% Mizar problem: t28_jordan1i,jordan1i,1904,64 fof(t28_jordan1i,conjecture,( ! [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))) ) => ( v1_sprect_2(A) <=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_finseq_6(u1_struct_0(k15_euclid(2)),A,k34_pscomp_1(k5_topreal1(2,A))),2),k28_pscomp_1(k5_topreal1(2,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_membered,cc1_relset_1,cc1_sprect_1,cc1_topreal6,cc20_membered,cc2_int_1,cc2_membered,cc2_sprect_1,cc2_topreal6,cc3_int_1,cc3_membered,cc3_topreal6,cc4_int_1,cc4_membered,cc4_topreal6,cc5_topreal6,cc6_membered,cc6_topreal6,cc7_topreal6,cc8_topreal6,cc9_membered,cc9_topreal6,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xboole_0,commutativity_k5_subset_1,connectedness_r1_xreal_0,d11_goboard1,d1_absvalue,d1_goboard9,d1_xboole_0,d3_jordan1a,d3_xboole_0,d4_finseq_4,d4_jordan5d,d5_goboard5,d5_tarski,d7_xboole_0,dt_g1_pre_topc,dt_k13_finseq_1,dt_k15_euclid,dt_k16_complex1,dt_k18_complex1,dt_k18_pscomp_1,dt_k19_pscomp_1,dt_k1_card_1,dt_k1_finseq_6,dt_k1_funct_1,dt_k1_matrix_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_tops_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_pscomp_1,dt_k21_euclid,dt_k21_pscomp_1,dt_k22_euclid,dt_k23_euclid,dt_k28_pscomp_1,dt_k2_goboard9,dt_k2_jordan1a,dt_k2_jordan2c,dt_k2_matrix_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k34_pscomp_1,dt_k35_pscomp_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_goboard2,dt_k3_goboard5,dt_k3_jordan1a,dt_k3_matrix_1,dt_k3_real_1,dt_k3_subset_1,dt_k3_xboole_0,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_gobrd13,dt_k4_jordan1a,dt_k4_jordan5d,dt_k4_tarski,dt_k4_xcmplx_0,dt_k5_binarith,dt_k5_finseq_4,dt_k5_goboard5,dt_k5_jordan1a,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_subset_1,dt_k5_topreal1,dt_k6_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_membered,fc11_membered,fc12_membered,fc12_sprect_1,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_int_1,fc1_revrot_1,fc1_sprect_1,fc1_sprect_3,fc27_membered,fc28_membered,fc29_membered,fc2_membered,fc2_revrot_1,fc2_sprect_1,fc2_sprect_3,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_int_1,fc3_jordan1a,fc3_revrot_1,fc3_sprect_1,fc4_int_1,fc4_jordan1a,fc4_revrot_1,fc5_goboard2,fc5_int_1,fc5_jordan1a,fc5_membered,fc5_revrot_1,fc6_int_1,fc6_jordan1a,fc6_membered,fc6_revrot_1,fc7_membered,fc7_revrot_1,fc8_int_1,fc8_membered,fc8_revrot_1,fc9_int_1,fc9_membered,fraenkel_a_1_1_jordan1i,fraenkel_a_2_5_goboard6,free_g1_pre_topc,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k3_subset_1,involutiveness_k4_xcmplx_0,projectivity_k16_complex1,projectivity_k18_complex1,rc1_int_1,rc1_membered,rc1_revrot_1,rc1_sprect_1,rc2_int_1,rc2_sprect_1,rc2_topreal6,redefinition_k18_complex1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_real_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_subset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r1_xboole_0,t104_pscomp_1,t108_pscomp_1,t10_revrot_1,t111_pscomp_1,t12_funct_1,t12_jordan1c,t15_jordan1c,t17_sprect_2,t17_sprect_5,t18_goboard9,t18_sppol_2,t1_arithm,t1_goboard5,t1_numerals,t1_real,t1_subset,t24_goboard9,t25_jordan1i,t26_goboard6,t27_finseq_3,t27_jordan1h,t28_gobrd13,t28_revrot_1,t29_nat_1,t2_boole,t2_real,t2_subset,t2_tarski,t2_xreal_1,t31_finseq_4,t33_finseq_3,t33_revrot_1,t38_nat_1,t39_binarith,t3_goboard5,t3_goboard9,t3_real,t3_subset,t3_topreal8,t3_xboole_0,t41_finseq_5,t48_jordan1h,t49_jordan1h,t4_arithm,t4_real,t4_subset,t50_binarith,t50_sprect_2,t50_xreal_1,t53_binarith,t56_euclid,t5_goboard5,t5_real,t5_subset,t6_boole,t6_real,t71_pscomp_1,t7_absvalue,t7_boole,t7_jordan1c,t7_jordan1g,t7_real,t8_boole,t8_real,t92_real_1,t96_finseq_6,t98_finseq_6]), [file(jordan1i,t28_jordan1i)]). 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_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v5_seqm_3(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & ~ v1_realset1(A) ) ) ), file(sprect_1,cc1_sprect_1), []). fof(cc1_topreal6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_connsp_1(B,A) ) ) ) ), file(topreal6,cc1_topreal6), []). fof(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_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(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_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(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(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(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_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v2_topreal4(A,k15_euclid(2)) => ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) ) ) ), file(topreal6,cc6_topreal6), []). fof(cc7_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) => v2_topreal4(A,k15_euclid(2)) ) ) ), file(topreal6,cc7_topreal6), []). fof(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(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(cc9_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v2_sppol_1(A) ) ) ), file(topreal6,cc9_topreal6), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). 