% Mizar problem: t45_jordan23,jordan23,2352,12 fof(t45_jordan23,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)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,k1_jordan2c(2,k5_topreal1(2,k1_jordan9(B,A)))) & ! [E] : ( ( v4_topreal1(E) & m2_finseq_1(E,u1_struct_0(k15_euclid(2))) ) => ~ ( E = k5_jordan3(k16_finseq_1(u1_struct_0(k15_euclid(2)),k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k2_jordan3(k1_jordan9(B,A),k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A)))))),k5_binarith(k3_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k2_jordan3(k1_jordan9(B,A),k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))))))),1)),k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))),k1_jordan18(C,k5_topreal1(2,k1_jordan9(B,A)))) & ? [F] : ( v4_topreal1(F) & m2_finseq_1(F,u1_struct_0(k15_euclid(2))) & r1_goboard1(u1_struct_0(k15_euclid(2)),F,k3_goboard2(k4_graph_2(u1_struct_0(k15_euclid(2)),E,k2_finseq_4(u1_struct_0(k15_euclid(2)),k1_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))))))) & k5_topreal1(2,k2_finseq_4(u1_struct_0(k15_euclid(2)),k1_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))))) = k5_topreal1(2,F) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),F,1) = k1_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),F,k3_finseq_1(F)) = k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))) & r1_xreal_0(2,k3_finseq_1(F)) & ? [G] : ( v4_topreal1(G) & m2_finseq_1(G,u1_struct_0(k15_euclid(2))) & r1_goboard1(u1_struct_0(k15_euclid(2)),G,k3_goboard2(k4_graph_2(u1_struct_0(k15_euclid(2)),E,k2_finseq_4(u1_struct_0(k15_euclid(2)),k1_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))),k2_jordan18(C,k5_topreal1(2,k1_jordan9(B,A))))))) & k5_topreal1(2,E) = k5_topreal1(2,G) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),E,1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),G,1) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),E,k3_finseq_1(E)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),G,k3_finseq_1(G)) & r1_xreal_0(k3_finseq_1(E),k3_finseq_1(G)) & ? [H] : ( ~ v1_xboole_0(H) & ~ v5_seqm_3(H) & v1_topreal1(H) & v2_topreal1(H) & v1_finseq_6(H,u1_struct_0(k15_euclid(2))) & v1_goboard5(H) & v2_goboard5(H) & m2_finseq_1(H,u1_struct_0(k15_euclid(2))) & H = k4_graph_2(u1_struct_0(k15_euclid(2)),G,F) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_topreal6,cc11_topreal6,cc1_arytm_3,cc1_finseq_5,cc1_finset_1,cc1_funct_7,cc1_jordan23,cc1_real_1,cc1_relset_1,cc1_sppol_2,cc1_sprect_1,cc1_topreal6,cc1_xreal_0,cc2_arytm_3,cc2_finset_1,cc2_funct_7,cc2_jordan23,cc2_sppol_2,cc2_sprect_1,cc2_topreal6,cc2_xreal_0,cc3_arytm_3,cc3_jordan23,cc3_sppol_2,cc3_topreal6,cc3_xreal_0,cc4_topreal6,cc4_xreal_0,cc5_topreal6,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_topreal6,cc8_xreal_0,cc9_topreal6,commutativity_k1_nat_1,commutativity_k2_struct_0,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_topreal1,commutativity_k3_xboole_0,commutativity_k4_subset_1,commutativity_k5_subset_1,connectedness_r1_xreal_0,d10_topreal1,d10_xboole_0,d1_finseq_6,d1_revrot_1,d1_tarski,d2_tarski,d2_xboole_0,d3_binarith,d3_finseq_1,d3_tarski,d3_xboole_0,d5_real_1,d5_tarski,d5_topreal1,d7_xboole_0,dt_g1_pre_topc,dt_k10_finseq_1,dt_k13_finseq_1,dt_k15_euclid,dt_k16_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_finseq_6,dt_k1_funct_1,dt_k1_jordan18,dt_k1_jordan2c,dt_k1_jordan8,dt_k1_jordan9,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_topreal1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_euclid,dt_k22_euclid,dt_k23_euclid,dt_k2_finseq_1,dt_k2_finseq_4,dt_k2_finseq_5,dt_k2_jordan18,dt_k2_jordan1a,dt_k2_jordan3,dt_k2_matrix_1,dt_k2_relat_1,dt_k2_struct_0,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_goboard2,dt_k3_graph_2,dt_k3_matrix_1,dt_k3_real_1,dt_k3_topreal1,dt_k3_xboole_0,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_graph_2,dt_k4_jordan1a,dt_k4_relset_1,dt_k4_subset_1,dt_k4_tarski,dt_k4_topreal1,dt_k5_binarith,dt_k5_finseq_4,dt_k5_jordan3,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_subset_1,dt_k5_topreal1,dt_k6_real_1,dt_k6_xcmplx_0,dt_k7_xcmplx_0,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_pre_topc,dt_u1_struct_0,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_finset_1,fc10_jordan23,fc10_xreal_0,fc11_finset_1,fc11_jordan23,fc11_sppol_2,fc11_xreal_0,fc12_jordan23,fc12_xreal_0,fc14_finset_1,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finset_1,fc1_jordan1j,fc1_revrot_1,fc1_sppol_2,fc1_sprect_1,fc1_sprect_3,fc20_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_finseq_5,fc2_finset_1,fc2_jordan23,fc2_revrot_1,fc2_sprect_1,fc2_topreal6,fc30_xreal_0,fc3_finseq_5,fc3_funct_7,fc3_revrot_1,fc3_sprect_1,fc3_xreal_0,fc4_finseq_6,fc4_jordan23,fc4_revrot_1,fc4_sppol_2,fc5_finseq_6,fc5_funct_7,fc5_goboard2,fc5_revrot_1,fc5_xreal_0,fc6_finseq_5,fc6_revrot_1,fc6_xreal_0,fc7_revrot_1,fc7_xreal_0,fc8_jordan23,fc8_revrot_1,fc8_sppol_2,fc8_xreal_0,fc9_finset_1,fc9_jordan23,fc9_xreal_0,free_g1_pre_topc,