% Mizar problem: t14_jordan19,jordan19,1535,61 fof(t14_jordan19,conjecture,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) => ~ ( ~ r1_xreal_0(C,1) & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C) & r1_xreal_0(1,E) & r1_xreal_0(E,D) & r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A))) & k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k5_topreal1(2,k1_jordan1e(B,A))) = k1_struct_0(k15_euclid(2),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)) & k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k5_topreal1(2,k2_jordan1e(B,A))) = k1_struct_0(k15_euclid(2),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r2_subset_1(k3_topreal1(2,k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k9_jordan6(B)) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_topreal6,cc11_topreal6,cc1_finseq_1,cc1_finseq_5,cc1_jordan1b,cc1_real_1,cc1_relset_1,cc1_sppol_2,cc1_sprect_1,cc1_topreal6,cc1_xreal_0,cc2_int_1,cc2_sppol_2,cc2_sprect_1,cc2_topreal6,cc2_xreal_0,cc3_int_1,cc3_sppol_2,cc3_topreal6,cc3_xreal_0,cc4_int_1,cc4_topreal6,cc4_xreal_0,cc5_topreal6,cc5_xreal_0,cc6_topreal6,cc6_xreal_0,cc7_topreal6,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_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_subset_1,commutativity_k5_subset_1,connectedness_r1_xreal_0,d10_topreal1,d10_xboole_0,d1_jordan1e,d1_jordan8,d1_jordan9,d1_tarski,d2_tarski,d2_xboole_0,d3_binarith,d3_jordan1a,d3_tarski,d3_xboole_0,d4_finseq_4,d4_jordan2c,d4_xboole_0,d5_real_1,d5_tarski,d5_topreal1,d6_goboard5,d8_topreal1,d9_jordan6,d9_topreal1,dt_g1_pre_topc,dt_k10_finseq_1,dt_k13_finseq_1,dt_k15_euclid,dt_k16_finseq_1,dt_k18_pscomp_1,dt_k19_pscomp_1,dt_k1_card_1,dt_k1_card_4,dt_k1_finseq_1,dt_k1_finseq_5,dt_k1_finseq_6,dt_k1_funct_1,dt_k1_jordan1e,dt_k1_jordan3,dt_k1_jordan5c,dt_k1_jordan8,dt_k1_jordan9,dt_k1_matrix_1,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_k20_pscomp_1,dt_k21_euclid,dt_k21_pscomp_1,dt_k22_euclid,dt_k23_euclid,dt_k26_pscomp_1,dt_k28_pscomp_1,dt_k2_finseq_1,dt_k2_finseq_4,dt_k2_goboard9,dt_k2_jordan1a,dt_k2_jordan1e,dt_k2_jordan2c,dt_k2_jordan3,dt_k2_jordan5c,dt_k2_matrix_1,dt_k2_newton,dt_k2_relat_1,dt_k2_struct_0,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k30_pscomp_1,dt_k31_pscomp_1,dt_k32_pscomp_1,dt_k33_pscomp_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_goboard9,dt_k3_gobrd13,dt_k3_graph_2,dt_k3_jordan1a,dt_k3_jordan3,dt_k3_matrix_1,dt_k3_real_1,dt_k3_subset_1,dt_k3_topreal1,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k4_card_1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_goboard5,dt_k4_gobrd13,dt_k4_graph_2,dt_k4_jordan1a,dt_k4_jordan3,dt_k4_real_1,dt_k4_relset_1,dt_k4_subset_1,dt_k4_tarski,dt_k4_topreal1,dt_k4_xboole_0,dt_k5_binarith,dt_k5_finseq_4,dt_k5_gobrd13,dt_k5_jordan1a,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_subset_1,dt_k5_topreal1,dt_k6_gobrd13,dt_k6_jordan6,dt_k6_real_1,dt_k6_subset_1,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_k8_jordan6,dt_k9_jordan6,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_sppol_2,fc10_xreal_0,fc11_finseq_1,fc11_sppol_2,fc11_xreal_0,fc12_sprect_1,fc12_xreal_0,fc13_pscomp_1,fc13_sprect_1,fc15_finseq_1,fc15_pscomp_1,fc15_xreal_0,fc16_finseq_1,fc16_xreal_0,fc17_finseq_1,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finseq_1,fc1_gobrd11,fc1_int_1,fc1_jordan1a,fc1_jordan1j,fc1_jordan8,fc1_pscomp_1,fc1_revrot_1,fc1_sppol_2,fc1_sprect_1,fc1_sprect_3,fc1_subset_1,fc1_xboole_0,fc20_xreal_0,fc21_xreal_0,fc22_xreal_0,fc23_xreal_0,fc24_xreal_0,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_euclid,fc2_finseq_1,fc2_finseq_5,fc2_int_1,fc2_jordan1a,fc2_jordan1g,fc2_jordan8,fc2_pscomp_1,fc2_revrot_1,fc2_sprect_1,fc2_sprect_3,fc2_subset_1,fc2_topreal6,fc2_xboole_0,fc30_xreal_0,fc3_finseq_5,fc3_jordan1a,fc3_jordan1g,fc3_revrot_1,fc3_sppol_2,fc3_sprect_1,fc3_sprect_3,fc3_subset_1,fc3_xboole_0,fc3_xreal_0,fc4_int_1,fc4_jordan1a,fc4_revrot_1,fc4_sppol_2,fc4_subset_1,fc4_xreal_0,fc5_finseq_1,fc5_finseq_5,fc5_goboard2,fc5_jordan1a,fc5_revrot_1,fc5_xreal_0,fc6_int_1,fc6_jordan1a,fc6_revrot_1,fc6_sppol_2,fc6_xreal_0,fc7_finseq_1,fc7_int_1,fc7_revrot_1,fc7_xreal_0,fc8_int_1,fc8_revrot_1,fc8_sppol_2,fc8_xreal_0,fc9_finseq_1,fc9_int_1,fc9_xreal_0,free_g1_pre_topc,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,involutiveness_k3_subset_1,irreflexivity_r1_subset_1,irreflexivity_r2_subset_1,rc1_finseq_1,rc1_finseq_5,rc1_int_1,rc1_jordan1a,rc1_jordan1g,rc1_jordan1j,rc1_pscomp_1,rc1_revrot_1,rc1_sppol_2,rc1_sprect_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_finseq_1,rc2_finseq_5,rc2_int_1,rc2_jordan1a,rc2_pscomp_1,rc2_sppol_2,rc2_sprect_1,rc2_subset_1,rc2_topreal6,rc2_xboole_0,rc2_xreal_0,rc3_finseq_1,rc3_jordan1a,rc3_pscomp_1,rc3_xreal_0,rc4_finseq_1,rc4_pscomp_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,rc9_pscomp_1,redefinition_k1_card_4,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_card_1,redefinition_k4_finseq_1,redefinition_k4_graph_2,redefinition_k4_real_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_subset_1,redefinition_k6_real_1,redefinition_k6_subset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_subset_1,redefinition_r2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,symmetry_r1_subset_1,symmetry_r1_xboole_0,symmetry_r2_subset_1,t104_jordan1a,t104_pscomp_1,t10_finseq_5,t10_goboard7,t10_jordan1e,t111_pscomp_1,t11_finseq_2,t11_jordan1e,t11_jordan6,t11_topreal3,t11_topreal8,t11_xreal_1,t12_topreal8,t13_graph_2,t13_jordan8,t13_realset1,t14_revrot_1,t15_jordan1e,t15_jordan8,t15_sprect_1,t16_jgraph_1,t16_jordan1a,t16_jordan2c,t16_sprect_2,t17_jordan1e,t18_sppol_2,t19_compts_1,t19_jordan1e,t19_jordan9,t1_arithm,t1_boole,t1_goboard5,t1_numerals,t1_real,t1_subset,t1_xboole_1,t1_xreal_1,t20_jordan1e,t21_goboard1,t21_jordan1j,t21_sppol_2,t21_xreal_1,t22_xreal_1,t23_sprect_5,t23_xboole_1,t24_sprect_5,t25_jordan1i,t25_jordan3,t25_sprect_5,t26_finseq_4,t26_jordan1g,t26_sprect_5,t26_topreal3,t26_xboole_1,t27_finseq_3,t27_jordan1i,t27_jordan2c,t27_topreal1,t27_xboole_1,t28_finseq_3,t28_revrot_1,t29_finseq_3,t29_finseq_4,t29_jordan1d,t29_jordan1h,t29_jordan9,t2_arithm,t2_boole,t2_goboard3,t2_goboard5,t2_real,t2_subset,t2_xreal_1,t31_finseq_4,t31_jordan4,t31_topreal8,t33_jordan1j,t33_revrot_1,t33_topreal8,t34_revrot_1,t34_topreal8,t35_jordan1j,t35_topreal8,t36_goboard7,t36_jordan1j,t37_jordan1j,t37_sppol_1,t38_jordan1j,t38_nat_1,t39_binarith,t39_jordan1a,t39_jordan1j,t39_sprect_3,t3_arithm,t3_boole,t3_goboard5,t3_real,t3_revrot_1,t3_subset,t3_xboole_0,t40_jordan1g,t40_jordan1j,t41_enumset1,t41_finseq_5,t41_jordan3,t42_jordan3,t43_jordan1j,t43_subset_1,t44_finseq_5,t45_jordan3,t46_finseq_6,t46_gobrd14,t46_jordan1j,t47_sprect_2,t4_arithm,t4_boole,t4_finseq_1,t4_jordan1g,t4_partfun2,t4_real,t4_subset,t4_topreal1,t4_xboole_1,t50_sprect_2,t51_jordan1j,t52_binarith,t52_jordan1h,t52_jordan1j,t53_binarith,t53_jordan1j,t54_jordan1j,t55_jordan1j,t56_jordan1j,t57_jordan1g,t57_jordan1j,t58_jordan3,t59_jordan3,t5_amistd_1,t5_arithm,t5_goboard7,t5_goboard9,t5_jordan10,t5_jordan1f,t5_jordan1g,t5_real,t5_subset,t61_finseq_1,t61_jordan3,t62_sprect_1,t63_xboole_1,t69_jordan3,t6_amistd_1,t6_arithm,t6_boole,t6_finseq_5,t6_jordan1f,t6_real,t6_topreal1,t70_jordan3,t70_xboole_1,t71_pscomp_1,t76_jordan3,t77_jordan3,t7_boole,t7_jordan1c,t7_jordan1f,t7_jordan1g,t7_jordan8,t7_real,t7_topreal8,t7_xboole_1,t84_pscomp_1,t85_finseq_4,t88_pscomp_1,t8_boole,t8_goboard7,t8_jordan1b,t8_jordan1f,t8_jordan1i,t8_jordan8,t8_real,t8_xboole_1,t92_jordan1a,t94_jordan1a,t95_finseq_6,t98_finseq_6,t9_amistd_1,t9_jordan1c,t9_jordan1i,t9_sppol_2,t9_xreal_1]), [file(jordan19,t14_jordan19)]). 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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finseq_5,axiom,( ! [A] : ( v1_xboole_0(A) => v1_realset1(A) ) ), file(finseq_5,cc1_finseq_5), []). fof(cc1_jordan1b,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_xboole_0(A) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v1_topreal2(A) ) ) ) ), file(jordan1b,cc1_jordan1b), []). fof(cc1_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_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_sppol_2,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ( v2_funct_1(A) & ~ v1_realset1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) ) => v4_topreal1(A) ) ) ), file(sppol_2,cc2_sppol_2), []). fof(cc2_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_realset1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) ) ), file(sprect_1,cc2_sprect_1), []). fof(cc2_topreal6,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v6_compts_1(B,A) ) ) ) ), file(topreal6,cc2_topreal6), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_sppol_1(A) => ~ v1_xboole_0(A) ) ) ), file(topreal6,cc4_topreal6), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v2_sppol_1(A) => ~ v1_xboole_0(A) ) ) ), file(topreal6,cc5_topreal6), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v2_topreal4(A,k15_euclid(2)) => ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) ) ) ), file(topreal6,cc6_topreal6), []). fof(cc6_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_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) => v2_topreal4(A,k15_euclid(2)) ) ) ), file(topreal6,cc7_topreal6), []). fof(cc7_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_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(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_jordan1e,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k1_jordan1e(A,B) = k1_finseq_5(u1_struct_0(k15_euclid(2)),k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(2,k1_jordan9(A,B)))) ) ) ), file(jordan1e,d1_jordan1e), []). fof(d1_jordan8,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [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)))) ) => ( C = k1_jordan8(A,B) <=> ( k3_finseq_1(C) = k1_nat_1(k1_card_4(2,B),3) & k3_finseq_1(C) = k1_matrix_1(C) & ! [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(C)) => k3_matrix_1(u1_struct_0(k15_euclid(2)),C,D,E) = k23_euclid(k3_real_1(k18_pscomp_1(A),k4_real_1(k6_real_1(k5_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),k1_card_4(2,B)),k5_real_1(D,2))),k3_real_1(k21_pscomp_1(A),k4_real_1(k6_real_1(k5_real_1(k19_pscomp_1(A),k21_pscomp_1(A)),k1_card_4(2,B)),k5_real_1(E,2)))) ) ) ) ) ) ) ) ) ), file(jordan8,d1_jordan8), []). fof(d1_jordan9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( v2_connsp_1(A,k15_euclid(2)) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_sprect_2(C) & ~ v5_seqm_3(C) & v1_topreal1(C) & v2_topreal1(C) & v1_finseq_6(C,u1_struct_0(k15_euclid(2))) & v1_goboard5(C) & v2_goboard5(C) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ( C = k1_jordan9(A,B) <=> ( r1_goboard1(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B)) & ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(1,D) & r1_xreal_0(k1_nat_1(D,1),k3_finseq_1(k1_jordan8(A,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_matrix_1(k1_jordan8(A,B))) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(D,1),k1_matrix_1(k1_jordan8(A,B))) & r2_hidden(k32_pscomp_1(A),k3_goboard5(k1_jordan8(A,B),D,k5_binarith(k1_matrix_1(k1_jordan8(A,B)),1))) & k32_pscomp_1(A) != k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k5_binarith(k1_matrix_1(k1_jordan8(A,B)),1)) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_xreal_0(k1_nat_1(D,2),k3_finseq_1(C)) ) => ( ( ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A) & r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),D),A) ) => r1_gobrd13(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B),D) ) & ( r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A) => ( r1_xboole_0(k5_gobrd13(C,k1_jordan8(A,B),D),A) | r3_gobrd13(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B),D) ) ) & ( ~ r1_xboole_0(k6_gobrd13(C,k1_jordan8(A,B),D),A) => r2_gobrd13(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B),D) ) ) ) ) ) ) ) ) ) ) ), file(jordan9,d1_jordan9), []). fof(d1_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_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_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). fof(d4_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_jordan2c,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_jordan2c(A,B,C) <=> ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C) & ~ v1_jordan2c(C,A) ) ) ) ) ) ), file(jordan2c,d4_jordan2c), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(d5_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(d6_goboard5,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) & 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)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( C = k4_goboard5(A,B) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [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) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k3_goboard2(A))) & r2_hidden(k4_tarski(F,G),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),D,E) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k3_goboard2(A),F,G) & ~ ( D = F & k1_nat_1(E,1) = G & C = k3_goboard5(k3_goboard2(A),D,E) ) & ~ ( k1_nat_1(D,1) = F & E = G & C = k3_goboard5(k3_goboard2(A),D,k5_binarith(E,1)) ) & ~ ( D = k1_nat_1(F,1) & E = G & C = k3_goboard5(k3_goboard2(A),F,G) ) & ~ ( D = F & E = k1_nat_1(G,1) & C = k3_goboard5(k3_goboard2(A),k5_binarith(D,1),G) ) ) ) ) ) ) ) ) ) ) ) ), file(goboard5,d6_goboard5), []). fof(d8_topreal1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_topreal1(A) <=> ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,B) & r1_xreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => k5_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal1(2,A,B),k4_topreal1(2,A,k1_nat_1(B,1))) = k1_struct_0(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1))) ) ) ) ) ), file(topreal1,d8_topreal1), []). fof(d9_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( B = k9_jordan6(A) <=> ( r1_topreal1(k15_euclid(2),k34_pscomp_1(A),k30_pscomp_1(A),B) & k5_subset_1(u1_struct_0(k15_euclid(2)),k8_jordan6(A),B) = k2_struct_0(k15_euclid(2),k30_pscomp_1(A),k34_pscomp_1(A)) & k4_subset_1(u1_struct_0(k15_euclid(2)),k8_jordan6(A),B) = A & ~ r1_xreal_0(k22_euclid(k1_jordan5c(k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),2)),k30_pscomp_1(A),k34_pscomp_1(A))),k22_euclid(k2_jordan5c(B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),2)),k34_pscomp_1(A),k30_pscomp_1(A)))) ) ) ) ) ) ), file(jordan6,d9_jordan6), []). fof(d9_topreal1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v3_topreal1(A) <=> ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(C,k1_nat_1(B,1)) => r1_xboole_0(k4_topreal1(2,A,B),k4_topreal1(2,A,C)) ) ) ) ) ) ), file(topreal1,d9_topreal1), []). 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_k18_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k18_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k18_pscomp_1), []). fof(dt_k19_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k19_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k19_pscomp_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_card_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_card_4(A,B),k1_numbers,k5_numbers) ) ), file(card_4,k1_card_4), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_finseq_5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k1_finseq_5(A,B,C),A) ) ), file(finseq_5,k1_finseq_5), []). fof(dt_k1_finseq_6,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k1_finseq_6(A,B,C),A) ) ), file(finseq_6,k1_finseq_6), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_jordan1e,axiom,( ! [A,B] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => m2_finseq_1(k1_jordan1e(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan1e,k1_jordan1e), []). fof(dt_k1_jordan3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) ) => m2_finseq_1(k1_jordan3(A,B,C,D),A) ) ), file(jordan3,k1_jordan3), []). fof(dt_k1_jordan5c,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) & m1_subset_1(D,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(k1_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(2))) ) ), file(jordan5c,k1_jordan5c), []). fof(dt_k1_jordan8,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( v1_matrix_1(k1_jordan8(A,B)) & m2_finseq_1(k1_jordan8(A,B),k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan8,k1_jordan8), []). fof(dt_k1_jordan9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k1_jordan9(A,B)) & v1_sprect_2(k1_jordan9(A,B)) & ~ v5_seqm_3(k1_jordan9(A,B)) & v1_topreal1(k1_jordan9(A,B)) & v2_topreal1(k1_jordan9(A,B)) & v1_finseq_6(k1_jordan9(A,B),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_jordan9(A,B)) & v2_goboard5(k1_jordan9(A,B)) & m2_finseq_1(k1_jordan9(A,B),u1_struct_0(k15_euclid(2))) ) ) ), file(jordan9,k1_jordan9), []). fof(dt_k1_matrix_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_1(A) ) => m2_subset_1(k1_matrix_1(A),k1_numbers,k5_numbers) ) ), file(matrix_1,k1_matrix_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_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_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_k26_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k26_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(pscomp_1,k26_pscomp_1), []). 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_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_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_jordan1e,axiom,( ! [A,B] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => m2_finseq_1(k2_jordan1e(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan1e,k2_jordan1e), []). 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_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_jordan5c,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) & m1_subset_1(D,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(k2_jordan5c(A,B,C,D),u1_struct_0(k15_euclid(2))) ) ), file(jordan5c,k2_jordan5c), []). fof(dt_k2_matrix_1,axiom,( $true ), file(matrix_1,k2_matrix_1), []). fof(dt_k2_newton,axiom,( $true ), file(newton,k2_newton), []). 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_k30_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k30_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k30_pscomp_1), []). fof(dt_k31_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k31_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k31_pscomp_1), []). fof(dt_k32_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k32_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k32_pscomp_1), []). fof(dt_k33_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k33_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k33_pscomp_1), []). fof(dt_k34_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k34_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k34_pscomp_1), []). fof(dt_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_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(k3_goboard9(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard9,k3_goboard9), []). fof(dt_k3_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k3_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k3_gobrd13), []). fof(dt_k3_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_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_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_finseq_1(k3_jordan3(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan3,k3_jordan3), []). 