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(d11_goboard1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_1(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( r1_goboard1(A,B,C) <=> ( ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C)) & k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F) ) ) ) ) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(k1_nat_1(D,1),k4_finseq_1(B)) ) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C)) & r2_hidden(k4_tarski(G,H),k2_matrix_1(C)) & k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F) & k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,1)) = k3_matrix_1(A,C,G,H) ) => k3_real_1(k18_complex1(k5_real_1(E,G)),k18_complex1(k5_real_1(F,H))) = 1 ) ) ) ) ) ) ) ) ) ) ) ), file(goboard1,d11_goboard1), []). fof(d1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xreal_0(0,A) => k16_complex1(A) = A ) & ( ~ r1_xreal_0(0,A) => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ), file(absvalue,d1_absvalue), []). fof(d1_goboard9,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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = k2_goboard9(A) <=> ( r4_connsp_1(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,A)),B) & r1_tarski(k1_tops_1(k15_euclid(2),k5_goboard5(A,1)),B) ) ) ) ) ), file(goboard9,d1_goboard9), []). fof(d1_xboole_0,axiom,( ! [A] : ( A = k1_xboole_0 <=> ! [B] : ~ r2_hidden(B,A) ) ), file(xboole_0,d1_xboole_0), []). fof(d3_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = k3_jordan1a(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,B) <=> ( r1_xreal_0(k21_euclid(A),k21_euclid(C)) & k22_euclid(C) = k22_euclid(A) ) ) ) ) ) ) ), file(jordan1a,d3_jordan1a), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). fof(d4_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). fof(d4_jordan5d,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) => ( B = k4_jordan5d(A) <=> ( r2_hidden(k4_tarski(k3_finseq_1(k3_goboard2(A)),B),k2_matrix_1(k3_goboard2(A))) & k3_matrix_1(u1_struct_0(k15_euclid(2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),B) = k34_pscomp_1(k5_topreal1(2,A)) ) ) ) ) ), file(jordan5d,d4_jordan5d), []). fof(d5_goboard5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( v2_goboard5(A) <=> r1_goboard1(u1_struct_0(k15_euclid(2)),A,k3_goboard2(A)) ) ) ), file(goboard5,d5_goboard5), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d7_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_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_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). fof(dt_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k18_complex1(A),k1_numbers) ) ), file(complex1,k18_complex1), []). fof(dt_k18_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k18_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k18_pscomp_1), []). fof(dt_k19_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k19_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k19_pscomp_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_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_matrix_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_1(A) ) => m2_subset_1(k1_matrix_1(A),k1_numbers,k5_numbers) ) ), file(matrix_1,k1_matrix_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_tops_1,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(tops_1,k1_tops_1), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k20_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k20_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k20_pscomp_1), []). fof(dt_k21_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k21_euclid(A),k1_numbers) ) ), file(euclid,k21_euclid), []). fof(dt_k21_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k21_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k21_pscomp_1), []). fof(dt_k22_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k22_euclid(A),k1_numbers) ) ), file(euclid,k22_euclid), []). fof(dt_k23_euclid,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k23_euclid(A,B),u1_struct_0(k15_euclid(2))) ) ), file(euclid,k23_euclid), []). fof(dt_k28_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k28_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(pscomp_1,k28_pscomp_1), []). fof(dt_k2_goboard9,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))) ) => m1_subset_1(k2_goboard9(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard9,k2_goboard9), []). 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_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(k2_jordan2c(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(jordan2c,k2_jordan2c), []). 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_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_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_k35_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k35_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k35_pscomp_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_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_goboard5,axiom,( ! [A,B,C] : ( ( v1_matrix_1(A) & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k3_goboard5(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard5,k3_goboard5), []). fof(dt_k3_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k3_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan1a,k3_jordan1a), []). 