% Mizar problem: t9_jordan1j,jordan1j,599,36 fof(t9_jordan1j,conjecture,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( 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)))) ) => ( r2_hidden(k34_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))),k2_relat_1(k1_jordan1e(B,A))) & r2_hidden(k34_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))),k5_topreal1(2,k1_jordan1e(B,A))) ) ) ) ), inference(mizar_bg_added,[status(thm)],[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_finseq_1,cc1_finseq_5,cc1_jordan1b,cc1_membered,cc1_relset_1,cc1_sppol_2,cc1_sprect_1,cc1_topreal6,cc1_xreal_0,cc20_membered,cc2_int_1,cc2_membered,cc2_sppol_2,cc2_sprect_1,cc2_topreal6,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_sppol_2,cc3_xreal_0,cc4_int_1,cc4_membered,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,connectedness_r1_xreal_0,d10_topreal1,d1_jordan1e,dt_g1_pre_topc,dt_k15_euclid,dt_k1_card_1,dt_k1_finseq_5,dt_k1_finseq_6,dt_k1_jordan1e,dt_k1_jordan9,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k30_pscomp_1,dt_k34_pscomp_1,dt_k3_finseq_1,dt_k5_finseq_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_topreal1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_sppol_2,fc11_finseq_1,fc1_jordan1e,fc1_ordinal2,fc1_revrot_1,fc1_sprect_1,fc1_sprect_3,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc2_jordan1g,fc2_membered,fc2_revrot_1,fc2_sprect_1,fc3_jordan1e,fc3_revrot_1,fc3_sppol_2,fc3_sprect_1,fc4_revrot_1,fc4_subset_1,fc5_finseq_5,fc5_jordan1e,fc5_membered,fc5_revrot_1,fc6_membered,fc6_revrot_1,fc6_sppol_2,fc7_revrot_1,fc8_revrot_1,free_g1_pre_topc,rc1_finseq_1,rc1_finseq_5,rc1_int_1,rc1_jordan1g,rc1_membered,rc1_pre_topc,rc1_revrot_1,rc1_sppol_2,rc1_sprect_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_finseq_1,rc2_finseq_5,rc2_int_1,rc2_pre_topc,rc2_sppol_2,rc2_sprect_1,rc2_subset_1,rc2_xboole_0,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc2_boole,spc2_numerals,t18_sppol_2,t1_real,t1_subset,t2_real,t2_subset,t3_real,t3_subset,t47_sprect_2,t49_finseq_5,t4_real,t4_subset,t50_sprect_2,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,t96_finseq_6]), [file(jordan1j,t9_jordan1j)]). 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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finseq_5,axiom,( ! [A] : ( v1_xboole_0(A) => v1_realset1(A) ) ), file(finseq_5,cc1_finseq_5), []). fof(cc1_jordan1b,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_xboole_0(A) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v1_topreal2(A) ) ) ) ), file(jordan1b,cc1_jordan1b), []). 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_sppol_2,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => ( v2_funct_1(A) & ~ v1_realset1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) ) ) ) ), file(sppol_2,cc1_sppol_2), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_sppol_2,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ( v2_funct_1(A) & ~ v1_realset1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) ) => v4_topreal1(A) ) ) ), file(sppol_2,cc2_sppol_2), []). 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_sppol_2,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => ~ v1_xboole_0(A) ) ) ), file(sppol_2,cc3_sppol_2), []). 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_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_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(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_topreal1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) <=> ( v2_funct_1(A) & r1_xreal_0(2,k3_finseq_1(A)) & v2_topreal1(A) & v3_topreal1(A) & v1_topreal1(A) ) ) ) ), file(topreal1,d10_topreal1), []). fof(d1_jordan1e,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] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k1_jordan1e(A,B) = k1_finseq_5(u1_struct_0(k15_euclid(2)),k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(2,k1_jordan9(A,B)))) ) ) ), file(jordan1e,d1_jordan1e), []). fof(dt_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(pre_topc,g1_pre_topc), []). fof(dt_k15_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & l1_pre_topc(k15_euclid(A)) ) ) ), file(euclid,k15_euclid), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k1_finseq_5(A,B,C),A) ) ), file(finseq_5,k1_finseq_5), []). fof(dt_k1_finseq_6,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k1_finseq_6(A,B,C),A) ) ), file(finseq_6,k1_finseq_6), []). fof(dt_k1_jordan1e,axiom,( ! [A,B] : ( ( 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) ) => m2_finseq_1(k1_jordan1e(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan1e,k1_jordan1e), []). 