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_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k3_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k3_topreal1), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). 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_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(k4_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard5,k4_goboard5), []). 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_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_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_finseq_1(k4_jordan3(A,B),u1_struct_0(k15_euclid(2))) ) ), file(jordan3,k4_jordan3), []). fof(dt_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_topreal1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k4_topreal1(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k4_topreal1), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_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_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k5_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k5_gobrd13), []). fof(dt_k5_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_gobrd13,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_1(B) & v3_goboard1(B) & v4_goboard1(B) & v5_goboard1(B) & v6_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k6_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(gobrd13,k6_gobrd13), []). fof(dt_k6_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k6_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(jordan6,k6_jordan6), []). fof(dt_k6_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ), file(real_1,k6_real_1), []). fof(dt_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_1), []). fof(dt_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_k8_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_xboole_0(k8_jordan6(A)) & m1_subset_1(k8_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan6,k8_jordan6), []). fof(dt_k9_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_xboole_0(k9_jordan6(A)) & m1_subset_1(k9_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ), file(jordan6,k9_jordan6), []). fof(dt_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_sppol_2,axiom,( ! [A,B] : ( ( v1_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc10_sppol_2), []). fof(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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(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_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(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_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)))) ) => ( ~ v1_xboole_0(k26_pscomp_1(A)) & v6_compts_1(k26_pscomp_1(A),k15_euclid(2)) ) ) ), file(pscomp_1,fc13_pscomp_1), []). fof(fc13_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(k3_goboard9(A)) ) ), file(sprect_1,fc13_sprect_1), []). fof(fc15_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_xboole_0(k16_finseq_1(A,B,0)) & v1_relat_1(k16_finseq_1(A,B,0)) & v1_funct_1(k16_finseq_1(A,B,0)) & v2_funct_1(k16_finseq_1(A,B,0)) & v1_finset_1(k16_finseq_1(A,B,0)) & v1_finseq_1(k16_finseq_1(A,B,0)) ) ) ), file(finseq_1,fc15_finseq_1), []). fof(fc15_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)))) ) => ( ~ v1_xboole_0(k28_pscomp_1(A)) & v6_compts_1(k28_pscomp_1(A),k15_euclid(2)) ) ) ), file(pscomp_1,fc15_pscomp_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_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). 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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). 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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_gobrd11,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(k3_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,A))) ) ), file(gobrd11,fc1_gobrd11), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k9_jordan6(A)) & v4_pre_topc(k9_jordan6(A),k15_euclid(2)) & v6_compts_1(k9_jordan6(A),k15_euclid(2)) & v1_jordan2c(k9_jordan6(A),2) ) ) ), file(jordan1a,fc1_jordan1a), []). fof(fc1_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_jordan8,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k1_jordan8(A,B)) & ~ v3_relat_1(k1_jordan8(A,B)) & v1_funct_1(k1_jordan8(A,B)) & v1_finset_1(k1_jordan8(A,B)) & v1_finseq_1(k1_jordan8(A,B)) & v1_matrix_1(k1_jordan8(A,B)) & v3_goboard1(k1_jordan8(A,B)) & v4_goboard1(k1_jordan8(A,B)) ) ) ), file(jordan8,fc1_jordan8), []). fof(fc1_pscomp_1,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) & ~ v1_setfam_1(k1_numbers) ), file(pscomp_1,fc1_pscomp_1), []). fof(fc1_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(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(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(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(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_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) ) ) ), file(euclid,fc2_euclid), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k8_jordan6(A)) & v4_pre_topc(k8_jordan6(A),k15_euclid(2)) & v6_compts_1(k8_jordan6(A),k15_euclid(2)) & v1_jordan2c(k8_jordan6(A),2) ) ) ), file(jordan1a,fc2_jordan1a), []). fof(fc2_jordan1g,axiom,( ! [A,B] : ( ( v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k1_jordan1e(A,B)) & v1_relat_1(k1_jordan1e(A,B)) & v1_funct_1(k1_jordan1e(A,B)) & v2_funct_1(k1_jordan1e(A,B)) & v1_finset_1(k1_jordan1e(A,B)) & v1_finseq_1(k1_jordan1e(A,B)) & ~ v1_realset1(k1_jordan1e(A,B)) & v1_topreal1(k1_jordan1e(A,B)) & v2_topreal1(k1_jordan1e(A,B)) & v3_topreal1(k1_jordan1e(A,B)) & v4_topreal1(k1_jordan1e(A,B)) & v2_goboard5(k1_jordan1e(A,B)) ) ) ), file(jordan1g,fc2_jordan1g), []). fof(fc2_jordan8,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k1_jordan8(A,B)) & ~ v3_relat_1(k1_jordan8(A,B)) & v1_funct_1(k1_jordan8(A,B)) & v1_finset_1(k1_jordan8(A,B)) & v1_finseq_1(k1_jordan8(A,B)) & v1_matrix_1(k1_jordan8(A,B)) & v3_goboard1(k1_jordan8(A,B)) & v4_goboard1(k1_jordan8(A,B)) & v5_goboard1(k1_jordan8(A,B)) & v6_goboard1(k1_jordan8(A,B)) ) ) ), file(jordan8,fc2_jordan8), []). fof(fc2_pscomp_1,axiom, ( ~ v1_xboole_0(k5_ordinal2) & v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) & ~ v1_setfam_1(k5_ordinal2) ), file(pscomp_1,fc2_pscomp_1), []). fof(fc2_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(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_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(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). 