% Mizar problem: t10_jordan22,jordan22,1079,20 fof(t10_jordan22,conjecture,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k2_jordan21(A),k4_jordan19(A)) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_metric_1,abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_membered,cc10_topreal6,cc11_membered,cc11_topreal6,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_4,cc1_jordan21,cc1_membered,cc1_relset_1,cc1_sprect_1,cc1_topreal6,cc1_xreal_0,cc20_membered,cc2_int_1,cc2_jordan21,cc2_membered,cc2_sprect_1,cc2_topreal6,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_sprect_1,cc3_topreal6,cc3_xreal_0,cc4_borsuk_2,cc4_int_1,cc4_membered,cc4_sprect_1,cc4_topreal6,cc4_xreal_0,cc5_topreal6,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_topreal6,cc8_xreal_0,cc9_membered,cc9_topreal6,commutativity_k1_gobrd14,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_topreal1,commutativity_k3_xboole_0,commutativity_k4_jordan1k,commutativity_k4_metric_1,commutativity_k5_subset_1,connectedness_r1_xreal_0,d10_toprns_1,d16_euclid,d1_absvalue,d1_euclid,d1_gobrd14,d1_jordan1k,d1_jordan9,d1_seq_4,d1_tarski,d29_pscomp_1,d2_gobrd13,d2_jordan19,d3_seq_4,d3_sppol_1,d3_tarski,d3_xboole_0,d4_jordan19,d4_seq_4,d5_real_1,d5_tarski,d7_euclid,d8_euclid,d9_toprns_1,dt_g1_metric_1,dt_g1_pre_topc,dt_k10_finseq_1,dt_k12_weierstr,dt_k13_euclid,dt_k13_finseq_1,dt_k14_euclid,dt_k15_euclid,dt_k16_complex1,dt_k17_pscomp_1,dt_k18_complex1,dt_k18_pscomp_1,dt_k19_pscomp_1,dt_k1_card_1,dt_k1_card_4,dt_k1_euclid,dt_k1_funct_1,dt_k1_gobrd14,dt_k1_jordan1k,dt_k1_jordan8,dt_k1_jordan9,dt_k1_matrix_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_real_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_topreal1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_euclid,dt_k20_pscomp_1,dt_k21_euclid,dt_k21_pscomp_1,dt_k22_euclid,dt_k23_euclid,dt_k2_funct_2,dt_k2_jordan19,dt_k2_jordan21,dt_k2_matrix_1,dt_k2_metric_1,dt_k2_newton,dt_k2_normsp_1,dt_k2_seq_1,dt_k2_seq_4,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k32_pscomp_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_goboard5,dt_k3_gobrd13,dt_k3_matrix_1,dt_k3_newton,dt_k3_pscomp_1,dt_k3_real_1,dt_k3_topreal1,dt_k3_xboole_0,dt_k4_finseq_2,dt_k4_finseq_4,dt_k4_gobrd13,dt_k4_jordan19,dt_k4_jordan1k,dt_k4_metric_1,dt_k4_pcomps_1,dt_k4_tarski,dt_k4_topreal1,dt_k4_xcmplx_0,dt_k5_binarith,dt_k5_gobrd13,dt_k5_numbers,dt_k5_ordinal2,dt_k5_pcomps_1,dt_k5_real_1,dt_k5_subset_1,dt_k5_topreal1,dt_k5_toprns_1,dt_k6_gobrd13,dt_k6_real_1,dt_k6_xcmplx_0,dt_k7_kurato_2,dt_k7_toprns_1,dt_k7_xcmplx_0,dt_k8_jordan6,dt_k8_kurato_2,dt_k9_jordan6,dt_k9_relat_1,dt_k9_weierstr,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_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_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc10_xreal_0,fc11_membered,fc11_sppol_2,fc11_xreal_0,fc12_membered,fc12_xreal_0,fc13_membered,fc13_xreal_0,fc14_membered,fc14_xreal_0,fc15_membered,fc15_xreal_0,fc16_membered,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_euclid,fc1_int_1,fc1_jordan1a,fc1_jordan21,fc1_jordan22,fc1_jordan8,fc1_revrot_1,fc1_sprect_3,fc1_struct_0,fc1_xreal_0,fc20_xreal_0,fc27_membered,fc27_xreal_0,fc28_membered,fc28_xreal_0,fc29_membered,fc29_xreal_0,fc2_euclid,fc2_jordan1a,fc2_jordan21,fc2_jordan22,fc2_jordan8,fc2_membered,fc2_sprect_1,fc2_topreal6,fc30_membered,fc30_xreal_0,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_int_1,fc3_revrot_1,fc3_sprect_1,fc3_xreal_0,fc4_gobrd14,fc4_int_1,fc4_jordan22,fc5_int_1,fc5_membered,fc5_xreal_0,fc6_int_1,fc6_membered,fc6_xreal_0,fc7_membered,fc7_xreal_0,fc8_int_1,fc8_membered,fc8_xreal_0,fc9_int_1,fc9_membered,fc9_xreal_0,fraenkel_a_1_2_jordan22,fraenkel_a_1_3_jordan22,free_g1_metric_1,free_g1_pre_topc,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,irreflexivity_r1_subset_1,irreflexivity_r2_subset_1,l1_jordan22,l2_jordan22,projectivity_k16_complex1,projectivity_k18_complex1,rc1_borsuk_4,rc1_int_1,rc1_jordan10,rc1_jordan1a,rc1_jordan21,rc1_membered,rc1_revrot_1,rc1_sprect_1,rc1_xreal_0,rc2_borsuk_4,rc2_int_1,rc2_jordan1a,rc2_sprect_1,rc2_topreal6,rc2_xreal_0,rc3_borsuk_4,rc3_jordan1a,rc3_sprect_1,rc3_struct_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,redefinition_k18_complex1,redefinition_k1_card_4,redefinition_k1_nat_1,redefinition_k1_real_1,redefinition_k1_struct_0,redefinition_k2_funct_2,redefinition_k2_normsp_1,redefinition_k2_seq_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_newton,redefinition_k3_pscomp_1,redefinition_k3_real_1,redefinition_k3_topreal1,redefinition_k4_jordan1k,redefinition_k4_metric_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_subset_1,redefinition_k6_real_1,redefinition_k7_kurato_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_subset_1,redefinition_r2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_toprns_1__e5_13_4_2_1__jordan22,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc4_boole,spc4_numerals,symmetry_r1_subset_1,symmetry_r1_xboole_0,symmetry_r2_subset_1,t105_real_2,t10_goboard7,t10_topreal1,t10_xreal_1,t12_gobrd14,t12_jordan3,t13_sppol_2,t14_jordan21,t15_gobrd14,t15_jordan21,t16_gobrd14,t16_jordan1a,t16_jordan21,t16_topmetr,t19_gobrd14,t19_jordan9,t1_arithm,t1_goboard5,t1_jordan10,t1_jordan1i,t1_numerals,t1_real,t1_subset,t20_gobrd14,t21_gobrd14,t27_jordan1a,t28_jordan21,t29_jordan21,t29_nat_1,t2_boole,t2_jordan10,t2_real,t2_subset,t2_tarski,t2_xreal_1,t30_gobrd13,t33_jordan9,t35_jordan21,t37_sppol_1,t38_nat_1,t3_jordan10,t3_real,t3_seq_2,t3_subset,t3_xboole_0,t40_weierstr,t41_jordan1g,t43_funct_2,t48_jordan21,t49_jgraph_1,t4_arithm,t4_jordan10,t4_real,t4_subset,t52_xreal_1,t55_jgraph_1,t56_euclid,t57_euclid,t58_kurato_2,t5_arithm,t5_real,t5_subset,t61_jordan21,t6_arithm,t6_boole,t6_jordan3,t6_jordan8,t6_real,t6_topreal1,t71_jordan21,t71_pscomp_1,t73_jordan2c,t77_jordan21,t7_boole,t7_jordan3,t7_real,t81_jordan21,t8_boole,t8_goboard7,t8_real,t8_xreal_1,t90_jordan1a,t92_real_1]), [file(jordan22,t10_jordan22)]). 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_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(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(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_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_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_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_borsuk_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_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_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v5_seqm_3(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & ~ v1_realset1(A) ) ) ), file(sprect_1,cc1_sprect_1), []). 