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_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k30_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k30_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k30_pscomp_1), []). fof(dt_k34_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k34_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k34_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_k5_finseq_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k5_finseq_4(A,B),k1_numbers,k5_numbers) ) ), file(finseq_4,k5_finseq_4), []). 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_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_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_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_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_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_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_sppol_2,axiom,( ! [A,B] : ( ( v1_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc10_sppol_2), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc1_jordan1e,axiom,( ! [A,B] : ( ( 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_jordan1e(A,B)) & v1_relat_1(k1_jordan1e(A,B)) & v1_funct_1(k1_jordan1e(A,B)) & v1_finset_1(k1_jordan1e(A,B)) & v1_finseq_1(k1_jordan1e(A,B)) ) ) ), file(jordan1e,fc1_jordan1e), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). 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_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) => v1_realset1(k2_relat_1(A)) ) ), file(sprect_1,fc1_sprect_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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_jordan1g,axiom,( ! [A,B] : ( ( v2_connsp_1(A,k15_euclid(2)) & 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_jordan1e(A,B)) & v1_relat_1(k1_jordan1e(A,B)) & v1_funct_1(k1_jordan1e(A,B)) & v2_funct_1(k1_jordan1e(A,B)) & v1_finset_1(k1_jordan1e(A,B)) & v1_finseq_1(k1_jordan1e(A,B)) & ~ v1_realset1(k1_jordan1e(A,B)) & v1_topreal1(k1_jordan1e(A,B)) & v2_topreal1(k1_jordan1e(A,B)) & v3_topreal1(k1_jordan1e(A,B)) & v4_topreal1(k1_jordan1e(A,B)) & v2_goboard5(k1_jordan1e(A,B)) ) ) ), file(jordan1g,fc2_jordan1g), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_revrot_1,axiom,( ! [A,B,C] : ( ( ~ v1_realset1(A) & m1_subset_1(B,A) & ~ v5_seqm_3(C) & v1_finseq_6(C,A) & m1_finseq_1(C,A) ) => ( ~ v1_xboole_0(k1_finseq_6(A,C,B)) & v1_relat_1(k1_finseq_6(A,C,B)) & v1_funct_1(k1_finseq_6(A,C,B)) & ~ v5_seqm_3(k1_finseq_6(A,C,B)) & v1_finset_1(k1_finseq_6(A,C,B)) & v1_finseq_1(k1_finseq_6(A,C,B)) & v1_finseq_6(k1_finseq_6(A,C,B),A) & ~ v1_realset1(k1_finseq_6(A,C,B)) ) ) ), file(revrot_1,fc2_revrot_1), []). 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(fc3_jordan1e,axiom,( ! [A,B] : ( ( 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_jordan1e(A,B)) & v1_relat_1(k1_jordan1e(A,B)) & v1_funct_1(k1_jordan1e(A,B)) & v2_funct_1(k1_jordan1e(A,B)) & v1_finset_1(k1_jordan1e(A,B)) & v1_finseq_1(k1_jordan1e(A,B)) & v1_topreal1(k1_jordan1e(A,B)) & v2_topreal1(k1_jordan1e(A,B)) & v3_topreal1(k1_jordan1e(A,B)) ) ) ), file(jordan1e,fc3_jordan1e), []). 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_sppol_2,axiom,( ! [A,B] : ( ( v2_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v2_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc3_sppol_2), []). 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(fc4_revrot_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m1_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(revrot_1,fc4_revrot_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_finseq_5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & v2_funct_1(C) & m1_finseq_1(C,A) ) => ( v1_relat_1(k1_finseq_5(A,C,B)) & v1_funct_1(k1_finseq_5(A,C,B)) & v2_funct_1(k1_finseq_5(A,C,B)) & v1_finset_1(k1_finseq_5(A,C,B)) & v1_finseq_1(k1_finseq_5(A,C,B)) ) ) ), file(finseq_5,fc5_finseq_5), []). fof(fc5_jordan1e,axiom,( ! [A,B] : ( ( 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_jordan1e(A,B)) & v1_relat_1(k1_jordan1e(A,B)) & v1_funct_1(k1_jordan1e(A,B)) & v2_funct_1(k1_jordan1e(A,B)) & v1_finset_1(k1_jordan1e(A,B)) & v1_finseq_1(k1_jordan1e(A,B)) & ~ v1_realset1(k1_jordan1e(A,B)) & v1_topreal1(k1_jordan1e(A,B)) & v2_topreal1(k1_jordan1e(A,B)) & v3_topreal1(k1_jordan1e(A,B)) & v4_topreal1(k1_jordan1e(A,B)) ) ) ), file(jordan1e,fc5_jordan1e), []). 