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_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ), file(subset_1,k3_subset_1), []). fof(dt_k3_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_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k4_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k4_gobrd13), []). fof(dt_k4_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_jordan5d,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))) ) => m2_subset_1(k4_jordan5d(A),k1_numbers,k5_numbers) ) ), file(jordan5d,k4_jordan5d), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_binarith,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k5_binarith(A,B),k1_numbers,k5_numbers) ) ), file(binarith,k5_binarith), []). fof(dt_k5_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_goboard5,axiom,( ! [A,B] : ( ( ~ 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) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k5_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard5,k5_goboard5), []). fof(dt_k5_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k5_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan1a,k5_jordan1a), []). 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_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_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_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_sprect_1,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(k2_goboard9(A)) ) ), file(sprect_1,fc12_sprect_1), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_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(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). fof(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(fc2_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(k2_goboard9(A)) & v2_topreal4(k2_goboard9(A),k15_euclid(2)) ) ) ), file(sprect_3,fc2_sprect_3), []). fof(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), []). fof(fc3_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ~ v1_xboole_0(k2_jordan1a(A)) & v2_connsp_1(k2_jordan1a(A),k15_euclid(2)) & v1_jordan1(k2_jordan1a(A),2) ) ) ), file(jordan1a,fc3_jordan1a), []). 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(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ~ v1_xboole_0(k3_jordan1a(A)) & v2_connsp_1(k3_jordan1a(A),k15_euclid(2)) & v1_jordan1(k3_jordan1a(A),2) ) ) ), file(jordan1a,fc4_jordan1a), []). 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(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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), []). fof(fc5_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ~ v1_xboole_0(k4_jordan1a(A)) & v2_connsp_1(k4_jordan1a(A),k15_euclid(2)) & v1_jordan1(k4_jordan1a(A),2) ) ) ), file(jordan1a,fc5_jordan1a), []). 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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc6_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ~ v1_xboole_0(k5_jordan1a(A)) & v2_connsp_1(k5_jordan1a(A),k15_euclid(2)) & v1_jordan1(k5_jordan1a(A),2) ) ) ), file(jordan1a,fc6_jordan1a), []). 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(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_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(fc9_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fraenkel_a_1_1_jordan1i,axiom,( ! [A,B] : ( ( ~ 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) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_1_jordan1i(B)) <=> ? [C,D] : ( m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) & A = k23_euclid(C,D) & ~ r1_xreal_0(C,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),k3_goboard2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,k34_pscomp_1(k5_topreal1(2,B)))),k3_finseq_1(k3_goboard2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,k34_pscomp_1(k5_topreal1(2,B))))),1))) & ~ r1_xreal_0(D,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),k3_goboard2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,k34_pscomp_1(k5_topreal1(2,B)))),1,k5_binarith(k4_jordan5d(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,k34_pscomp_1(k5_topreal1(2,B)))),1)))) & ~ r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),k3_goboard2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,k34_pscomp_1(k5_topreal1(2,B)))),1,k1_nat_1(k5_binarith(k4_jordan5d(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,k34_pscomp_1(k5_topreal1(2,B)))),1),1))),D) ) ) ) ), file(jordan1i,a_1_1_jordan1i), []). fof(fraenkel_a_2_5_goboard6,axiom,( ! [A,B,C] : ( ( m2_subset_1(B,k1_numbers,k5_numbers) & ~ v3_relat_1(C) & v1_matrix_1(C) & v3_goboard1(C) & v4_goboard1(C) & v5_goboard1(C) & v6_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_5_goboard6(B,C)) <=> ? [D,E] : ( m1_subset_1(D,k1_numbers) & m1_subset_1(E,k1_numbers) & A = k23_euclid(D,E) & ~ r1_xreal_0(D,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),1))) & ~ r1_xreal_0(E,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,1,B))) & ~ r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1))),E) ) ) ) ), file(goboard6,a_2_5_goboard6), []). fof(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(involutiveness_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,k3_subset_1(A,B)) = B ) ), file(subset_1,k3_subset_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ), file(complex1,k18_complex1), []). fof(rc1_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_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_revrot_1,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & ~ v5_seqm_3(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_finseq_6(B,A) & ~ v1_realset1(B) ) ) ), file(revrot_1,rc1_revrot_1), []). fof(rc1_sprect_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v5_seqm_3(A) ) ), file(sprect_1,rc1_sprect_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). 