_topgrp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v2_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A)) ) ) ), file(topgrp_1,rc2_topgrp_1), []). fof(rc2_topreal6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v2_connsp_1(A,k15_euclid(2)) & v1_jordan1(A,2) ) ), file(topreal6,rc2_topreal6), []). 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_borsuk_4,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ), file(borsuk_4,rc3_borsuk_4), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_tops_1(B,A) & v6_tops_1(B,A) ) ) ), file(isomichi,rc3_isomichi), []). fof(rc3_jordan,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) & v3_pre_topc(B,k15_euclid(A)) & v1_jordan2c(B,A) & v1_jordan1(B,A) ) ) ), file(jordan,rc3_jordan), []). fof(rc3_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & v2_sppol_1(A) & v1_jordan2c(A,2) ) ), file(jordan1a,rc3_jordan1a), []). fof(rc3_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & ~ v3_struct_0(A) & v1_metric_1(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) ) ), file(metric_1,rc3_metric_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_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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_tops_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc3_tops_1), []). fof(rc3_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_isomichi,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v3_isomichi(B,A) & v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ), file(isomichi,rc4_isomichi), []). 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_rcomp_3,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) & v2_connsp_1(B,A) ) ) ), file(rcomp_3,rc4_rcomp_3), []). fof(rc4_topgrp_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) & v1_tops_1(B,A) ) ) ), file(topgrp_1,rc4_topgrp_1), []). fof(rc4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) ) ) ), file(tops_1,rc4_tops_1), []). fof(rc4_waybel_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v3_compts_1(A) & v4_compts_1(A) & v5_compts_1(A) & v6_waybel_3(A) ) ), file(waybel_3,rc4_waybel_3), []). 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(rc4_yellow13,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(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) & v6_group_1(A) & v3_realset2(A) ) ), file(yellow13,rc4_yellow13), []). 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_rcomp_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(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) & v2_connsp_1(B,A) ) ) ), file(rcomp_3,rc5_rcomp_3), []). 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_topgrp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v2_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(B,A,A) & v3_tops_2(B,A,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v1_t_0topsp(B,A,A) ) ) ), file(topgrp_1,rc5_topgrp_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(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_topgrp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_topgrp_1(A) ) ), file(topgrp_1,rc6_topgrp_1), []). fof(rc7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ), file(isomichi,rc7_isomichi), []). 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_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_seq_1(B) & v1_partfun1(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) ) ) ), file(pscomp_1,rc7_pscomp_1), []). fof(rc8_pscomp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(B),k1_numbers) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v1_seq_1(C) & v1_partfun1(C,u1_struct_0(B),k1_numbers) & v9_pscomp_1(C,B) ) ) ), file(pscomp_1,rc8_pscomp_1), []). 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(redefinition_k1_pscomp_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k1_pscomp_1(A,B,C) = k2_relat_1(C) ) ), file(pscomp_1,k1_pscomp_1), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). 