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_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_jordan1g,axiom,( ! [A,B] : ( ( v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k2_jordan1e(A,B)) & v1_relat_1(k2_jordan1e(A,B)) & v1_funct_1(k2_jordan1e(A,B)) & v2_funct_1(k2_jordan1e(A,B)) & v1_finset_1(k2_jordan1e(A,B)) & v1_finseq_1(k2_jordan1e(A,B)) & ~ v1_realset1(k2_jordan1e(A,B)) & v1_topreal1(k2_jordan1e(A,B)) & v2_topreal1(k2_jordan1e(A,B)) & v3_topreal1(k2_jordan1e(A,B)) & v4_topreal1(k2_jordan1e(A,B)) & v2_goboard5(k2_jordan1e(A,B)) ) ) ), file(jordan1g,fc3_jordan1g), []). fof(fc3_revrot_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & ~ v3_realset2(k15_euclid(A)) ) ) ), file(revrot_1,fc3_revrot_1), []). fof(fc3_sppol_2,axiom,( ! [A,B] : ( ( v2_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v2_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc3_sppol_2), []). fof(fc3_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) ) ), file(sprect_1,fc3_sprect_1), []). fof(fc3_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(k3_goboard9(A)) & v2_topreal4(k3_goboard9(A),k15_euclid(2)) ) ) ), file(sprect_3,fc3_sprect_3), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). 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_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(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(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). fof(fc5_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc5_finseq_1), []). fof(fc5_finseq_5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & v2_funct_1(C) & m1_finseq_1(C,A) ) => ( v1_relat_1(k1_finseq_5(A,C,B)) & v1_funct_1(k1_finseq_5(A,C,B)) & v2_funct_1(k1_finseq_5(A,C,B)) & v1_finset_1(k1_finseq_5(A,C,B)) & v1_finseq_1(k1_finseq_5(A,C,B)) ) ) ), file(finseq_5,fc5_finseq_5), []). fof(fc5_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_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_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_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_revrot_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_relat_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_funct_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & ~ v5_seqm_3(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finset_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v2_topreal1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & v1_finseq_6(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) & ~ v1_realset1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A)) ) ) ), file(revrot_1,fc6_revrot_1), []). fof(fc6_sppol_2,axiom,( ! [A,B] : ( ( v3_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( v1_relat_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_funct_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finset_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v1_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) & v3_topreal1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B)) ) ) ), file(sppol_2,fc6_sppol_2), []). fof(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_finseq_1,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)) ) ), file(finseq_1,fc7_finseq_1), []). fof(fc7_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). 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_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_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_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_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_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(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(irreflexivity_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r1_subset_1(A,A) ) ), file(subset_1,r1_subset_1), []). fof(irreflexivity_r2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r2_subset_1(A,A) ) ), file(subset_1,r2_subset_1), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finseq_5,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_5,rc1_finseq_5), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v1_jordan2c(A,2) & v1_topreal2(A) ) ), file(jordan1a,rc1_jordan1a), []). fof(rc1_jordan1g,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_realset1(A) & v5_seqm_3(A) ) ), file(jordan1g,rc1_jordan1g), []). fof(rc1_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_pscomp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(pscomp_1,rc1_pscomp_1), []). fof(rc1_revrot_1,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & ~ v5_seqm_3(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_finseq_6(B,A) & ~ v1_realset1(B) ) ) ), file(revrot_1,rc1_revrot_1), []). fof(rc1_sppol_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v4_topreal1(A) ) ), file(sppol_2,rc1_sppol_2), []). fof(rc1_sprect_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v5_seqm_3(A) ) ), file(sprect_1,rc1_sprect_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(finseq_5,rc2_finseq_5), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & v1_sppol_1(A) & v1_jordan2c(A,2) ) ), file(jordan1a,rc2_jordan1a), []). fof(rc2_pscomp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) ), file(pscomp_1,rc2_pscomp_1), []). fof(rc2_sppol_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & ~ v1_realset1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) & v4_topreal1(A) ) ), file(sppol_2,rc2_sppol_2), []). fof(rc2_sprect_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) ) ), file(sprect_1,rc2_sprect_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_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_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & v2_sppol_1(A) & v1_jordan2c(A,2) ) ), file(jordan1a,rc3_jordan1a), []). fof(rc3_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v1_setfam_1(A) ) ), file(pscomp_1,rc3_pscomp_1), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & ~ v1_setfam_1(A) ) ), file(pscomp_1,rc4_pscomp_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(rc9_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v6_compts_1(B,A) ) ) ), file(pscomp_1,rc9_pscomp_1), []). fof(redefinition_k1_card_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_card_4(A,B) = k2_newton(A,B) ) ), file(card_4,k1_card_4), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_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_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_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_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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_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_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r1_subset_1), []). fof(redefinition_r2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(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(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc4_boole,axiom,( ~ v1_xboole_0(4) ), file(boole,spc4_boole), []). fof(spc4_numerals,axiom, ( v2_xreal_0(4) & m1_subset_1(4,k5_numbers) ), file(numerals,spc4_numerals), []). fof(symmetry_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) => r1_subset_1(B,A) ) ) ), file(subset_1,r1_subset_1), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(symmetry_r2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_subset_1(A,B) => r2_subset_1(B,A) ) ) ), file(subset_1,r2_subset_1), []). fof(t104_jordan1a,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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,k28_pscomp_1(B)) & r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(2)),k3_jordan1a(C),k5_topreal1(2,k1_jordan9(B,A)))) ) => k21_euclid(D) = k20_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))) ) ) ) ) ) ), file(jordan1a,t104_jordan1a), []). 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(t10_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B,C] : ( ( r2_hidden(B,k2_relat_1(A)) & r2_hidden(C,k2_relat_1(A)) & k5_finseq_4(A,B) = k5_finseq_4(A,C) ) => B = C ) ) ), file(finseq_5,t10_finseq_5), []). fof(t10_goboard7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_matrix_1(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(D)) & r1_xreal_0(1,C) & r1_xreal_0(C,k1_matrix_1(D)) ) => r2_hidden(k4_tarski(B,C),k2_matrix_1(D)) ) ) ) ) ) ), file(goboard7,t10_goboard7), []). fof(t10_jordan1e,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( k1_nat_1(A,B) = k1_nat_1(C,D) & r1_xreal_0(A,C) & r1_xreal_0(B,D) ) => A = C ) ) ) ) ) ), file(jordan1e,t10_jordan1e), []). 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(t11_finseq_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k2_relat_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A ) ) ) ) ), file(finseq_2,t11_finseq_2), []). fof(t11_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,k5_topreal1(2,A)) & r2_hidden(k1_funct_1(A,1),k5_topreal1(2,k3_jordan3(A,B))) ) => k1_funct_1(A,1) = B ) ) ) ) ), file(jordan1e,t11_jordan1e), []). fof(t11_jordan6,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r1_topreal1(k15_euclid(A),C,D,B) => v2_connsp_1(B,k15_euclid(A)) ) ) ) ) ) ), file(jordan6,t11_jordan6), []). fof(t11_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( k21_euclid(A) = k21_euclid(B) & k22_euclid(A) = k22_euclid(B) ) => A = B ) ) ) ), file(topreal3,t11_topreal3), []). fof(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(t11_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(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t11_xreal_1), []). 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(t13_jordan8,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_xreal_0(4,k3_finseq_1(k1_jordan8(B,A))) ) ) ), file(jordan8,t13_jordan8), []). fof(t13_realset1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_realset1(A) <=> ~ r1_xreal_0(2,k4_card_1(A)) ) ) ), file(realset1,t13_realset1), []). 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(t15_jordan1e,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(2,k1_jordan9(A,B)))) = k4_graph_2(u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),k2_jordan1e(A,B)) ) ) ), file(jordan1e,t15_jordan1e), []). fof(t15_jordan8,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) ) => k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),k5_binarith(k3_finseq_1(k1_jordan8(C,B)),1),A)) = k20_pscomp_1(C) ) ) ) ) ), file(jordan8,t15_jordan8), []). fof(t15_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(k30_pscomp_1(A),A) & r2_hidden(k31_pscomp_1(A),A) ) ) ), file(sprect_1,t15_sprect_1), []). fof(t16_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v3_topreal1(A) => v1_goboard5(A) ) ) ), file(jgraph_1,t16_jgraph_1), []). fof(t16_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_tarski(k9_jordan6(A),A) & r1_tarski(k8_jordan6(A),A) ) ) ), file(jordan1a,t16_jordan1a), []). fof(t16_jordan2c,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v1_jordan2c(C,A) & r1_tarski(B,C) ) => v1_jordan2c(B,A) ) ) ) ) ), file(jordan2c,t16_jordan2c), []). fof(t16_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) = k18_pscomp_1(A) ) => r2_hidden(B,k26_pscomp_1(A)) ) ) ) ), file(sprect_2,t16_sprect_2), []). fof(t17_jordan1e,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k5_topreal1(2,k1_jordan9(A,B)) = k4_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,k1_jordan1e(A,B)),k5_topreal1(2,k2_jordan1e(A,B))) ) ) ), file(jordan1e,t17_jordan1e), []). 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(t19_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v6_compts_1(B,A) & v6_compts_1(C,A) ) => v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ), file(compts_1,t19_compts_1), []). fof(t19_jordan1e,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_xreal_0(3,k3_finseq_1(k1_jordan1e(A,B))) & r1_xreal_0(3,k3_finseq_1(k2_jordan1e(A,B))) ) ) ) ), file(jordan1e,t19_jordan1e), []). fof(t19_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_1(A) & v3_goboard1(A) & v4_goboard1(A) & v5_goboard1(A) & v6_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xreal_0(1,D) & r1_xreal_0(k1_nat_1(D,1),k1_matrix_1(A)) ) => ( r2_hidden(B,k3_goboard5(A,C,D)) <=> ( r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,D)),k21_euclid(B)) & r1_xreal_0(k21_euclid(B),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1),D))) & r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,D)),k22_euclid(B)) & r1_xreal_0(k22_euclid(B),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,k1_nat_1(D,1)))) ) ) ) ) ) ) ) ), file(jordan9,t19_jordan9), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). 