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(redefinition_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(A) = k16_complex1(A) ) ), file(complex1,k18_complex1), []). 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_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_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_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_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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(t104_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( k21_euclid(k35_pscomp_1(A)) = k20_pscomp_1(A) & k21_euclid(k34_pscomp_1(A)) = k20_pscomp_1(A) ) ) ), file(pscomp_1,t104_pscomp_1), []). fof(t108_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,k28_pscomp_1(B)) => ( k21_euclid(A) = k21_euclid(k35_pscomp_1(B)) & ( v6_compts_1(B,k15_euclid(2)) => ( r1_xreal_0(k22_euclid(k35_pscomp_1(B)),k22_euclid(A)) & r1_xreal_0(k22_euclid(A),k22_euclid(k34_pscomp_1(B))) ) ) ) ) ) ) ), file(pscomp_1,t108_pscomp_1), []). fof(t10_revrot_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( ( r2_hidden(C,k2_relat_1(D)) & r1_xreal_0(k5_finseq_4(D,C),A) & r1_xreal_0(A,k3_finseq_1(D)) ) => k4_finseq_4(k5_numbers,B,D,A) = k4_finseq_4(k5_numbers,B,k1_finseq_6(B,D,C),k5_binarith(k1_nat_1(A,1),k5_finseq_4(D,C))) ) ) ) ) ) ), file(revrot_1,t10_revrot_1), []). fof(t111_pscomp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(k35_pscomp_1(A),k28_pscomp_1(A)) & r2_hidden(k34_pscomp_1(A),k28_pscomp_1(A)) ) ) ), file(pscomp_1,t111_pscomp_1), []). fof(t12_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k1_relat_1(B)) => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ), file(funct_1,t12_funct_1), []). fof(t12_jordan1c,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r4_connsp_1(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A),k2_jordan2c(2,A)) ) ), file(jordan1c,t12_jordan1c), []). fof(t15_jordan1c,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xboole_0(k3_jordan1a(B),A) => r1_tarski(k3_jordan1a(B),k2_jordan2c(2,A)) ) ) ) ), file(jordan1c,t15_jordan1c), []). fof(t17_sprect_2,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,A) & k21_euclid(B) = k20_pscomp_1(A) ) => r2_hidden(B,k28_pscomp_1(A)) ) ) ) ), file(sprect_2,t17_sprect_2), []). fof(t17_sprect_5,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),k5_finseq_4(A,k34_pscomp_1(k5_topreal1(2,A)))) ) ), file(sprect_5,t17_sprect_5), []). fof(t18_goboard9,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(1,B) & r1_xreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & k1_tops_1(k15_euclid(2),k5_goboard5(A,B)) = k1_xboole_0 ) ) ) ), file(goboard9,t18_goboard9), []). 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_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_goboard5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(k4_tarski(B,C),k2_matrix_1(A)) => ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) & r1_xreal_0(1,C) & r1_xreal_0(C,k1_matrix_1(A)) ) ) ) ) ) ), file(goboard5,t1_goboard5), []). fof(t1_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(t24_goboard9,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(1,B) & r1_xreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => r1_tarski(k1_tops_1(k15_euclid(2),k5_goboard5(A,B)),k2_goboard9(A)) ) ) ) ), file(goboard9,t24_goboard9), []). fof(t25_jordan1i,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) & v1_sprect_2(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r1_goboard1(u1_struct_0(k15_euclid(2)),A,B) & r1_xreal_0(1,C) & r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,C) = k34_pscomp_1(k5_topreal1(2,A)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_1(B)) & 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,k1_nat_1(E,1)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),B,D,E) ) ) ) ) ) ) ) ), file(jordan1i,t25_jordan1i), []). fof(t26_goboard6,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [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)))) ) => ( r1_xreal_0(1,A) => ( r1_xreal_0(k1_matrix_1(B),A) | k1_tops_1(k15_euclid(2),k3_goboard5(B,k3_finseq_1(B),A)) = a_2_5_goboard6(A,B) ) ) ) ) ), file(goboard6,t26_goboard6), []). 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_jordan1h,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(B)) ) => k4_gobrd13(B,k3_goboard2(B),A) = k5_goboard5(B,A) ) ) ) ), file(jordan1h,t27_jordan1h), []). fof(t28_gobrd13,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_1(E) & v3_goboard1(E) & v4_goboard1(E) & v5_goboard1(E) & v6_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xreal_0(1,A) & r1_xreal_0(k1_nat_1(A,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(B,k1_nat_1(C,1)),k2_matrix_1(E)) & r2_hidden(k4_tarski(B,C),k2_matrix_1(E)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(2)),E,B,k1_nat_1(C,1)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),D,k1_nat_1(A,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),E,B,C) ) => k4_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) ), file(gobrd13,t28_gobrd13), []). fof(t28_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => k3_goboard2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) = k3_goboard2(B) ) ) ), file(revrot_1,t28_revrot_1), []). 