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_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_int_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) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). 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_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_realset1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) ) ), file(sprect_1,cc2_sprect_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_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_seq_4(A) => ( v1_membered(A) & v2_membered(A) & v1_seq_4(A) & v2_seq_4(A) ) ) ) ), file(sprect_1,cc3_sprect_1), []). 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_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(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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( v1_seq_4(A) & v2_seq_4(A) ) => ( v1_membered(A) & v2_membered(A) & v3_seq_4(A) ) ) ) ), file(sprect_1,cc4_sprect_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_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(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_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_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(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(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_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). 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_k4_jordan1k,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v6_compts_1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(C) & v6_compts_1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => k4_jordan1k(A,B,C) = k4_jordan1k(A,C,B) ) ), file(jordan1k,k4_jordan1k), []). fof(commutativity_k4_metric_1,axiom,( ! [A,B,C] : ( ( v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_metric_1(A,B,C) = k4_metric_1(A,C,B) ) ), file(metric_1,k4_metric_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(d10_toprns_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(k15_euclid(A))) & m2_relset_1(B,k5_numbers,u1_struct_0(k15_euclid(A))) ) => ( v3_toprns_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( C = k7_toprns_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_numbers) => ~ ( ~ r1_xreal_0(D,0) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & r1_xreal_0(E,F) & r1_xreal_0(D,k5_toprns_1(A,k20_euclid(A,k2_normsp_1(k15_euclid(A),B,F),C))) ) ) ) ) ) ) ) ) ) ), file(toprns_1,d10_toprns_1), []). 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_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xreal_0(0,A) => k16_complex1(A) = A ) & ( ~ r1_xreal_0(0,A) => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ), file(absvalue,d1_absvalue), []). 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_gobrd14,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_numbers) => ( D = k1_gobrd14(A,B,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) & ? [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(A))) & E = B & F = C & D = k4_metric_1(k14_euclid(A),E,F) ) ) ) ) ) ) ) ), file(gobrd14,d1_gobrd14), []). fof(d1_jordan1k,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)))) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( D = k1_jordan1k(A,B,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k14_euclid(A))))) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k14_euclid(A))))) & B = E & C = F & D = k9_weierstr(k14_euclid(A),E,F) ) ) ) ) ) ) ) ), file(jordan1k,d1_jordan1k), []). fof(d1_jordan9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( v2_connsp_1(A,k15_euclid(2)) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_sprect_2(C) & ~ v5_seqm_3(C) & v1_topreal1(C) & v2_topreal1(C) & v1_finseq_6(C,u1_struct_0(k15_euclid(2))) & v1_goboard5(C) & v2_goboard5(C) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ( C = k1_jordan9(A,B) <=> ( r1_goboard1(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B)) & ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(1,D) & r1_xreal_0(k1_nat_1(D,1),k3_finseq_1(k1_jordan8(A,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_matrix_1(k1_jordan8(A,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(D,1),k1_matrix_1(k1_jordan8(A,B))) & r2_hidden(k32_pscomp_1(A),k3_goboard5(k1_jordan8(A,B),D,k5_binarith(k1_matrix_1(k1_jordan8(A,B)),1))) & k32_pscomp_1(A) != k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k5_binarith(k1_matrix_1(k1_jordan8(A,B)),1)) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_xreal_0(k1_nat_1(D,2),k3_finseq_1(C)) ) => ( ( ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A) & r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),D),A) ) => r1_gobrd13(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B),D) ) & ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A) => ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),D),A) | r3_gobrd13(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B),D) ) ) & ( ~ r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A) => r2_gobrd13(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B),D) ) ) ) ) ) ) ) ) ) ) ), file(jordan9,d1_jordan9), []). fof(d1_seq_4,axiom,( ! [A] : ( v2_membered(A) => ( v1_seq_4(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xreal_0(C,B) ) ) ) ) ) ), file(seq_4,d1_seq_4), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d29_pscomp_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k15_euclid(2)),k1_numbers) & m2_relset_1(A,u1_struct_0(k15_euclid(2)),k1_numbers) ) => ( A = k17_pscomp_1 <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k2_seq_1(u1_struct_0(k15_euclid(2)),k1_numbers,A,B) = k22_euclid(B) ) ) ) ), file(pscomp_1,d29_pscomp_1), []). fof(d2_gobrd13,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_goboard1(u1_struct_0(k15_euclid(2)),A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k3_gobrd13(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(B)) & r2_hidden(k4_tarski(G,H),k2_matrix_1(B)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(2)),B,E,F) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),B,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & D = k3_goboard5(B,E,F) ) & ~ ( k1_nat_1(E,1) = G & F = H & D = k3_goboard5(B,E,k5_binarith(F,1)) ) & ~ ( E = k1_nat_1(G,1) & F = H & D = k3_goboard5(B,G,H) ) & ~ ( E = G & F = k1_nat_1(H,1) & D = k3_goboard5(B,k5_binarith(E,1),H) ) ) ) ) ) ) ) ) ) ) ) ) ), file(gobrd13,d2_gobrd13), []). fof(d2_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( B = k2_jordan19(A) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k7_kurato_2(u1_struct_0(k15_euclid(2)),B,C) = k9_jordan6(k5_topreal1(2,k1_jordan9(A,C))) ) ) ) ) ), file(jordan19,d2_jordan19), []). fof(d3_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_seq_4(A) <=> ( v2_seq_4(A) & v1_seq_4(A) ) ) ) ), file(seq_4,d3_seq_4), []). 