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(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,A) ) => A = B ) ) ) ), file(xreal_1,t1_xreal_1), []). fof(t20_jordan1e,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k5_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,k1_jordan1e(A,B)),k5_topreal1(2,k2_jordan1e(A,B))) = k2_struct_0(k15_euclid(2),k30_pscomp_1(k5_topreal1(2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(2,k1_jordan9(A,B)))) ) ) ), file(jordan1e,t20_jordan1e), []). fof(t21_goboard1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E,F] : ( ( ~ v3_relat_1(F) & v1_matrix_1(F) & v3_goboard1(F) & v4_goboard1(F) & v5_goboard1(F) & v6_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( E = k3_matrix_1(u1_struct_0(k15_euclid(2)),F,A,B) & E = k3_matrix_1(u1_struct_0(k15_euclid(2)),F,C,D) & r2_hidden(k4_tarski(A,B),k2_matrix_1(F)) & r2_hidden(k4_tarski(C,D),k2_matrix_1(F)) ) => ( A = C & B = D ) ) ) ) ) ) ) ), file(goboard1,t21_goboard1), []). fof(t21_jordan1j,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)))) ) => ! [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)))) ) => ( ( r1_tarski(A,B) & r2_hidden(k30_pscomp_1(B),A) ) => k30_pscomp_1(A) = k30_pscomp_1(B) ) ) ) ), file(jordan1j,t21_jordan1j), []). 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_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_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_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))) ) => ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k30_pscomp_1(k5_topreal1(2,A)) & r1_xreal_0(k5_finseq_4(A,k31_pscomp_1(k5_topreal1(2,A))),1) ) ) ), file(sprect_5,t23_sprect_5), []). fof(t23_xboole_1,axiom,( ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ), file(xboole_1,t23_xboole_1), []). fof(t24_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) & v1_sprect_2(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k30_pscomp_1(k5_topreal1(2,A)) & k31_pscomp_1(k5_topreal1(2,A)) != k32_pscomp_1(k5_topreal1(2,A)) & r1_xreal_0(k5_finseq_4(A,k32_pscomp_1(k5_topreal1(2,A))),k5_finseq_4(A,k31_pscomp_1(k5_topreal1(2,A)))) ) ) ), file(sprect_5,t24_sprect_5), []). 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(t25_jordan3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(1,C) => k1_jordan3(A,B,1,C) = k16_finseq_1(A,B,C) ) ) ) ) ), file(jordan3,t25_jordan3), []). fof(t25_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) & v1_sprect_2(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k30_pscomp_1(k5_topreal1(2,A)) & r1_xreal_0(k5_finseq_4(A,k33_pscomp_1(k5_topreal1(2,A))),k5_finseq_4(A,k32_pscomp_1(k5_topreal1(2,A)))) ) ) ), file(sprect_5,t25_sprect_5), []). 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_jordan1g,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k2_jordan1e(B,A) = k1_finseq_5(u1_struct_0(k15_euclid(2)),k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(2,k1_jordan9(B,A)))),k30_pscomp_1(k5_topreal1(2,k1_jordan9(B,A)))) ) ) ), file(jordan1g,t26_jordan1g), []). fof(t26_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) & v1_sprect_2(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k30_pscomp_1(k5_topreal1(2,A)) & k33_pscomp_1(k5_topreal1(2,A)) != k34_pscomp_1(k5_topreal1(2,A)) & r1_xreal_0(k5_finseq_4(A,k34_pscomp_1(k5_topreal1(2,A))),k5_finseq_4(A,k33_pscomp_1(k5_topreal1(2,A)))) ) ) ), file(sprect_5,t26_sprect_5), []). 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_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) & 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,k30_pscomp_1(k5_topreal1(2,A))),2),k26_pscomp_1(k5_topreal1(2,A))) ) ) ), file(jordan1i,t27_jordan1i), []). fof(t27_jordan2c,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_jordan2c(A,B,C) => r1_tarski(C,k2_jordan2c(A,B)) ) ) ) ) ), file(jordan2c,t27_jordan2c), []). fof(t27_topreal1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(A))) => ( ( r1_xreal_0(1,B) & r1_xreal_0(k1_nat_1(B,1),k3_finseq_1(C)) ) => ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),C,B),k4_topreal1(A,C,B)) & r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(A)),C,k1_nat_1(B,1)),k4_topreal1(A,C,B)) ) ) ) ) ) ), file(topreal1,t27_topreal1), []). 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(t28_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)) <=> ( m2_subset_1(k6_xcmplx_0(B,1),k1_numbers,k5_numbers) & m2_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k1_numbers,k5_numbers) ) ) ) ) ), file(finseq_3,t28_finseq_3), []). 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_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_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k2_relat_1(A)) => k1_funct_1(A,k5_finseq_4(A,B)) = B ) ) ), file(finseq_4,t29_finseq_4), []). fof(t29_jordan1d,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(1,C) & r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A))) & k34_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) ), file(jordan1d,t29_jordan1d), []). fof(t29_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)) ) => k3_gobrd13(B,k3_goboard2(B),A) = k4_goboard5(B,A) ) ) ) ), file(jordan1h,t29_jordan1h), []). fof(t29_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_1(A) & v3_goboard1(A) & v4_goboard1(A) & v5_goboard1(A) & v6_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ 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))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,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)) ) => ( r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(2)),k3_gobrd13(B,A,C),k5_topreal1(2,B)),k3_goboard9(B)) & r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(2)),k4_gobrd13(B,A,C),k5_topreal1(2,B)),k2_goboard9(B)) ) ) ) ) ) ) ), file(jordan9,t29_jordan9), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_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_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)))) ) => ( ( v4_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)) ) => k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,B,A)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),C,1,A)) ) ) ) ) ), file(goboard5,t2_goboard5), []). 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(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(t31_jordan4,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) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,B) & r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(1,D) ) => ( r1_xreal_0(C,B) | r1_xreal_0(k1_nat_1(k5_binarith(C,B),1),D) | k4_topreal1(2,k1_jordan3(u1_struct_0(k15_euclid(2)),A,B,C),D) = k4_topreal1(2,A,k5_binarith(k1_nat_1(D,B),1)) ) ) ) ) ) ) ), file(jordan4,t31_jordan4), []). fof(t31_topreal8,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( ~ v1_realset1(C) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ( 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)),C,1) => ( r1_xreal_0(k3_finseq_1(C),k1_nat_1(A,1)) | k4_topreal1(2,k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),k1_nat_1(k3_finseq_1(B),A)) = k4_topreal1(2,C,k1_nat_1(A,1)) ) ) ) ) ) ), file(topreal8,t31_topreal8), []). fof(t33_jordan1j,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)))) ) => ! [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)))) ) => ( ~ r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A)) => k30_pscomp_1(k4_subset_1(u1_struct_0(k15_euclid(2)),A,B)) = k30_pscomp_1(A) ) ) ) ), file(jordan1j,t33_jordan1j), []). 