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_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t31_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k2_relat_1(A)) => ( r1_xreal_0(1,k5_finseq_4(A,B)) & r1_xreal_0(k5_finseq_4(A,B),k3_finseq_1(A)) ) ) ) ), file(finseq_4,t31_finseq_4), []). fof(t33_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k2_relat_1(A)) => r2_hidden(1,k4_finseq_1(A)) ) ) ), file(finseq_3,t33_finseq_3), []). 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(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(t39_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => k5_binarith(k2_xcmplx_0(A,B),B) = A ) ) ), file(binarith,t39_binarith), []). fof(t3_goboard5,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_matrix_1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v3_goboard1(C) & r1_xreal_0(1,A) & r1_xreal_0(A,k1_matrix_1(C)) & r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(C)) ) => k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,B,A)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,B,1)) ) ) ) ) ), file(goboard5,t3_goboard5), []). fof(t3_goboard9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r4_connsp_1(A,D,B) & r4_connsp_1(A,D,C) & B != C & ~ r1_xboole_0(B,C) ) ) ) ) ) ), file(goboard9,t3_goboard9), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_topreal8,axiom,( ! [A] : ( ~ v1_realset1(A) => ! [B] : ( ( ~ v5_seqm_3(B) & v1_finseq_6(B,A) & m2_finseq_1(B,A) ) => ~ r1_xreal_0(k3_finseq_1(B),2) ) ) ), file(topreal8,t3_topreal8), []). fof(t3_xboole_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), []). fof(t41_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)) => k4_finseq_4(k5_numbers,A,C,k5_finseq_4(C,B)) = B ) ) ) ) ), file(finseq_5,t41_finseq_5), []). fof(t48_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_sprect_2(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) => v1_sprect_2(B) ) ) ) ), file(jordan1h,t48_jordan1h), []). fof(t49_jordan1h,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))) ) => ( k2_goboard9(A) = k2_jordan2c(2,k5_topreal1(2,A)) => v1_sprect_2(A) ) ) ), file(jordan1h,t49_jordan1h), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). 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_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(A,B) => k5_binarith(B,A) = k6_xcmplx_0(B,A) ) ) ) ), file(binarith,t50_binarith), []). 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(t50_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => r1_xreal_0(0,k6_xcmplx_0(B,A)) ) ) ) ), file(xreal_1,t50_xreal_1), []). 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(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_goboard5,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_matrix_1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( v5_goboard1(D) & r1_xreal_0(1,A) & ~ r1_xreal_0(B,A) & r1_xreal_0(B,k1_matrix_1(D)) & r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(D)) & r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),D,C,B)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),D,C,A))) ) ) ) ) ) ), file(goboard5,t5_goboard5), []). 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(t71_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,B) => ( r1_xreal_0(k18_pscomp_1(B),k21_euclid(A)) & r1_xreal_0(k21_euclid(A),k20_pscomp_1(B)) & r1_xreal_0(k21_pscomp_1(B),k22_euclid(A)) & r1_xreal_0(k22_euclid(A),k19_pscomp_1(B)) ) ) ) ) ), file(pscomp_1,t71_pscomp_1), []). fof(t7_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( A = 0 <=> k18_complex1(A) = 0 ) ) ), file(absvalue,t7_absvalue), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,k5_jordan1a(A)) & r2_hidden(A,k3_jordan1a(A)) & r2_hidden(A,k2_jordan1a(A)) & r2_hidden(A,k4_jordan1a(A)) ) ) ), file(jordan1c,t7_jordan1c), []). fof(t7_jordan1g,axiom,( ! [A] : ( ( v1_matrix_1(A) & v3_goboard1(A) & v6_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r2_hidden(k4_tarski(B,D),k2_matrix_1(A)) & r2_hidden(k4_tarski(C,E),k2_matrix_1(A)) & k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,B,D)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,E)) ) => B = C ) ) ) ) ) ) ), file(jordan1g,t7_jordan1g), []). 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(t92_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) ) & ~ ( ( ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) ) | ( r1_xreal_0(A,B) & ~ r1_xreal_0(D,C) ) ) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ) ), file(real_1,t92_real_1), []). 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), []). fof(t98_finseq_6,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)) => k4_finseq_4(k5_numbers,A,k1_finseq_6(A,C,B),1) = B ) ) ) ) ), file(finseq_6,t98_finseq_6), []).