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_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_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k4_jordan19(A) = k8_kurato_2(k15_euclid(2),k2_jordan19(A)) ) ), file(jordan19,d4_jordan19), []). fof(d4_seq_4,axiom,( ! [A] : ( v2_membered(A) => ( v1_seq_4(A) => ( v1_xboole_0(A) | ! [B] : ( v1_xreal_0(B) => ( B = k2_seq_4(A) <=> ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xreal_0(C,B) ) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xreal_0(C,0) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,A) & ~ r1_xreal_0(D,k6_xcmplx_0(B,C)) ) ) ) ) ) ) ) ) ) ) ), file(seq_4,d4_seq_4), []). 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(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). 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(d9_toprns_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(k15_euclid(A))) & m2_relset_1(B,k5_numbers,u1_struct_0(k15_euclid(A))) ) => ( v3_toprns_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) & ! [D] : ( m1_subset_1(D,k1_numbers) => ~ ( ~ r1_xreal_0(D,0) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & r1_xreal_0(E,F) & r1_xreal_0(D,k5_toprns_1(A,k20_euclid(A,k2_normsp_1(k15_euclid(A),B,F),C))) ) ) ) ) ) ) ) ) ), file(toprns_1,d9_toprns_1), []). 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_weierstr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) ) => m1_subset_1(k12_weierstr(A,B,C),k1_numbers) ) ), file(weierstr,k12_weierstr), []). 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_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_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_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). 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_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k18_complex1(A),k1_numbers) ) ), file(complex1,k18_complex1), []). 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_k19_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k19_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k19_pscomp_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_card_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_card_4(A,B),k1_numbers,k5_numbers) ) ), file(card_4,k1_card_4), []). 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_jordan1k,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => m1_subset_1(k1_jordan1k(A,B,C),k1_numbers) ) ), file(jordan1k,k1_jordan1k), []). fof(dt_k1_jordan8,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( v1_matrix_1(k1_jordan8(A,B)) & m2_finseq_1(k1_jordan8(A,B),k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan8,k1_jordan8), []). fof(dt_k1_jordan9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k1_jordan9(A,B)) & v1_sprect_2(k1_jordan9(A,B)) & ~ v5_seqm_3(k1_jordan9(A,B)) & v1_topreal1(k1_jordan9(A,B)) & v2_topreal1(k1_jordan9(A,B)) & v1_finseq_6(k1_jordan9(A,B),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_jordan9(A,B)) & v2_goboard5(k1_jordan9(A,B)) & m2_finseq_1(k1_jordan9(A,B),u1_struct_0(k15_euclid(2))) ) ) ), file(jordan9,k1_jordan9), []). fof(dt_k1_matrix_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_1(A) ) => m2_subset_1(k1_matrix_1(A),k1_numbers,k5_numbers) ) ), file(matrix_1,k1_matrix_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). 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_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_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_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(k20_euclid(A,B,C),u1_struct_0(k15_euclid(A))) ) ), file(euclid,k20_euclid), []). 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_k21_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k21_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k21_pscomp_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_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_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_funct_1(k2_jordan19(A)) & v1_funct_2(k2_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m2_relset_1(k2_jordan19(A),k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan19,k2_jordan19), []). 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_matrix_1,axiom,( $true ), file(matrix_1,k2_matrix_1), []). fof(dt_k2_metric_1,axiom,( ! [A,B,C] : ( ( l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_metric_1(A,B,C),k1_numbers) ) ), file(metric_1,k2_metric_1), []). fof(dt_k2_newton,axiom,( $true ), file(newton,k2_newton), []). fof(dt_k2_normsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k2_normsp_1(A,B,C),u1_struct_0(A)) ) ), file(normsp_1,k2_normsp_1), []). fof(dt_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ), file(seq_1,k2_seq_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_tarski,axiom,( $true ), file(tarski,k2_tarski), []). 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_k32_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k32_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k32_pscomp_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_goboard5,axiom,( ! [A,B,C] : ( ( v1_matrix_1(A) & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k3_goboard5(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard5,k3_goboard5), []). fof(dt_k3_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k3_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k3_gobrd13), []). fof(dt_k3_matrix_1,axiom,( ! [A,B,C,D] : ( ( v1_matrix_1(B) & m1_finseq_1(B,k3_finseq_2(A)) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) ) => m1_subset_1(k3_matrix_1(A,B,C,D),A) ) ), file(matrix_1,k3_matrix_1), []). fof(dt_k3_newton,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & v4_ordinal2(B) ) => m1_subset_1(k3_newton(A,B),k1_numbers) ) ), file(newton,k3_newton), []). 