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,irreflexivity_r2_subset_1,rc1_arytm_3,rc1_finseq_5,rc1_finseq_6,rc1_finset_1,rc1_jordan1j,rc1_jordan23,rc1_revrot_1,rc1_sppol_2,rc1_sprect_1,rc1_xreal_0,rc2_finseq_5,rc2_finseq_6,rc2_finset_1,rc2_jordan23,rc2_sppol_2,rc2_sprect_1,rc2_topreal6,rc2_xreal_0,rc3_finset_1,rc3_jordan23,rc3_xreal_0,rc4_finset_1,rc4_jordan23,rc4_xreal_0,redefinition_k1_nat_1,redefinition_k1_struct_0,redefinition_k2_finseq_1,redefinition_k2_finseq_4,redefinition_k2_struct_0,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_real_1,redefinition_k3_topreal1,redefinition_k4_finseq_1,redefinition_k4_graph_2,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_subset_1,redefinition_k6_real_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc4_boole,spc4_numerals,symmetry_r1_xboole_0,symmetry_r2_subset_1,t10_amistd_1,t10_topreal1,t11_topreal3,t11_topreal8,t12_topreal1,t12_topreal8,t13_graph_2,t14_revrot_1,t17_sppol_2,t19_jordan23,t19_nat_1,t19_sprect_3,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t1_xboole_1,t20_jordan18,t20_jordan23,t20_sprect_3,t21_sppol_2,t21_sprect_3,t21_xreal_1,t22_jordan18,t22_xreal_1,t23_jordan18,t23_jordan23,t24_revrot_1,t25_finseq_1,t25_goboard2,t25_jordan18,t25_jordan23,t26_finseq_4,t26_topreal3,t26_xboole_1,t27_finseq_3,t27_jordan18,t27_jordan5b,t27_topreal3,t27_xboole_1,t29_finseq_3,t29_nat_1,t2_boole,t2_goboard3,t2_real,t2_subset,t2_xreal_1,t30_revrot_1,t33_revrot_1,t33_topreal8,t34_jordan3,t34_topreal8,t36_goboard7,t37_sppol_1,t38_goboard7,t38_nat_1,t3_finseq_1,t3_real,t3_sppol_2,t3_subset,t3_topreal3,t41_jordan3,t41_sppol_1,t42_finseq_5,t42_jordan3,t49_jordan4,t4_arithm,t4_finseq_1,t4_partfun2,t4_real,t4_subset,t51_binarith,t52_binarith,t52_finseq_6,t53_binarith,t53_finseq_5,t56_euclid,t5_arithm,t5_jordan23,t5_real,t5_subset,t61_finseq_1,t6_arithm,t6_boole,t6_finseq_5,t6_real,t6_topreal1,t72_jordan3,t7_boole,t7_jordan8,t7_real,t80_finseq_1,t8_boole,t8_goboard2,t8_goboard7,t8_jordan1b,t8_real,t9_amistd_1]), [file(jordan23,t45_jordan23)]). 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_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_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(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_finseq_5,axiom,( ! [A] : ( v1_xboole_0(A) => v1_realset1(A) ) ), file(finseq_5,cc1_finseq_5), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). fof(cc1_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_jordan23(A) ) ) ), file(jordan23,cc1_jordan23), []). fof(cc1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ( v1_xreal_0(A) & v1_xcmplx_0(A) ) ) ), file(real_1,cc1_real_1), []). fof(cc1_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(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(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) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). fof(cc2_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_jordan23(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_jordan23(A) ) ) ), file(jordan23,cc2_jordan23), []). 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_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_jordan23(A) ) ) ), file(jordan23,cc3_jordan23), []). 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_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_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_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_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_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_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_struct_0(A,B,C) = k2_struct_0(A,C,B) ) ), file(struct_0,k2_struct_0), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k3_topreal1(A,B,C) = k3_topreal1(A,C,B) ) ), file(topreal1,k3_topreal1), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(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(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d1_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_finseq_6(B,A) <=> k4_finseq_4(k5_numbers,A,B,1) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)) ) ) ) ), file(finseq_6,d1_finseq_6), []). fof(d1_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v5_seqm_3(B) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(B)) ) => k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,D) ) ) ) ) ) ) ), file(revrot_1,d1_revrot_1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ( r1_xreal_0(0,k6_xcmplx_0(A,B)) => k5_binarith(A,B) = k6_xcmplx_0(A,B) ) & ( ~ r1_xreal_0(0,k6_xcmplx_0(A,B)) => k5_binarith(A,B) = 0 ) ) ) ) ), file(binarith,d3_binarith), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_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(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(d5_topreal1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(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(B)) ) => k4_topreal1(A,B,C) = k3_topreal1(A,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,C),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,k1_nat_1(C,1))) ) & ( ~ ( r1_xreal_0(1,C) & r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => k4_topreal1(A,B,C) = k1_xboole_0 ) ) ) ) ) ), file(topreal1,d5_topreal1), []). fof(d7_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), []). 