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_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ), file(funct_2,k2_funct_2), []). fof(redefinition_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_struct_0(A,B,C) = k2_tarski(B,C) ) ), file(struct_0,k2_struct_0), []). fof(redefinition_k3_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k3_pscomp_1(A) = k2_seq_4(A) ) ), file(pscomp_1,k3_pscomp_1), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). fof(redefinition_k3_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k3_topreal1(A,B,C) = k1_topreal1(A,B,C) ) ), file(topreal1,k3_topreal1), []). fof(redefinition_k4_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)) ) => k4_pre_topc(A,B,C,D) = k9_relat_1(C,D) ) ), file(pre_topc,k4_pre_topc), []). fof(redefinition_k4_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k4_pscomp_1(A) = k3_seq_4(A) ) ), file(pscomp_1,k4_pscomp_1), []). fof(redefinition_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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_k5_topmetr,axiom,( k5_topmetr = k22_borsuk_1 ), file(topmetr,k5_topmetr), []). fof(redefinition_k6_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) ), file(real_1,k6_real_1), []). fof(redefinition_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). fof(redefinition_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_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r1_subset_1), []). fof(redefinition_r2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r2_subset_1), []). 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_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc10_boole,axiom,( ~ v1_xboole_0(10) ), file(boole,spc10_boole), []). fof(spc10_numerals,axiom, ( v2_xreal_0(10) & m1_subset_1(10,k5_numbers) ), file(numerals,spc10_numerals), []). 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(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_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_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) => r1_subset_1(B,A) ) ) ), file(subset_1,r1_subset_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_r2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_subset_1(A,B) => r2_subset_1(B,A) ) ) ), file(subset_1,r2_subset_1), []). fof(t100_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r1_jordan2c(2,A,B) ) => r1_xboole_0(k3_topreal1(2,k2_jordan21(A),k23_euclid(0,k1_real_1(3))),B) ) ) ) ), file(jordan,t100_jordan), []). fof(t101_jordan,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & v1_jordan21(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,3),k1_jordan21(A)),A) = k1_struct_0(k15_euclid(2),k1_jordan21(A)) ) ) ), file(jordan,t101_jordan), []). fof(t103_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v6_compts_1(A,k15_euclid(2)) & r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r1_jordan2c(2,A,B) ) => r1_tarski(B,k2_jgraph_6(k1_real_1(1),1,k1_real_1(3),3)) ) ) ) ), file(jordan,t103_jordan), []). fof(t114_xboole_1,axiom,( ! [A,B,C,D] : ( ( r1_xboole_0(A,D) & r1_xboole_0(B,D) & r1_xboole_0(C,D) ) => r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) ) ), file(xboole_1,t114_xboole_1), []). fof(t11_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r1_xreal_0(A,B) & r2_hidden(D,k3_topreal1(2,k23_euclid(A,C),k23_euclid(B,C))) ) => ( k22_euclid(D) = C & r1_xreal_0(A,k21_euclid(D)) & r1_xreal_0(k21_euclid(D),B) ) ) ) ) ) ) ), file(jgraph_6,t11_jgraph_6), []). fof(t11_jordan6,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r1_topreal1(k15_euclid(A),C,D,B) => v2_connsp_1(B,k15_euclid(A)) ) ) ) ) ) ), file(jordan6,t11_jordan6), []). fof(t11_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( k21_euclid(A) = k21_euclid(B) & k22_euclid(A) = k22_euclid(B) ) => A = B ) ) ) ), file(topreal3,t11_topreal3), []). fof(t12_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal1(k15_euclid(2),B,C,A) => v4_pre_topc(A,k15_euclid(2)) ) ) ) ) ), file(jordan6,t12_jordan6), []). fof(t12_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => k2_pre_topc(A) = u1_struct_0(A) ) ), file(pre_topc,t12_pre_topc), []). fof(t146_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ), file(relat_1,t146_relat_1), []). fof(t14_weierstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_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)) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v6_compts_1(D,A) & v5_pre_topc(C,A,B) ) => v6_compts_1(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ), file(weierstr,t14_weierstr), []). fof(t16_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_compts_1(A) & v6_compts_1(B,A) ) => v4_pre_topc(B,A) ) ) ) ), file(compts_1,t16_compts_1), []). fof(t16_jordan2c,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v1_jordan2c(C,A) & r1_tarski(B,C) ) => v1_jordan2c(B,A) ) ) ) ) ), file(jordan2c,t16_jordan2c), []). fof(t17_jordan2c,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r1_jordan2c(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B))))) & D = C & r3_connsp_1(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)),D) & v6_tbsp_1(D,k14_euclid(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) ) ), file(jordan2c,t17_jordan2c), []). fof(t17_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v2_sppol_1(A) <=> k18_pscomp_1(A) = k20_pscomp_1(A) ) ) ), file(sprect_1,t17_sprect_1), []). fof(t17_xboole_1,axiom,( ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ), file(xboole_1,t17_xboole_1), []). fof(t18_sprect_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v3_pre_topc(A,k15_euclid(2)) & r4_connsp_1(k15_euclid(2),A,B) ) => v3_pre_topc(B,k15_euclid(2)) ) ) ) ), file(sprect_3,t18_sprect_3), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_jordan,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( B != C & k18_euclid(k6_real_1(1,2),A,k17_euclid(A,B,C)) = B ) ) ) ) ), file(jordan,t1_jordan), []). fof(t1_jordan1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => u1_struct_0(k3_pre_topc(A,B)) = B ) ) ), file(jordan1,t1_jordan1), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). 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(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,A) ) => A = B ) ) ) ), file(xreal_1,t1_xreal_1), []). fof(t20_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(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))) => ( ( v3_compts_1(A) & v6_compts_1(B,A) & v6_compts_1(C,A) ) => v6_compts_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ), file(compts_1,t20_compts_1), []). fof(t20_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) ) => ( B = D | r1_topreal1(k15_euclid(2),B,D,k5_jordan6(A,B,C,B,D)) ) ) ) ) ) ) ), file(jordan20,t20_jordan20), []). fof(t23_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(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))) => ~ ( v2_connsp_1(B,A) & ~ r1_xboole_0(B,C) & k6_subset_1(u1_struct_0(A),B,C) != k1_pre_topc(A) & r1_xboole_0(B,k2_tops_1(A,C)) ) ) ) ) ), file(connsp_1,t23_connsp_1), []). fof(t24_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v2_connsp_1(C,A) <=> v2_connsp_1(D,B) ) ) ) ) ) ) ), file(connsp_1,t24_connsp_1), []). fof(t24_jordan,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_xreal_0(B) & v2_xreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r2_hidden(C,k1_topreal9(A,C,B)) ) ) ) ), file(jordan,t24_jordan), []). fof(t26_connsp_3,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))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(C,k6_connsp_3(A,B,C)) ) ) ) ) ), file(connsp_3,t26_connsp_3), []). fof(t27_connsp_3,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))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => k6_connsp_3(A,B,C) = k1_connsp_1(k3_pre_topc(A,B),k2_connsp_3(A,B,C)) ) ) ) ) ), file(connsp_3,t27_connsp_3), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) & r1_xreal_0(k22_euclid(k18_euclid(k6_real_1(1,2),2,k17_euclid(2,A,B))),k22_euclid(A)) ) ) ) ), file(jordan,t2_jordan), []). fof(t2_jordan1e,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_tarski(A,B) => r1_xreal_0(k20_pscomp_1(A),k20_pscomp_1(B)) ) ) ) ), file(jordan1e,t2_jordan1e), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t30_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( v2_topreal4(C,k15_euclid(2)) & r2_hidden(A,C) & r2_hidden(B,C) & A != B & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(D,A,B) & r1_tarski(D,C) ) ) ) ) ) ) ), file(topreal4,t30_topreal4), []). fof(t33_jordan,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v4_pre_topc(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( ~ r2_hidden(C,B) & ! [D] : ( ( v1_xreal_0(D) & v2_xreal_0(D) ) => ~ r1_xboole_0(k1_topreal9(A,C,D),B) ) ) ) ) ) ), file(jordan,t33_jordan), []). fof(t33_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k21_euclid(k1_jordan21(A)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),2) ) ), file(jordan21,t33_jordan21), []). fof(t34_connsp_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))) => ~ ( r3_connsp_1(A,B) & B = k1_pre_topc(A) ) ) ) ), file(connsp_1,t34_connsp_1), []). fof(t34_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k6_jordan6(A)) <=> k21_euclid(B) = A ) ) ) ), file(jordan6,t34_jordan6), []). fof(t35_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k21_euclid(k2_jordan21(A)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),2) ) ), file(jordan21,t35_jordan21), []). fof(t35_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(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))) => ( ( v4_pre_topc(B,A) & v4_pre_topc(C,A) ) => v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ), file(tops_1,t35_tops_1), []). fof(t36_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k22_euclid(A) = k22_euclid(B) <=> v1_sppol_1(k3_topreal1(2,A,B)) ) ) ) ), file(sppol_1,t36_sppol_1), []). fof(t37_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(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))) => ~ ( r3_connsp_1(A,B) & r3_connsp_1(A,C) & B != C & ~ r1_xboole_0(B,C) ) ) ) ) ), file(connsp_1,t37_connsp_1), []). fof(t37_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k21_euclid(A) = k21_euclid(B) <=> v2_sppol_1(k3_topreal1(2,A,B)) ) ) ) ), file(sppol_1,t37_sppol_1), []). fof(t37_zfmisc_1,axiom,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_1), []). fof(t38_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_connsp_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r3_connsp_1(A,C) & ~ r1_xboole_0(B,C) & ~ r1_tarski(B,C) ) ) ) ) ) ), file(connsp_1,t38_connsp_1), []). fof(t38_jordan,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,A,C,D) => ( ( C = E & D = F & r1_borsuk_6(A,C,D) & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),u1_struct_0(B)) ) => ( r1_borsuk_6(B,E,F) & m1_borsuk_2(G,B,E,F) ) ) ) ) ) ) ) ) ) ), file(jordan,t38_jordan), []). fof(t39_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(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,A,C,D) => ( ( C = E & D = F & r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),u1_struct_0(B)) ) => ( r1_borsuk_6(B,E,F) & m1_borsuk_2(G,B,E,F) ) ) ) ) ) ) ) ) ) ), file(jordan,t39_jordan), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xreal_0(k22_euclid(B),k22_euclid(A)) & r1_xreal_0(k22_euclid(B),k22_euclid(k18_euclid(k6_real_1(1,2),2,k17_euclid(2,A,B)))) ) ) ) ), file(jordan,t3_jordan), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal4(A,B,C) => r1_topreal1(k15_euclid(2),B,C,A) ) ) ) ) ), file(topreal4,t3_topreal4), []). 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(t41_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(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) => k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),D) = k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k2_borsuk_2(A,B,C,D)) ) ) ) ) ), file(jordan,t41_jordan), []). fof(t41_jordan21,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,k5_subset_1(u1_struct_0(k15_euclid(2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),2)))) => r1_xreal_0(k22_euclid(A),k22_euclid(k1_jordan21(B))) ) ) ) ), file(jordan21,t41_jordan