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_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_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_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k4_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k4_gobrd13), []). fof(dt_k4_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => m1_subset_1(k4_jordan19(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan19,k4_jordan19), []). fof(dt_k4_jordan1k,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v6_compts_1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(C) & v6_compts_1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => m1_subset_1(k4_jordan1k(A,B,C),k1_numbers) ) ), file(jordan1k,k4_jordan1k), []). fof(dt_k4_metric_1,axiom,( ! [A,B,C] : ( ( v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_metric_1(A,B,C),k1_numbers) ) ), file(metric_1,k4_metric_1), []). fof(dt_k4_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => m1_subset_1(k4_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pcomps_1,k4_pcomps_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k4_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k4_topreal1), []). 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_binarith,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k5_binarith(A,B),k1_numbers,k5_numbers) ) ), file(binarith,k5_binarith), []). fof(dt_k5_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k5_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k5_gobrd13), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_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_topreal1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k5_topreal1(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k5_topreal1), []). fof(dt_k5_toprns_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k5_toprns_1(A,B),k1_numbers) ) ), file(toprns_1,k5_toprns_1), []). fof(dt_k6_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k6_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k6_gobrd13), []). 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_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_kurato_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k7_kurato_2(A,B,C),k1_zfmisc_1(A)) ) ), file(kurato_2,k7_kurato_2), []). fof(dt_k7_toprns_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(k15_euclid(A))) & m1_relset_1(B,k5_numbers,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k7_toprns_1(A,B),u1_struct_0(k15_euclid(A))) ) ), file(toprns_1,k7_toprns_1), []). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). fof(dt_k8_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_xboole_0(k8_jordan6(A)) & m1_subset_1(k8_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan6,k8_jordan6), []). fof(dt_k8_kurato_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k8_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(kurato_2,k8_kurato_2), []). fof(dt_k9_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_xboole_0(k9_jordan6(A)) & m1_subset_1(k9_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan6,k9_jordan6), []). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_k9_weierstr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) ) => m1_subset_1(k9_weierstr(A,B,C),k1_numbers) ) ), file(weierstr,k9_weierstr), []). 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_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). 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_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_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_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). 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_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_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_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_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_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_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_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). 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_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_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(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). 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(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). 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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k9_jordan6(A)) & v4_pre_topc(k9_jordan6(A),k15_euclid(2)) & v6_compts_1(k9_jordan6(A),k15_euclid(2)) & v1_jordan2c(k9_jordan6(A),2) ) ) ), file(jordan1a,fc1_jordan1a), []). fof(fc1_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k9_jordan6(A)) & v4_pre_topc(k9_jordan6(A),k15_euclid(2)) & v1_jordan2c(k9_jordan6(A),2) & v6_compts_1(k9_jordan6(A),k15_euclid(2)) & v1_jordan21(k9_jordan6(A)) ) ) ), file(jordan21,fc1_jordan21), []). fof(fc1_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k8_jordan6(A)) & v4_pre_topc(k8_jordan6(A),k15_euclid(2)) & v2_connsp_1(k8_jordan6(A),k15_euclid(2)) & v1_jordan2c(k8_jordan6(A),2) & v6_compts_1(k8_jordan6(A),k15_euclid(2)) & v1_jordan21(k8_jordan6(A)) ) ) ), file(jordan22,fc1_jordan22), []). fof(fc1_jordan8,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k1_jordan8(A,B)) & ~ v3_relat_1(k1_jordan8(A,B)) & v1_funct_1(k1_jordan8(A,B)) & v1_finset_1(k1_jordan8(A,B)) & v1_finseq_1(k1_jordan8(A,B)) & v1_matrix_1(k1_jordan8(A,B)) & v3_goboard1(k1_jordan8(A,B)) & v4_goboard1(k1_jordan8(A,B)) ) ) ), file(jordan8,fc1_jordan8), []). fof(fc1_revrot_1,axiom,( ! [A] : ( ( ~ v3_realset2(A) & l1_struct_0(A) ) => ( ~ v1_xboole_0(u1_struct_0(A)) & ~ v1_realset1(u1_struct_0(A)) ) ) ), file(revrot_1,fc1_revrot_1), []). fof(fc1_sprect_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k5_topreal1(2,A)) & ~ v1_sppol_1(k5_topreal1(2,A)) & ~ v2_sppol_1(k5_topreal1(2,A)) & v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) & v1_topreal2(k5_topreal1(2,A)) ) ) ), file(sprect_3,fc1_sprect_3), []). 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_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(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). 