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_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). 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_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & v4_ordinal2(C) ) => m2_finseq_1(k16_finseq_1(A,B,C),A) ) ), file(finseq_1,k16_finseq_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). 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_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_jordan18,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => m1_subset_1(k1_jordan18(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan18,k1_jordan18), []). fof(dt_k1_jordan2c,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => m1_subset_1(k1_jordan2c(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(jordan2c,k1_jordan2c), []). 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_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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_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_k21_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k21_euclid(A),k1_numbers) ) ), file(euclid,k21_euclid), []). fof(dt_k22_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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_finseq_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k2_finseq_4(A,B,C),A) ) ), file(finseq_4,k2_finseq_4), []). fof(dt_k2_finseq_5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k2_finseq_5(A,B,C),A) ) ), file(finseq_5,k2_finseq_5), []). fof(dt_k2_jordan18,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => m1_subset_1(k2_jordan18(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan18,k2_jordan18), []). fof(dt_k2_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k2_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan1a,k2_jordan1a), []). fof(dt_k2_jordan3,axiom,( ! [A,B] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => m2_subset_1(k2_jordan3(A,B),k1_numbers,k5_numbers) ) ), file(jordan3,k2_jordan3), []). fof(dt_k2_matrix_1,axiom,( $true ), file(matrix_1,k2_matrix_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k2_struct_0), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_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_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( v1_matrix_1(k3_goboard2(A)) & m2_finseq_1(k3_goboard2(A),k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) ) ), file(goboard2,k3_goboard2), []). fof(dt_k3_graph_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k3_graph_2(A,B)) & v1_funct_1(k3_graph_2(A,B)) & v1_finseq_1(k3_graph_2(A,B)) ) ) ), file(graph_2,k3_graph_2), []). 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_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_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). 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_graph_2,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k4_graph_2(A,B,C),A) ) ), file(graph_2,k4_graph_2), []). fof(dt_k4_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k4_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan1a,k4_jordan1a), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), []). fof(dt_k4_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_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_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_jordan3,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => m2_finseq_1(k5_jordan3(A,B,C),u1_struct_0(k15_euclid(2))) ) ), file(jordan3,k5_jordan3), []). 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_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_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_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). 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_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_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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_jordan23,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_finseq_6(B,A) & v3_jordan23(B) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => ( v1_relat_1(k1_finseq_6(A,B,C)) & v1_funct_1(k1_finseq_6(A,B,C)) & v1_finseq_1(k1_finseq_6(A,B,C)) & v3_jordan23(k1_finseq_6(A,B,C)) ) ) ), file(jordan23,fc10_jordan23), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_jordan23,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_jordan9(A,B)) & v1_relat_1(k1_jordan9(A,B)) & v1_funct_1(k1_jordan9(A,B)) & v1_finseq_1(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)) & v1_sprect_2(k1_jordan9(A,B)) & ~ v1_realset1(k1_jordan9(A,B)) & v1_jordan23(k1_jordan9(A,B)) & v3_jordan23(k1_jordan9(A,B)) ) ) ), file(jordan23,fc11_jordan23), []). 