21), []). fof(t42_jordan21,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,k5_subset_1(u1_struct_0(k15_euclid(2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),2)))) => r1_xreal_0(k22_euclid(k2_jordan21(B)),k22_euclid(A)) ) ) ) ), file(jordan21,t42_jordan21), []). fof(t43_connsp_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))) => ( r3_connsp_1(A,B) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k1_connsp_1(A,C) ) ) ) ) ), file(connsp_1,t43_connsp_1), []). fof(t43_jordan21,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & v1_jordan21(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k1_jordan21(A),A) ) ), file(jordan21,t43_jordan21), []). fof(t43_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) <=> r1_tarski(B,k3_subset_1(A,C)) ) ) ) ), file(subset_1,t43_subset_1), []). fof(t44_jordan21,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & v1_jordan21(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k2_jordan21(A),A) ) ), file(jordan21,t44_jordan21), []). fof(t45_xboole_1,axiom,( ! [A,B] : ( r1_tarski(A,B) => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) ), file(xboole_1,t45_xboole_1), []). fof(t49_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(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_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( m1_borsuk_2(H,A,D,E) => k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),F),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),H)) ) ) ) ) ) ) ) ) ), file(jordan,t49_jordan), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_goboard9,axiom,( ! [A] : ( ( v2_pre_topc(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))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C)))) => ( B = D => k3_pre_topc(A,B) = k3_pre_topc(k3_pre_topc(A,C),D) ) ) ) ) ) ), file(goboard9,t4_goboard9), []). fof(t4_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => v2_sppol_1(k5_subset_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(jordan,t4_jordan), []). fof(t4_jordan1e,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_tarski(A,B) => r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A)) ) ) ) ), file(jordan1e,t4_jordan1e), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). 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_topreal1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_topreal1(A,C,D,B) => ( r2_hidden(C,B) & r2_hidden(D,B) ) ) ) ) ) ) ), file(topreal1,t4_topreal1), []). fof(t50_subset_1,axiom,( ! [A] : ( A != k1_xboole_0 => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,A) => ( ~ r2_hidden(C,B) => r2_hidden(C,k3_subset_1(A,B)) ) ) ) ) ), file(subset_1,t50_subset_1), []). fof(t51_jordan,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ~ ( r1_topreal1(k15_euclid(A),B,C,D) & ! [E] : ( m1_borsuk_2(E,k15_euclid(A),B,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),D))) & m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),D))) ) => ~ ( k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),D)),F) = D & E = F ) ) ) ) ) ) ) ) ), file(jordan,t51_jordan), []). fof(t52_jordan,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ? [D] : ( m1_borsuk_2(D,k15_euclid(A),B,C) & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C)))) & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C)))) & k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))),E) = k3_topreal1(A,B,C) & D = E ) ) ) ) ) ), file(jordan,t52_jordan), []). fof(t53_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & r2_hidden(E,A) & D != B & D != C & E != B & E != C & ! [F] : ( m1_borsuk_2(F,k15_euclid(2),D,E) => ~ ( r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),F),A) & r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2)),F),k2_struct_0(k15_euclid(2),B,C)) ) ) ) ) ) ) ) ) ), file(jordan,t53_jordan), []). fof(t53_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => u1_struct_0(k1_topreala(A,B,C,D)) = k2_jgraph_6(A,B,C,D) ) ) ) ) ), file(topreala,t53_topreala), []). fof(t55_zfmisc_1,axiom,( ! [A,B,C] : ~ ( r1_xboole_0(k2_tarski(A,B),C) & r2_hidden(A,C) ) ), file(zfmisc_1,t55_zfmisc_1), []). fof(t56_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k21_euclid(k23_euclid(A,B)) = A & k22_euclid(k23_euclid(A,B)) = B ) ) ) ), file(euclid,t56_euclid), []). fof(t56_zfmisc_1,axiom,( ! [A,B] : ( ~ r2_hidden(A,B) => r1_xboole_0(k1_tarski(A),B) ) ), file(zfmisc_1,t56_zfmisc_1), []). fof(t57_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => A = k23_euclid(k21_euclid(A),k22_euclid(A)) ) ), file(euclid,t57_euclid), []). fof(t57_zfmisc_1,axiom,( ! [A,B,C] : ~ ( ~ r2_hidden(A,B) & ~ r2_hidden(C,B) & ~ r1_xboole_0(k2_tarski(A,C),B) ) ), file(zfmisc_1,t57_zfmisc_1), []). fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). fof(t5_jordan15,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( v2_sppol_1(k3_topreal1(2,A,B)) & v2_sppol_1(k3_topreal1(2,C,D)) & k21_euclid(A) = k21_euclid(C) & r1_xreal_0(k22_euclid(A),k22_euclid(C)) & r1_xreal_0(k22_euclid(C),k22_euclid(D)) & r1_xreal_0(k22_euclid(D),k22_euclid(B)) ) => r1_tarski(k3_topreal1(2,C,D),k3_topreal1(2,A,B)) ) ) ) ) ) ), file(jordan15,t5_jordan15), []). fof(t5_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => r1_tarski(k5_jordan6(A,B,C,D,E),A) ) ) ) ) ) ), file(jordan16,t5_jordan16), []). fof(t5_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => v2_connsp_1(k6_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,A,B),k2_struct_0(k15_euclid(2),A,B)),k15_euclid(2)) ) ) ), file(jordan1h,t5_jordan1h), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). 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(t61_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xreal_0(B,A) & ~ r1_xreal_0(D,C) & k2_tops_1(k15_euclid(2),k2_jgraph_6(A,B,C,D)) != k1_sppol_2(A,B,C,D) ) ) ) ) ) ), file(jordan,t61_jordan), []). fof(t62_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xreal_0(k21_euclid(A),k21_euclid(B)) => k18_pscomp_1(k3_topreal1(2,A,B)) = k21_euclid(A) ) ) ) ), file(sprect_1,t62_sprect_1), []). fof(t63_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_xboole_0(B,C) ) => r1_xboole_0(A,C) ) ), file(xboole_1,t63_xboole_1), []). fof(t64_zfmisc_1,axiom,( ! [A,B,C] : ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C))) <=> ( r2_hidden(A,B) & A != C ) ) ), file(zfmisc_1,t64_zfmisc_1), []). fof(t65_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xreal_0(k21_euclid(A),k21_euclid(B)) => k20_pscomp_1(k3_topreal1(2,A,B)) = k21_euclid(B) ) ) ) ), file(sprect_1,t65_sprect_1), []). fof(t66_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r2_hidden(E,k2_jgraph_6(A,B,C,D)) & r1_topreal1(k15_euclid(2),E,F,G) ) => ( r1_xreal_0(B,A) | r1_xreal_0(D,C) | r2_hidden(F,k2_jgraph_6(A,B,C,D)) | r1_tarski(k5_jordan6(G,E,F,E,k1_jordan5c(G,k1_sppol_2(A,B,C,D),E,F)),k2_jgraph_6(A,B,C,D)) ) ) ) ) ) ) ) ) ) ), file(jordan,t66_jordan), []). fof(t6_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_jgraph_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_topreala(A,B,C,D))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_topreala(A,B,C,D))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k1_topreala(A,B,C,D))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_topreala(A,B,C,D))) => ! [I] : ( m1_borsuk_2(I,k1_topreala(A,B,C,D),E,F) => ! [J] : ( m1_borsuk_2(J,k1_topreala(A,B,C,D),H,G) => ! [K] : ( m1_subset_1(K,u1_struct_0(k15_euclid(2))) => ! [L] : ( m1_subset_1(L,u1_struct_0(k15_euclid(2))) => ! [M] : ( m1_subset_1(M,u1_struct_0(k15_euclid(2))) => ! [N] : ( m1_subset_1(N,u1_struct_0(k15_euclid(2))) => ~ ( k21_euclid(K) = A & k21_euclid(L) = B & k22_euclid(M) = C & k22_euclid(N) = D & E = K & F = L & G = M & H = N & ! [O] : ( m1_subset_1(O,u1_struct_0(k22_borsuk_1)) => ! [P] : ( m1_subset_1(P,u1_struct_0(k22_borsuk_1)) => k8_funct_2(u1_struct_0(k22_borsuk_1),u1_struct_0(k1_topreala(A,B,C,D)),I,O) != k8_funct_2(u1_struct_0(k22_borsuk_1),u1_struct_0(k1_topreala(A,B,C,D)),J,P) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(jgraph_8,t6_jgraph_8), []). fof(t6_jordan15,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( v1_sppol_1(k3_topreal1(2,A,B)) & v1_sppol_1(k3_topreal1(2,C,D)) & k22_euclid(A) = k22_euclid(C) & r1_xreal_0(k21_euclid(A),k21_euclid(C)) & r1_xreal_0(k21_euclid(C),k21_euclid(D)) & r1_xreal_0(k21_euclid(D),k21_euclid(B)) ) => r1_tarski(k3_topreal1(2,C,D),k3_topreal1(2,A,B)) ) ) ) ) ) ), file(jordan15,t6_jordan15), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t6_topreal1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k1_topreal1(A,B,C)) & r2_hidden(C,k1_topreal1(A,B,C)) ) ) ) ) ), file(topreal1,t6_topreal1), []). fof(t70_xboole_1,axiom,( ! [A,B,C] : ( ~ ( ~ r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,B) & r1_xboole_0(A,C) ) & ~ ( ~ ( r1_xboole_0(A,B) & r1_xboole_0(A,C) ) & r1_xboole_0(A,k2_xboole_0(B,C)) ) ) ), file(xboole_1,t70_xboole_1), []). fof(t78_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A))))) => ( r3_connsp_1(k3_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),B) => v1_borsuk_2(k3_pre_topc(k3_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),B)) ) ) ) ), file(jordan,t78_jordan), []). fof(t79_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A))))) => ( ( C = B & r3_connsp_1(k3_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),C) ) => A = k2_tops_1(k15_euclid(2),B) ) ) ) ) ), file(jordan,t79_jordan), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_goboard7,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r2_hidden(k18_euclid(k6_real_1(1,2),A,k17_euclid(A,B,C)),k3_topreal1(A,B,C)) ) ) ) ), file(goboard7,t7_goboard7), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t7_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k21_euclid(k17_euclid(2,A,B)) = k3_real_1(k21_euclid(A),k21_euclid(B)) & k22_euclid(k17_euclid(2,A,B)) = k3_real_1(k22_euclid(A),k22_euclid(B)) ) ) ) ), file(topreal3,t7_topreal3), []). fof(t7_xboole_1,axiom,( ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ), file(xboole_1,t7_xboole_1), []). fof(t81_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => r1_tarski(A,k2_jgraph_6(k1_real_1(1),1,k1_real_1(3),3)) ) ) ), file(jordan,t81_jordan), []). fof(t85_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => k18_pscomp_1(A) = k1_real_1(1) ) ) ), file(jordan,t85_jordan), []). fof(t86_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) => k20_pscomp_1(A) = 1 ) ) ), file(jordan,t86_jordan), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( k21_euclid(A) = k21_euclid(B) & k21_euclid(B) = k21_euclid(C) & r1_xreal_0(k22_euclid(A),k22_euclid(B)) & r1_xreal_0(k22_euclid(B),k22_euclid(C)) ) => r2_hidden(B,k3_topreal1(2,A,C)) ) ) ) ) ), file(goboard7,t8_goboard7), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t8_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(C,B) ) => r1_tarski(k2_xboole_0(A,C),B) ) ), file(xboole_1,t8_xboole_1), []). fof(t93_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_jordan24(2,B,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(A,B) & r1_xreal_0(3,k22_euclid(A)) ) ) ) ), file(jordan,t93_jordan), []). fof(t94_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_jordan24(2,B,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r2_hidden(A,B) & r1_xreal_0(k22_euclid(A),k1_real_1(3)) ) ) ) ), file(jordan,t94_jordan), []). fof(t99_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_jordan24(2,A,k23_euclid(k1_real_1(1),0),k23_euclid(1,0)) & r1_jordan2c(2,A,B) ) => r1_xboole_0(k3_topreal1(2,k23_euclid(0,3),k1_jordan21(A)),B) ) ) ) ), file(jordan,t99_jordan), []). fof(t9_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r1_xreal_0(B,C) & r2_hidden(D,k3_topreal1(2,k23_euclid(A,B),k23_euclid(A,C))) ) => ( k21_euclid(D) = A & r1_xreal_0(B,k22_euclid(D)) & r1_xreal_0(k22_euclid(D),C) ) ) ) ) ) ) ), file(jgraph_6,t9_jgraph_6), []). fof(t9_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( k21_euclid(k18_euclid(B,2,A)) = k3_xcmplx_0(B,k21_euclid(A)) & k22_euclid(k18_euclid(B,2,A)) = k3_xcmplx_0(B,k22_euclid(A)) ) ) ) ), file(topreal3,t9_topreal3), []).