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_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k8_jordan6(A)) & v4_pre_topc(k8_jordan6(A),k15_euclid(2)) & v6_compts_1(k8_jordan6(A),k15_euclid(2)) & v1_jordan2c(k8_jordan6(A),2) ) ) ), file(jordan1a,fc2_jordan1a), []). fof(fc2_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k8_jordan6(A)) & v4_pre_topc(k8_jordan6(A),k15_euclid(2)) & v1_jordan2c(k8_jordan6(A),2) & v6_compts_1(k8_jordan6(A),k15_euclid(2)) & v1_jordan21(k8_jordan6(A)) ) ) ), file(jordan21,fc2_jordan21), []). fof(fc2_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k9_jordan6(A)) & v4_pre_topc(k9_jordan6(A),k15_euclid(2)) & v2_connsp_1(k9_jordan6(A),k15_euclid(2)) & v1_jordan2c(k9_jordan6(A),2) & v6_compts_1(k9_jordan6(A),k15_euclid(2)) & v1_jordan21(k9_jordan6(A)) ) ) ), file(jordan22,fc2_jordan22), []). fof(fc2_jordan8,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k1_jordan8(A,B)) & ~ v3_relat_1(k1_jordan8(A,B)) & v1_funct_1(k1_jordan8(A,B)) & v1_finset_1(k1_jordan8(A,B)) & v1_finseq_1(k1_jordan8(A,B)) & v1_matrix_1(k1_jordan8(A,B)) & v3_goboard1(k1_jordan8(A,B)) & v4_goboard1(k1_jordan8(A,B)) & v5_goboard1(k1_jordan8(A,B)) & v6_goboard1(k1_jordan8(A,B)) ) ) ), file(jordan8,fc2_jordan8), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_sprect_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_realset1(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) ) => ~ v1_xboole_0(k5_topreal1(A,B)) ) ), file(sprect_1,fc2_sprect_1), []). 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(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(fc3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), []). fof(fc3_revrot_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & ~ v3_realset2(k15_euclid(A)) ) ) ), file(revrot_1,fc3_revrot_1), []). fof(fc3_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) ) ), file(sprect_1,fc3_sprect_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(fc4_gobrd14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k5_topreal1(2,A)) & v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) & v2_connsp_1(k5_topreal1(2,A),k15_euclid(2)) & v2_jordan1(k5_topreal1(2,A)) & v1_jordan2c(k5_topreal1(2,A),2) & ~ v1_sppol_1(k5_topreal1(2,A)) & ~ v2_sppol_1(k5_topreal1(2,A)) & v1_topreal2(k5_topreal1(2,A)) & v2_tops_1(k5_topreal1(2,A),k15_euclid(2)) ) ) ), file(gobrd14,fc4_gobrd14), []). fof(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => v6_compts_1(k4_jordan19(A),k15_euclid(2)) ) ), file(jordan22,fc4_jordan22), []). fof(fc5_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). 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_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), []). 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_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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), []). 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_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_1_2_jordan22,axiom,( ! [A,B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_2_jordan22(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(B,C)))) & ~ r1_xreal_0(C,0) ) ) ) ), file(jordan22,a_1_2_jordan22), []). fof(fraenkel_a_1_3_jordan22,axiom,( ! [A,B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_3_jordan22(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(B,C))))) & ~ r1_xreal_0(C,0) ) ) ) ), file(jordan22,a_1_3_jordan22), []). 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_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(involutiveness_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_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(l1_jordan22,axiom,( k15_euclid(2) = k5_pcomps_1(k14_euclid(2)) ), file(jordan22,l1_jordan22), []). fof(l2_jordan22,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r2_hidden(A,k2_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k17_pscomp_1,B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,B) & k2_seq_1(u1_struct_0(k15_euclid(2)),k1_numbers,k17_pscomp_1,C) = A ) ) ) ) ) ), file(jordan22,l2_jordan22), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ), file(complex1,k18_complex1), []). 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_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_jordan10,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)) & v1_jordan2c(A,2) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) ) ), file(jordan10,rc1_jordan10), []). 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_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_revrot_1,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & ~ v5_seqm_3(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_finseq_6(B,A) & ~ v1_realset1(B) ) ) ), file(revrot_1,rc1_revrot_1), []). fof(rc1_sprect_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v5_seqm_3(A) ) ), file(sprect_1,rc1_sprect_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). 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_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). 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_sprect_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) ) ), file(sprect_1,rc2_sprect_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_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_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_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_sprect_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v1_seq_4(A) & v2_seq_4(A) ) ), file(sprect_1,rc3_sprect_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_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(redefinition_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(A) = k16_complex1(A) ) ), file(complex1,k18_complex1), []). fof(redefinition_k1_card_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_card_4(A,B) = k2_newton(A,B) ) ), file(card_4,k1_card_4), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_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_normsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => k2_normsp_1(A,B,C) = k1_funct_1(B,C) ) ), file(normsp_1,k2_normsp_1), []). fof(redefinition_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(seq_1,k2_seq_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k3_newton,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & v4_ordinal2(B) ) => k3_newton(A,B) = k2_newton(A,B) ) ), file(newton,k3_newton), []). 