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_jordan23,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_jordan9(A,B)) & v1_relat_1(k1_jordan9(A,B)) & v1_funct_1(k1_jordan9(A,B)) & v1_finseq_1(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)) & v1_sprect_2(k1_jordan9(A,B)) & ~ v1_realset1(k1_jordan9(A,B)) & v1_jordan23(k1_jordan9(A,B)) & v2_jordan23(k1_jordan9(A,B)) & v3_jordan23(k1_jordan9(A,B)) ) ) ), file(jordan23,fc12_jordan23), []). 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(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). 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_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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_jordan1j,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k3_graph_2(A,B)) & v1_relat_1(k3_graph_2(A,B)) & v1_funct_1(k3_graph_2(A,B)) & v1_finset_1(k3_graph_2(A,B)) & v1_finseq_1(k3_graph_2(A,B)) ) ) ), file(jordan1j,fc1_jordan1j), []). 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_sppol_2,axiom,( ! [A,B] : ( ( v2_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v2_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc1_sppol_2), []). 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(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_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_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_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_finseq_5,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & ~ v1_realset1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) ) ), file(finseq_5,fc2_finseq_5), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_jordan23,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) & v5_seqm_3(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_realset1(k1_xboole_0) & v1_jordan23(k1_xboole_0) & v2_jordan23(k1_xboole_0) & v3_jordan23(k1_xboole_0) ), file(jordan23,fc2_jordan23), []). 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(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_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(fc3_finseq_5,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v2_funct_1(C) & m1_finseq_1(C,B) ) => ( v1_relat_1(k16_finseq_1(B,C,A)) & v1_funct_1(k16_finseq_1(B,C,A)) & v2_funct_1(k16_finseq_1(B,C,A)) & v1_finset_1(k16_finseq_1(B,C,A)) & v1_finseq_1(k16_finseq_1(B,C,A)) ) ) ), file(finseq_5,fc3_finseq_5), []). fof(fc3_funct_7,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) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). 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_finseq_6,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => ( ~ v1_xboole_0(k1_finseq_6(A,B,C)) & v1_relat_1(k1_finseq_6(A,B,C)) & v1_funct_1(k1_finseq_6(A,B,C)) & v1_finset_1(k1_finseq_6(A,B,C)) & v1_finseq_1(k1_finseq_6(A,B,C)) ) ) ), file(finseq_6,fc4_finseq_6), []). fof(fc4_jordan23,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & ~ v1_realset1(k10_finseq_1(A,B)) & v3_jordan23(k10_finseq_1(A,B)) ) ), file(jordan23,fc4_jordan23), []). 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_sppol_2,axiom,( ! [A,B] : ( ( v3_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc4_sppol_2), []). fof(fc5_finseq_6,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & ~ v1_xboole_0(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)) & 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) ) ) ), file(finseq_6,fc5_finseq_6), []). fof(fc5_funct_7,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funcop_1(k10_finseq_1(A,B)) ) ) ), file(funct_7,fc5_funct_7), []). fof(fc5_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k3_goboard2(A)) & ~ v3_relat_1(k3_goboard2(A)) & v1_funct_1(k3_goboard2(A)) & v1_finset_1(k3_goboard2(A)) & v1_finseq_1(k3_goboard2(A)) & v1_matrix_1(k3_goboard2(A)) & v3_goboard1(k3_goboard2(A)) & v4_goboard1(k3_goboard2(A)) & v5_goboard1(k3_goboard2(A)) & v6_goboard1(k3_goboard2(A)) ) ) ), file(goboard2,fc5_goboard2), []). 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(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_finseq_5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_finseq_1(C,A) ) => ( ~ v1_xboole_0(k2_finseq_5(A,C,B)) & v1_relat_1(k2_finseq_5(A,C,B)) & v1_funct_1(k2_finseq_5(A,C,B)) & v1_finset_1(k2_finseq_5(A,C,B)) & v1_finseq_1(k2_finseq_5(A,C,B)) ) ) ), file(finseq_5,fc6_finseq_5), []). 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_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_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(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_jordan23,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_jordan23(B) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => ( v1_relat_1(k1_finseq_6(A,B,C)) & v1_funct_1(k1_finseq_6(A,B,C)) & v1_finseq_1(k1_finseq_6(A,B,C)) & v1_jordan23(k1_finseq_6(A,B,C)) & v3_jordan23(k1_finseq_6(A,B,C)) ) ) ), file(jordan23,fc8_jordan23), []). 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(fc8_sppol_2,axiom,( ! [A,B] : ( ( v1_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) & v1_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc8_sppol_2), []). 