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_revrot_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(revrot_1,fc5_revrot_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_revrot_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & ~ v5_seqm_3(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v2_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & ~ v1_realset1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(revrot_1,fc6_revrot_1), []). fof(fc6_sppol_2,axiom,( ! [A,B] : ( ( v3_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v3_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc6_sppol_2), []). fof(fc7_revrot_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v2_goboard5(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A),u1_struct_0(k15_euclid(2))) & v2_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(revrot_1,fc7_revrot_1), []). fof(fc8_revrot_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & v1_sprect_2(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & ~ v5_seqm_3(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v2_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v2_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_sprect_2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & ~ v1_realset1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(revrot_1,fc8_revrot_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(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finseq_5,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_5,rc1_finseq_5), []). 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_jordan1g,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_realset1(A) & v5_seqm_3(A) ) ), file(jordan1g,rc1_jordan1g), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) ), file(pre_topc,rc1_pre_topc), []). fof(rc1_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_sppol_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v4_topreal1(A) ) ), file(sppol_2,rc1_sppol_2), []). 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_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(finseq_5,rc2_finseq_5), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) ), file(pre_topc,rc2_pre_topc), []). fof(rc2_sppol_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & ~ v1_realset1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) & v4_topreal1(A) ) ), file(sppol_2,rc2_sppol_2), []). 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_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). 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_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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(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(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(t18_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( r1_xreal_0(2,k3_finseq_1(A)) => r1_tarski(k2_relat_1(A),k5_topreal1(2,A)) ) ) ), file(sppol_2,t18_sppol_2), []). 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(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(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t47_sprect_2,axiom,( ! [A] : ( ( ~ v1_realset1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => r2_hidden(k30_pscomp_1(k5_topreal1(2,A)),k2_relat_1(A)) ) ), file(sprect_2,t47_sprect_2), []). fof(t49_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( r2_hidden(D,k2_relat_1(C)) & r2_hidden(B,k2_relat_1(C)) & r1_xreal_0(k5_finseq_4(C,D),k5_finseq_4(C,B)) ) => r2_hidden(D,k2_relat_1(k1_finseq_5(A,C,B))) ) ) ) ) ), file(finseq_5,t49_finseq_5), []). 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(t50_sprect_2,axiom,( ! [A] : ( ( ~ v1_realset1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => r2_hidden(k34_pscomp_1(k5_topreal1(2,A)),k2_relat_1(A)) ) ), file(sprect_2,t50_sprect_2), []). 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(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). 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(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). 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(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). 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(t96_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( v1_finseq_6(C,A) & r2_hidden(B,k2_relat_1(C)) ) => k2_relat_1(k1_finseq_6(A,C,B)) = k2_relat_1(C) ) ) ) ) ), file(finseq_6,t96_finseq_6), []).