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_jordan1k,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v6_compts_1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(C) & v6_compts_1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => k4_jordan1k(A,B,C) = k1_jordan1k(A,B,C) ) ), file(jordan1k,k4_jordan1k), []). fof(redefinition_k4_metric_1,axiom,( ! [A,B,C] : ( ( v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_metric_1(A,B,C) = k2_metric_1(A,B,C) ) ), file(metric_1,k4_metric_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_k6_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_k7_kurato_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) & m1_subset_1(C,k5_numbers) ) => k7_kurato_2(A,B,C) = k1_funct_1(B,C) ) ), file(kurato_2,k7_kurato_2), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). 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_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_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(s1_toprns_1__e5_13_4_2_1__jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(k15_euclid(2))) & m2_relset_1(B,k5_numbers,u1_struct_0(k15_euclid(2))) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k2_normsp_1(k15_euclid(2),B,C) = k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(A,C)))) ) ) ) ), file(jordan22,s1_toprns_1__e5_13_4_2_1__jordan22), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc4_boole,axiom,( ~ v1_xboole_0(4) ), file(boole,spc4_boole), []). fof(spc4_numerals,axiom, ( v2_xreal_0(4) & m1_subset_1(4,k5_numbers) ), file(numerals,spc4_numerals), []). 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(t105_real_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ ( ~ r1_xreal_0(k2_xcmplx_0(A,k4_xcmplx_0(B)),0) & ~ r1_xreal_0(0,k6_xcmplx_0(B,A)) & ~ r1_xreal_0(0,k2_xcmplx_0(B,k4_xcmplx_0(A))) & ~ r1_xreal_0(k6_xcmplx_0(A,C),k2_xcmplx_0(B,k4_xcmplx_0(C))) & ~ r1_xreal_0(k2_xcmplx_0(A,k4_xcmplx_0(C)),k6_xcmplx_0(B,C)) & ~ r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) ) => r1_xreal_0(A,B) ) ) ) ) ), file(real_2,t105_real_2), []). fof(t10_goboard7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_matrix_1(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(D)) & r1_xreal_0(1,C) & r1_xreal_0(C,k1_matrix_1(D)) ) => r2_hidden(k4_tarski(B,C),k2_matrix_1(D)) ) ) ) ) ) ), file(goboard7,t10_goboard7), []). fof(t10_topreal1,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))) => ( ( r1_xreal_0(k22_euclid(A),k22_euclid(B)) & r2_hidden(C,k3_topreal1(2,A,B)) ) => ( r1_xreal_0(k22_euclid(A),k22_euclid(C)) & r1_xreal_0(k22_euclid(C),k22_euclid(B)) ) ) ) ) ) ), file(topreal1,t10_topreal1), []). fof(t10_xreal_1,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(C,D) & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ), file(xreal_1,t10_xreal_1), []). fof(t12_gobrd14,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))) => ( ( r1_xreal_0(A,k21_euclid(E)) & r1_xreal_0(k21_euclid(E),B) & r1_xreal_0(C,k22_euclid(E)) & r1_xreal_0(k22_euclid(E),D) & r1_xreal_0(A,k21_euclid(F)) & r1_xreal_0(k21_euclid(F),B) & r1_xreal_0(C,k22_euclid(F)) & r1_xreal_0(k22_euclid(F),D) ) => r1_xreal_0(k1_gobrd14(2,E,F),k2_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) ), file(gobrd14,t12_gobrd14), []). fof(t12_jordan3,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ ( r1_xreal_0(B,A) & ~ r1_xreal_0(k2_xcmplx_0(A,1),B) ) => r1_xreal_0(A,k5_binarith(B,1)) ) ) ) ), file(jordan3,t12_jordan3), []). fof(t13_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,k5_topreal1(2,A)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,C) & r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r2_hidden(B,k4_topreal1(2,A,C)) ) ) ) ) ) ), file(sppol_2,t13_sppol_2), []). fof(t14_jordan21,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r2_hidden(k4_tarski(1,1),k2_matrix_1(k1_jordan8(A,B))) ) ) ), file(jordan21,t14_jordan21), []). fof(t15_gobrd14,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_1(D) & v3_goboard1(D) & v4_goboard1(D) & v5_goboard1(D) & v6_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(D)) & r2_hidden(k4_tarski(k1_nat_1(A,C),B),k2_matrix_1(D)) ) => k1_gobrd14(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),D,A,B),k3_matrix_1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(A,C),B)) = k5_real_1(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(A,C),B)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),D,A,B))) ) ) ) ) ) ), file(gobrd14,t15_gobrd14), []). fof(t15_jordan21,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r2_hidden(k4_tarski(1,2),k2_matrix_1(k1_jordan8(A,B))) ) ) ), file(jordan21,t15_jordan21), []). fof(t16_gobrd14,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_1(D) & v3_goboard1(D) & v4_goboard1(D) & v5_goboard1(D) & v6_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(D)) & r2_hidden(k4_tarski(A,k1_nat_1(B,C)),k2_matrix_1(D)) ) => k1_gobrd14(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),D,A,B),k3_matrix_1(u1_struct_0(k15_euclid(2)),D,A,k1_nat_1(B,C))) = k5_real_1(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),D,A,k1_nat_1(B,C))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),D,A,B))) ) ) ) ) ) ), file(gobrd14,t16_gobrd14), []). fof(t16_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_tarski(k9_jordan6(A),A) & r1_tarski(k8_jordan6(A),A) ) ) ), file(jordan1a,t16_jordan1a), []). fof(t16_jordan21,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r2_hidden(k4_tarski(2,1),k2_matrix_1(k1_jordan8(A,B))) ) ) ), file(jordan21,t16_jordan21), []). fof(t16_topmetr,axiom,( ! [A] : ( l1_metric_1(A) => ( u1_struct_0(A) = u1_struct_0(k5_pcomps_1(A)) & u1_pre_topc(k5_pcomps_1(A)) = k4_pcomps_1(A) ) ) ), file(topmetr,t16_topmetr), []). fof(t19_gobrd14,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v6_compts_1(D,k15_euclid(2)) & ~ v1_sppol_1(D) & ~ v2_sppol_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(k1_jordan8(D,C))) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_1(k1_jordan8(D,C))) ) => k1_gobrd14(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),A,k1_nat_1(B,1))) = k6_real_1(k5_real_1(k19_pscomp_1(D),k21_pscomp_1(D)),k1_card_4(2,C)) ) ) ) ) ) ), file(gobrd14,t19_gobrd14), []). fof(t19_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_1(A) & v3_goboard1(A) & v4_goboard1(A) & v5_goboard1(A) & v6_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xreal_0(1,D) & r1_xreal_0(k1_nat_1(D,1),k1_matrix_1(A)) ) => ( r2_hidden(B,k3_goboard5(A,C,D)) <=> ( r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,D)),k21_euclid(B)) & r1_xreal_0(k21_euclid(B),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1),D))) & r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,D)),k22_euclid(B)) & r1_xreal_0(k22_euclid(B),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,k1_nat_1(D,1)))) ) ) ) ) ) ) ) ), file(jordan9,t19_jordan9), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_goboard5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(k4_tarski(B,C),k2_matrix_1(A)) => ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) & r1_xreal_0(1,C) & r1_xreal_0(C,k1_matrix_1(A)) ) ) ) ) ) ), file(goboard5,t1_goboard5), []). fof(t1_jordan10,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v2_connsp_1(E,k15_euclid(2)) & v6_compts_1(E,k15_euclid(2)) & ~ v1_sppol_1(E) & ~ v2_sppol_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(k1_jordan9(E,B))) & r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B))) & r2_hidden(k4_tarski(C,k1_nat_1(D,1)),k2_matrix_1(k1_jordan8(E,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),C,D) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),k1_nat_1(A,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),C,k1_nat_1(D,1)) & r1_xreal_0(k3_finseq_1(k1_jordan8(E,B)),C) ) ) ) ) ) ) ), file(jordan10,t1_jordan10), []). fof(t1_jordan1i,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(B,A) | v1_jordan2c(C,A) ) => v1_jordan2c(k5_subset_1(u1_struct_0(k15_euclid(A)),B,C),A) ) ) ) ) ), file(jordan1i,t1_jordan1i), []). 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(t20_gobrd14,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v6_compts_1(D,k15_euclid(2)) & ~ v1_sppol_1(D) & ~ v2_sppol_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(k1_jordan8(D,C))) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_1(k1_jordan8(D,C))) ) => k1_gobrd14(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),k1_nat_1(A,1),B)) = k6_real_1(k5_real_1(k20_pscomp_1(D),k18_pscomp_1(D)),k1_card_4(2,C)) ) ) ) ) ) ), file(gobrd14,t20_gobrd14), []). fof(t21_gobrd14,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xreal_0(B,0) & ~ r1_xreal_0(C,0) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( ~ r1_xreal_0(D,1) & ~ r1_xreal_0(B,k1_gobrd14(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,1),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,2))) & ~ r1_xreal_0(C,k1_gobrd14(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,1),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),2,1))) ) ) ) ) ) ) ), file(gobrd14,t21_gobrd14), []). fof(t27_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_jordan2c(A,2) => v3_seq_4(k2_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k17_pscomp_1,A)) ) ) ), file(jordan1a,t27_jordan1a), []). fof(t28_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k18_pscomp_1(A) = k18_pscomp_1(k9_jordan6(A)) ) ), file(jordan21,t28_jordan21), []). fof(t29_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k20_pscomp_1(A) = k20_pscomp_1(k9_jordan6(A)) ) ), file(jordan21,t29_jordan21), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_jordan10,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v2_connsp_1(E,k15_euclid(2)) & v6_compts_1(E,k15_euclid(2)) & ~ v1_sppol_1(E) & ~ v2_sppol_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(k1_jordan9(E,B))) & r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B))) & r2_hidden(k4_tarski(C,k1_nat_1(D,1)),k2_matrix_1(k1_jordan8(E,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),C,k1_nat_1(D,1)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),k1_nat_1(A,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),C,D) & r1_xreal_0(C,1) ) ) ) ) ) ) ), file(jordan10,t2_jordan10), []). 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_gobrd13,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_1(C) & v3_goboard1(C) & v4_goboard1(C) & v5_goboard1(C) & v6_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(B)) & r1_goboard1(u1_struct_0(k15_euclid(2)),B,C) ) => k5_subset_1(u1_struct_0(k15_euclid(2)),k4_gobrd13(B,C,A),k3_gobrd13(B,C,A)) = k4_topreal1(2,B,A) ) ) ) ) ), file(gobrd13,t30_gobrd13), []). fof(t33_jordan9,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( ~ v1_xboole_0(C) & v6_compts_1(C,k15_euclid(2)) & ~ v1_sppol_1(C) & ~ v2_sppol_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( v2_connsp_1(C,k15_euclid(2)) & r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(k1_jordan9(C,B))) ) => ( r1_xboole_0(k4_gobrd13(k1_jordan9(C,B),k1_jordan8(C,B),A),C) & ~ r1_xboole_0(k3_gobrd13(k1_jordan9(C,B),k1_jordan8(C,B),A),C) ) ) ) ) ) ), file(jordan9,t33_jordan9), []). 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(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(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_jordan10,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v2_connsp_1(E,k15_euclid(2)) & v6_compts_1(E,k15_euclid(2)) & ~ v1_sppol_1(E) & ~ v2_sppol_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(k1_jordan9(E,B))) & r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B))) & r2_hidden(k4_tarski(k1_nat_1(C,1),D),k2_matrix_1(k1_jordan8(E,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),C,D) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),k1_nat_1(A,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),k1_nat_1(C,1),D) & r1_xreal_0(D,1) ) ) ) ) ) ) ), file(jordan10,t3_jordan10), []). 