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_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_jordan23,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_finseq_6(B,A) & v2_jordan23(B) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => ( v1_relat_1(k1_finseq_6(A,B,C)) & v1_funct_1(k1_finseq_6(A,B,C)) & v1_finseq_1(k1_finseq_6(A,B,C)) & v2_jordan23(k1_finseq_6(A,B,C)) ) ) ), file(jordan23,fc9_jordan23), []). 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(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(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(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). 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_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_realset1(B) & v1_finseq_6(B,A) ) ) ), file(finseq_6,rc1_finseq_6), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_jordan1j,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_finset_1(A) & v1_finseq_1(A) & ~ v1_realset1(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) & v4_topreal1(A) & v1_goboard5(A) & v2_goboard5(A) ) ), file(jordan1j,rc1_jordan1j), []). fof(rc1_jordan23,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_jordan23(A) ) ), file(jordan23,rc1_jordan23), []). 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_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). 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_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & ~ v1_realset1(B) & v1_finseq_6(B,A) ) ) ), file(finseq_6,rc2_finseq_6), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_jordan23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finseq_6(B,A) & v2_jordan23(B) ) ) ), file(jordan23,rc2_jordan23), []). 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_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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_jordan23,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finseq_1(A) & v1_jordan23(A) & v3_jordan23(A) ) ), file(jordan23,rc3_jordan23), []). 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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_jordan23,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_finseq_1(B) & v1_finseq_6(B,A) & v1_jordan23(B) & v3_jordan23(B) ) ) ), file(jordan23,rc4_jordan23), []). 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(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_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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_finseq_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k2_finseq_4(A,B,C) = k10_finseq_1(B,C) ) ), file(finseq_4,k2_finseq_4), []). fof(redefinition_k2_struct_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_struct_0(A,B,C) = k2_tarski(B,C) ) ), file(struct_0,k2_struct_0), []). fof(redefinition_k3_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_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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_graph_2,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k4_graph_2(A,B,C) = k3_graph_2(B,C) ) ), file(graph_2,k4_graph_2), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_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_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_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(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_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(t10_amistd_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( r1_xreal_0(1,B) => ( r1_xreal_0(k3_finseq_1(D),B) | k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),k1_nat_1(k3_finseq_1(C),B)) = k4_finseq_4(k5_numbers,A,D,k1_nat_1(B,1)) ) ) ) ) ) ) ), file(amistd_1,t10_amistd_1), []). 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(t11_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( k21_euclid(A) = k21_euclid(B) & k22_euclid(A) = k22_euclid(B) ) => A = B ) ) ) ), file(topreal3,t11_topreal3), []). fof(t11_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( ( ~ v1_realset1(C) & m2_finseq_1(C,A) ) => ( k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,A,B,1) => v1_finseq_6(k4_graph_2(A,B,C),A) ) ) ) ) ), file(topreal8,t11_topreal8), []). fof(t12_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))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(D,k3_topreal1(A,B,C)) & r2_hidden(E,k3_topreal1(A,B,C)) ) => r1_tarski(k3_topreal1(A,D,E),k3_topreal1(A,B,C)) ) ) ) ) ) ) ), file(topreal1,t12_topreal1), []). fof(t12_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_1(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,A) ) => ( ( k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,A,D,1) & r1_goboard1(A,C,B) & r1_goboard1(A,D,B) ) => r1_goboard1(A,k4_graph_2(A,C,D),B) ) ) ) ) ) ), file(topreal8,t12_topreal8), []). fof(t13_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( A != k1_xboole_0 => k1_nat_1(k3_finseq_1(k3_graph_2(B,A)),1) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(A)) ) ) ) ), file(graph_2,t13_graph_2), []). fof(t14_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k3_finseq_1(k1_finseq_6(A,C,B)) = k3_finseq_1(C) ) ) ) ), file(revrot_1,t14_revrot_1), []). fof(t17_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))) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(B,k4_topreal1(2,A,C)) => r2_hidden(B,k5_topreal1(2,A)) ) ) ) ) ), file(sppol_2,t17_sppol_2), []). fof(t19_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_jordan23(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,k5_topreal1(2,A)) & r2_hidden(C,k5_topreal1(2,A)) ) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k5_jordan3(A,B,C),1) = B ) ) ) ) ) ), file(jordan23,t19_jordan23), []). fof(t19_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ~ ( 0 != A & r1_xreal_0(A,0) ) ) ), file(nat_1,t19_nat_1), []). fof(t19_sprect_3,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))) => ( ( v1_sppol_1(k3_topreal1(2,A,B)) & r2_hidden(C,k3_topreal1(2,A,B)) ) => k22_euclid(A) = k22_euclid(C) ) ) ) ) ), file(sprect_3,t19_sprect_3), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t20_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k21_euclid(k1_jordan18(B,A)) = k21_euclid(B) & k21_euclid(k2_jordan18(B,A)) = k21_euclid(B) ) ) ) ), file(jordan18,t20_jordan18), []). fof(t20_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_jordan23(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,k5_topreal1(2,A)) & r2_hidden(C,k5_topreal1(2,A)) ) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k5_jordan3(A,B,C),k3_finseq_1(k5_jordan3(A,B,C))) = C ) ) ) ) ) ), file(jordan23,t20_jordan23), []). fof(t20_sprect_3,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))) => ( ( v2_sppol_1(k3_topreal1(2,A,B)) & r2_hidden(C,k3_topreal1(2,A,B)) ) => k21_euclid(A) = k21_euclid(C) ) ) ) ) ), file(sprect_3,t20_sprect_3), []). fof(t21_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k5_topreal1(2,k2_finseq_4(u1_struct_0(k15_euclid(2)),A,B)) = k3_topreal1(2,A,B) ) ) ), file(sppol_2,t21_sppol_2), []). fof(t21_sprect_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( v1_sppol_1(k3_topreal1(2,A,B)) & v1_sppol_1(k3_topreal1(2,C,D)) ) => ( r2_subset_1(k3_topreal1(2,A,B),k3_topreal1(2,C,D)) | k22_euclid(A) = k22_euclid(C) ) ) ) ) ) ) ), file(sprect_3,t21_sprect_3), []). fof(t21_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(k2_xcmplx_0(A,B),C) <=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ), file(xreal_1,t21_xreal_1), []). fof(t22_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,k1_jordan2c(2,B)) => ( r2_hidden(k1_jordan18(A,B),B) & r2_hidden(k1_jordan18(A,B),k2_jordan1a(A)) & r2_hidden(k2_jordan18(A,B),B) & r2_hidden(k2_jordan18(A,B),k4_jordan1a(A)) ) ) ) ) ), file(jordan18,t22_jordan18), []). fof(t22_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,k2_xcmplx_0(B,C)) <=> r1_xreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) ), file(xreal_1,t22_xreal_1), []). fof(t23_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,k1_jordan2c(2,B)) => ( ~ r1_xreal_0(k22_euclid(A),k22_euclid(k2_jordan18(A,B))) & ~ r1_xreal_0(k22_euclid(k1_jordan18(A,B)),k22_euclid(A)) ) ) ) ) ), file(jordan18,t23_jordan18), []). fof(t23_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r1_tarski(k4_finseq_1(A),k4_finseq_1(k3_graph_2(A,B))) ) ) ), file(jordan23,t23_jordan23), []). fof(t24_revrot_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,k2_relat_1(C)) & r1_xreal_0(1,A) ) => ( r1_xreal_0(k3_finseq_1(k2_finseq_5(u1_struct_0(k15_euclid(2)),C,B)),A) | k4_topreal1(2,k1_finseq_6(u1_struct_0(k15_euclid(2)),C,B),A) = k4_topreal1(2,C,k1_nat_1(k5_binarith(A,1),k5_finseq_4(C,B))) ) ) ) ) ) ), file(revrot_1,t24_revrot_1), []). fof(t25_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) = 0 <=> A = k1_xboole_0 ) ) ), file(finseq_1,t25_finseq_1), []). fof(t25_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k3_goboard2(A))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k3_goboard2(A),C,D) ) ) ) ) ) ) ), file(goboard2,t25_goboard2), []). fof(t25_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r2_hidden(A,k1_jordan2c(2,B)) & k2_jordan18(A,B) = k1_jordan18(A,B) ) ) ) ), file(jordan18,t25_jordan18), []). fof(t25_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v5_seqm_3(k3_graph_2(A,B)) => v5_seqm_3(A) ) ) ) ), file(jordan23,t25_jordan23), []). fof(t26_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( k4_finseq_4(k5_numbers,A,k2_finseq_4(A,B,C),1) = B & k4_finseq_4(k5_numbers,A,k2_finseq_4(A,B,C),2) = C ) ) ) ) ), file(finseq_4,t26_finseq_4), []). fof(t26_topreal3,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r1_tarski(k4_topreal1(A,B,C),k5_topreal1(A,B)) ) ) ) ), file(topreal3,t26_topreal3), []). fof(t26_xboole_1,axiom,( ! [A,B,C] : ( r1_tarski(A,B) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ), file(xboole_1,t26_xboole_1), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t27_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,k1_jordan2c(2,B)) => k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k1_jordan18(A,B),k2_jordan18(A,B)),B) = k2_struct_0(k15_euclid(2),k1_jordan18(A,B),k2_jordan18(A,B)) ) ) ) ), file(jordan18,t27_jordan18), []). fof(t27_jordan5b,axiom,( ! [A] : ( m2_finseq_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))) => ( ( r2_hidden(B,k5_topreal1(2,A)) & r2_hidden(C,k5_topreal1(2,A)) & v4_topreal1(A) ) => r1_tarski(k5_topreal1(2,k5_jordan3(A,B,C)),k5_topreal1(2,A)) ) ) ) ) ), file(jordan5b,t27_jordan5b), []). fof(t27_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r1_tarski(k5_topreal1(2,k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)),k5_topreal1(2,A)) ) ) ), file(topreal3,t27_topreal3), []). fof(t27_xboole_1,axiom,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ), file(xboole_1,t27_xboole_1), []). fof(t29_finseq_3,axiom,( ! [A,B] : k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(2) ), file(finseq_3,t29_finseq_3), []). 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_goboard3,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) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(k4_tarski(D,E),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,D,E) ) ) ) ) ) & v4_topreal1(A) & ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_goboard1(u1_struct_0(k15_euclid(2)),C,B) & v4_topreal1(C) & k5_topreal1(2,A) = k5_topreal1(2,C) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),C,1) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) ) ) ) ) ) ), file(goboard3,t2_goboard3), []). 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_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_revrot_1,axiom,( ! [A] : ( ( v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ r1_xreal_0(k3_finseq_1(A),4) => k5_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal1(2,A,k5_binarith(k3_finseq_1(A),1)),k4_topreal1(2,A,1)) = k1_struct_0(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1)) ) ) ), file(revrot_1,t30_revrot_1), []). fof(t33_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => k5_topreal1(2,k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) = k5_topreal1(2,B) ) ) ), file(revrot_1,t33_revrot_1), []). fof(t33_topreal8,axiom,( ! [A] : ( ( v2_funct_1(A) & ~ v1_realset1(A) & v2_topreal1(A) & v3_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( v2_funct_1(B) & ~ v1_realset1(B) & v2_topreal1(B) & v3_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ( k5_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,A),k5_topreal1(2,B)) = k2_struct_0(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,1)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) ) => v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ), file(topreal8,t33_topreal8), []). fof(t34_jordan3,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ( r1_xreal_0(2,k3_finseq_1(B)) => ( r2_hidden(k1_funct_1(B,1),k5_topreal1(A,B)) & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,1),k5_topreal1(A,B)) & r2_hidden(k1_funct_1(B,k3_finseq_1(B)),k5_topreal1(A,B)) & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),B,k3_finseq_1(B)),k5_topreal1(A,B)) ) ) ) ) ), file(jordan3,t34_jordan3), []). fof(t34_topreal8,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( ( v2_topreal1(A) & v2_topreal1(B) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,1) & k5_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal1(2,A,k5_binarith(k3_finseq_1(A),1)),k4_topreal1(2,B,1)) = k1_struct_0(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A))) ) => v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ), file(topreal8,t34_topreal8), []). fof(t36_goboard7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & ~ v5_seqm_3(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ r1_xreal_0(k3_finseq_1(A),4) ) ), file(goboard7,t36_goboard7), []). 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_goboard7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & ~ v5_seqm_3(A) & m2_finseq_1(A,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(1,B) & ~ r1_xreal_0(C,B) & ~ r1_xreal_0(k3_finseq_1(A),C) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,B) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,C) ) ) ) ) ), file(goboard7,t38_goboard7), []). 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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xreal_0(1,A) & r1_xreal_0(A,B) ) ) ) ) ), file(finseq_1,t3_finseq_1), []). 