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_seq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xreal_0(A,0) => ( ~ r1_xreal_0(k7_xcmplx_0(A,2),0) & ~ r1_xreal_0(k7_xcmplx_0(A,4),0) ) ) ) ), file(seq_2,t3_seq_2), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_xboole_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), []). fof(t40_weierstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) => ( ( v6_compts_1(B,k5_pcomps_1(A)) & v6_compts_1(C,k5_pcomps_1(A)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,C) ) => ( r1_xreal_0(k9_weierstr(A,B,C),k4_metric_1(A,D,E)) & r1_xreal_0(k4_metric_1(A,D,E),k12_weierstr(A,B,C)) ) ) ) ) ) ) ) ) ), file(weierstr,t40_weierstr), []). fof(t41_jordan1g,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k3_real_1(k18_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))),k20_pscomp_1(k5_topreal1(2,k1_jordan9(B,A)))) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) ) ) ), file(jordan1g,t41_jordan1g), []). fof(t43_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( B != k1_xboole_0 => ! [E] : ( ? [F] : ( r2_hidden(F,A) & r2_hidden(F,C) & E = k1_funct_1(D,F) ) => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ), file(funct_2,t43_funct_2), []). fof(t48_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)))) ) => k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),2),k21_pscomp_1(A))),A) = k1_struct_0(k15_euclid(2),k2_jordan21(A)) ) ), file(jordan21,t48_jordan21), []). fof(t49_jgraph_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(k5_toprns_1(2,k20_euclid(2,A,B)),k3_real_1(k18_complex1(k5_real_1(k21_euclid(A),k21_euclid(B))),k18_complex1(k5_real_1(k22_euclid(A),k22_euclid(B))))) ) ) ), file(jgraph_1,t49_jgraph_1), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_jordan10,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v2_connsp_1(E,k15_euclid(2)) & v6_compts_1(E,k15_euclid(2)) & ~ v1_sppol_1(E) & ~ v2_sppol_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(k1_jordan9(E,B))) & r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B))) & r2_hidden(k4_tarski(k1_nat_1(C,1),D),k2_matrix_1(k1_jordan8(E,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),k1_nat_1(C,1),D) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(E,B),k1_nat_1(A,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(E,B),C,D) & r1_xreal_0(k1_matrix_1(k1_jordan8(E,B)),D) ) ) ) ) ) ) ), file(jordan10,t4_jordan10), []). 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(t52_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(B,A) & r1_xreal_0(k6_xcmplx_0(B,A),0) ) ) ) ), file(xreal_1,t52_xreal_1), []). fof(t55_jgraph_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) => ( ( v6_compts_1(B,k5_pcomps_1(A)) & v6_compts_1(C,k5_pcomps_1(A)) ) => ( B = k1_xboole_0 | C = k1_xboole_0 | ( r1_xboole_0(B,C) <=> ~ r1_xreal_0(k9_weierstr(A,B,C),0) ) ) ) ) ) ) ), file(jgraph_1,t55_jgraph_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(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(t58_kurato_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & m2_relset_1(B,k5_numbers,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(k15_euclid(A))) & m2_relset_1(D,k5_numbers,u1_struct_0(k15_euclid(A))) & v3_toprns_1(D,A) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => r2_hidden(k2_normsp_1(k15_euclid(A),D,E),k7_kurato_2(u1_struct_0(k15_euclid(A)),B,E)) ) & C = k7_toprns_1(A,D) ) => r2_hidden(C,k8_kurato_2(k15_euclid(A),B)) ) ) ) ) ), file(kurato_2,t58_kurato_2), []). fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). 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_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_xreal_0(k21_pscomp_1(A),k22_euclid(k2_jordan21(k9_jordan6(A)))) ) ), file(jordan21,t61_jordan21), []). 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_jordan3,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ( r1_xreal_0(1,k5_binarith(A,B)) | r1_xreal_0(1,k6_xcmplx_0(A,B)) ) => k2_xcmplx_0(k5_binarith(A,B),B) = A ) ) ) ), file(jordan3,t6_jordan3), []). fof(t6_jordan8,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B,C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_1(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ~ ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_goboard1(B,C,D) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(D)) & k4_finseq_4(k5_numbers,B,C,A) = k3_matrix_1(B,D,E,F) & r2_hidden(k4_tarski(G,H),k2_matrix_1(D)) & k4_finseq_4(k5_numbers,B,C,k1_nat_1(A,1)) = k3_matrix_1(B,D,G,H) & ~ ( ~ ( E = G & k1_nat_1(F,1) = H ) & ~ ( k1_nat_1(E,1) = G & F = H ) & ~ ( E = k1_nat_1(G,1) & F = H ) & ~ ( E = G & F = k1_nat_1(H,1) ) ) ) ) ) ) ) ) ) ) ) ), file(jordan8,t6_jordan8), []). 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(t71_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r2_hidden(k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(A,B)))),k9_jordan6(k5_topreal1(2,k1_jordan9(A,B)))) ) ) ), file(jordan21,t71_jordan21), []). fof(t71_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,B) => ( r1_xreal_0(k18_pscomp_1(B),k21_euclid(A)) & r1_xreal_0(k21_euclid(A),k20_pscomp_1(B)) & r1_xreal_0(k21_pscomp_1(B),k22_euclid(A)) & r1_xreal_0(k22_euclid(A),k19_pscomp_1(B)) ) ) ) ) ), file(pscomp_1,t71_pscomp_1), []). fof(t73_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)))) => ( v6_compts_1(B,k15_euclid(A)) => v1_jordan2c(B,A) ) ) ) ), file(jordan2c,t73_jordan2c), []). fof(t77_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( ~ r1_xreal_0(B,0) & r1_xreal_0(k22_euclid(k2_jordan21(A)),k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(A,B)))))) ) ) ) ), file(jordan21,t77_jordan21), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_jordan3,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(A,B) => r1_xreal_0(k5_binarith(A,1),B) ) ) ) ), file(jordan3,t7_jordan3), []). 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(t81_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(B,C) => ( r1_xreal_0(B,0) | r1_xreal_0(k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(A,B))))),k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(2,k1_jordan9(A,C)))))) ) ) ) ) ) ), file(jordan21,t81_jordan21), []). 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_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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t8_xreal_1), []). fof(t90_jordan1a,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v2_connsp_1(C,k15_euclid(2)) & v6_compts_1(C,k15_euclid(2)) & ~ v1_sppol_1(C) & ~ v2_sppol_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( ~ r1_xreal_0(B,A) & r1_xreal_0(k21_pscomp_1(k5_topreal1(2,k1_jordan9(C,B))),k21_pscomp_1(k5_topreal1(2,k1_jordan9(C,A)))) ) ) ) ) ), file(jordan1a,t90_jordan1a), []). fof(t92_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) ) & ~ ( ( ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) ) | ( r1_xreal_0(A,B) & ~ r1_xreal_0(D,C) ) ) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ) ), file(real_1,t92_real_1), []).