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_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,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(k1_nat_1(B,1),k3_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,C))) => k4_topreal1(2,k16_finseq_1(u1_struct_0(k15_euclid(2)),A,C),B) = k4_topreal1(2,A,B) ) ) ) ) ), file(sppol_2,t3_sppol_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_topreal3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xreal_0(B,A) => ( ~ r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(A,B),2),A) & ~ r1_xreal_0(B,k7_xcmplx_0(k2_xcmplx_0(A,B),2)) ) ) ) ) ), file(topreal3,t3_topreal3), []). fof(t41_jordan3,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)) => ( r1_xreal_0(1,k2_jordan3(A,B)) & ~ r1_xreal_0(k3_finseq_1(A),k2_jordan3(A,B)) ) ) ) ) ), file(jordan3,t41_jordan3), []). fof(t41_sppol_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ~ ( v1_topreal1(B) & ~ v2_sppol_1(k4_topreal1(2,B,A)) & ~ v1_sppol_1(k4_topreal1(2,B,A)) ) ) ) ), file(sppol_1,t41_sppol_1), []). fof(t42_finseq_5,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r1_xreal_0(k5_finseq_4(C,k4_finseq_4(k5_numbers,B,C,A)),A) ) ) ) ) ), file(finseq_5,t42_finseq_5), []). fof(t42_jordan3,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)) => r2_hidden(B,k4_topreal1(2,A,k2_jordan3(A,B))) ) ) ) ), file(jordan3,t42_jordan3), []). fof(t49_jordan4,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) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_xreal_0(k1_nat_1(B,1),k3_finseq_1(A)) => ( r1_xreal_0(B,1) | v4_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ) ), file(jordan4,t49_jordan4), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_finseq_1,axiom, ( k2_finseq_1(0) = k1_xboole_0 & k2_finseq_1(1) = k1_tarski(1) & k2_finseq_1(2) = k2_tarski(1,2) ), file(finseq_1,t4_finseq_1), []). fof(t4_partfun2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m2_relset_1(D,C,B) ) => ( r2_hidden(A,k2_relat_1(D)) <=> ? [E] : ( m1_subset_1(E,C) & r2_hidden(E,k4_relset_1(C,B,D)) & A = k4_finseq_4(C,B,D,E) ) ) ) ) ) ), file(partfun2,t4_partfun2), []). 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(t51_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => k5_binarith(A,A) = 0 ) ), file(binarith,t51_binarith), []). fof(t52_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(k5_binarith(A,B),A) ) ) ), file(binarith,t52_binarith), []). fof(t52_finseq_6,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( ( r2_hidden(A,k4_finseq_1(C)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,D) & ~ r1_xreal_0(A,D) & k4_finseq_4(k5_numbers,B,C,D) = k4_finseq_4(k5_numbers,B,C,A) ) ) ) => k5_finseq_4(C,k4_finseq_4(k5_numbers,B,C,A)) = A ) ) ) ) ), file(finseq_6,t52_finseq_6), []). fof(t53_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(B,A) => k2_xcmplx_0(k5_binarith(A,B),B) = A ) ) ) ), file(binarith,t53_binarith), []). fof(t53_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k2_relat_1(C)) => k3_finseq_1(k2_finseq_5(A,C,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(C),k5_finseq_4(C,B)),1) ) ) ) ) ), file(finseq_5,t53_finseq_5), []). 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(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). fof(t5_jordan23,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v2_jordan23(B) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,C) & ~ r1_xreal_0(k3_finseq_1(B),C) & k4_finseq_4(k5_numbers,A,B,C) = k4_finseq_4(k5_numbers,A,B,k1_nat_1(C,1)) ) ) ) ) ), file(jordan23,t5_jordan23), []). 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_finseq_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k10_finseq_1(A,B) <=> ( k3_finseq_1(C) = 2 & k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) ) ) ), file(finseq_1,t61_finseq_1), []). 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_finseq_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(1,k4_finseq_1(A)) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) ), file(finseq_5,t6_finseq_5), []). 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(t72_jordan3,axiom,( ! [A] : ( m2_finseq_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))) => ( ( v4_topreal1(A) & r2_hidden(B,k5_topreal1(2,A)) & r2_hidden(C,k5_topreal1(2,A)) ) => ( B = C | v4_topreal1(k5_jordan3(A,B,C)) ) ) ) ) ) ), file(jordan3,t72_jordan3), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_jordan8,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] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ( v2_goboard5(B) & v1_topreal1(B) ) ) ) ) ), file(jordan8,t7_jordan8), []). 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(t80_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ! [C] : ( v4_ordinal2(C) => ( r1_xreal_0(C,k3_finseq_1(B)) => k3_finseq_1(k16_finseq_1(A,B,C)) = C ) ) ) ), file(finseq_1,t80_finseq_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( k3_finseq_1(A) = k1_nat_1(B,1) => ( B = 0 | k5_topreal1(2,A) = k4_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,k16_finseq_1(u1_struct_0(k15_euclid(2)),A,B)),k4_topreal1(2,A,B)) ) ) ) ) ), file(goboard2,t8_goboard2), []). 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_jordan1b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( v2_sppol_1(k3_topreal1(2,A,B)) => ( A = B | v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ) ), file(jordan1b,t8_jordan1b), []). 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(t9_amistd_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(C)) ) => k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),B) = k4_finseq_4(k5_numbers,A,C,B) ) ) ) ) ) ), file(amistd_1,t9_amistd_1), []).