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_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))) ) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_1(C) & v3_goboard1(C) & v4_goboard1(C) & v5_goboard1(C) & v6_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,C) <=> r1_goboard1(u1_struct_0(k15_euclid(2)),k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A),C) ) ) ) ) ), file(revrot_1,t34_revrot_1), []). 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(t35_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( v4_topreal1(A) & r2_hidden(B,k5_topreal1(2,A)) ) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k3_jordan3(A,B),k3_finseq_1(k3_jordan3(A,B))) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) ) ) ) ), file(jordan1j,t35_jordan1j), []). fof(t35_topreal8,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( 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) => ( v1_xboole_0(A) | v1_realset1(B) | k5_topreal1(2,k4_graph_2(u1_struct_0(k15_euclid(2)),A,B)) = k4_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,A),k5_topreal1(2,B)) ) ) ) ) ), file(topreal8,t35_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(t36_jordan1j,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,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( v2_connsp_1(D,k15_euclid(2)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r2_hidden(B,k3_goboard9(A)) & r2_hidden(C,k2_goboard9(A)) & r2_hidden(B,D) & r2_hidden(C,D) & r1_xboole_0(D,k5_topreal1(2,A)) ) ) ) ) ) ), file(jordan1j,t36_jordan1j), []). fof(t37_jordan1j,axiom,( ! [A] : ( ( v4_topreal1(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,k2_relat_1(A)) => k3_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(2)),A,k5_finseq_4(A,B),k3_finseq_1(A)) ) ) ) ), file(jordan1j,t37_jordan1j), []). 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_jordan1j,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] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k2_relat_1(B)) => r1_goboard1(u1_struct_0(k15_euclid(2)),k4_jordan3(B,C),A) ) ) ) ) ) ), file(jordan1j,t38_jordan1j), []). 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(t39_jordan1a,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( ~ 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(A,k1_matrix_1(E)) & r1_xreal_0(1,B) & r1_xreal_0(B,k1_matrix_1(E)) & r1_xreal_0(1,C) & r1_xreal_0(C,D) & r1_xreal_0(D,k3_finseq_1(E)) ) => r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),E,C,A)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),E,D,B))) ) ) ) ) ) ) ), file(jordan1a,t39_jordan1a), []). fof(t39_jordan1j,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] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k2_relat_1(B)) => r1_goboard1(u1_struct_0(k15_euclid(2)),k3_jordan3(B,C),A) ) ) ) ) ) ), file(jordan1j,t39_jordan1j), []). fof(t39_sprect_3,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)) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k4_jordan3(A,B),1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) ) ) ) ), file(sprect_3,t39_sprect_3), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_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_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_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => r2_hidden(k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)),k2_relat_1(B)) ) ) ), file(revrot_1,t3_revrot_1), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_xboole_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), []). fof(t40_jordan1g,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k2_jordan1e(B,A),2)) = k20_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))) ) ) ), file(jordan1g,t40_jordan1g), []). fof(t40_jordan1j,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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(1,D) & r1_xreal_0(D,k1_matrix_1(A)) & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,D),k5_topreal1(2,B)) ) => r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(2)),A,C,D),k2_relat_1(B)) ) ) ) ) ) ) ), file(jordan1j,t40_jordan1j), []). fof(t41_enumset1,axiom,( ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ), file(enumset1,t41_enumset1), []). 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(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(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(t43_jordan1j,axiom,( ! [A] : ( ( v4_topreal1(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(k1_funct_1(A,k3_finseq_1(A)),k5_topreal1(2,k4_jordan3(A,B))) ) => k1_funct_1(A,k3_finseq_1(A)) = B ) ) ) ), file(jordan1j,t43_jordan1j), []). fof(t43_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) <=> r1_tarski(B,k3_subset_1(A,C)) ) ) ) ), file(subset_1,t43_subset_1), []). fof(t44_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)) & v2_funct_1(C) ) => k5_finseq_4(C,k4_finseq_4(k5_numbers,B,C,A)) = A ) ) ) ) ), file(finseq_5,t44_finseq_5), []). fof(t45_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] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( v4_topreal1(A) & r1_xreal_0(C,k3_finseq_1(A)) & B = k1_funct_1(A,C) ) => ( r1_xreal_0(C,1) | k1_nat_1(k2_jordan3(A,B),1) = C ) ) ) ) ) ), file(jordan3,t45_jordan3), []). fof(t46_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( B != k1_xboole_0 => r2_hidden(k4_finseq_4(k5_numbers,A,B,1),k2_relat_1(B)) ) ) ) ), file(finseq_6,t46_finseq_6), []). fof(t46_gobrd14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & v1_sprect_2(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k2_jordan2c(2,k5_topreal1(2,A)) = k2_goboard9(A) ) ), file(gobrd14,t46_gobrd14), []). fof(t46_jordan1j,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(C,k5_topreal1(2,k1_jordan1e(B,A))) & k21_euclid(C) = k20_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))) ) => C = k34_pscomp_1(k5_topreal1(2,k1_jordan9(B,A))) ) ) ) ) ), file(jordan1j,t46_jordan1j), []). fof(t47_sprect_2,axiom,( ! [A] : ( ( ~ v1_realset1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => r2_hidden(k30_pscomp_1(k5_topreal1(2,A)),k2_relat_1(A)) ) ), file(sprect_2,t47_sprect_2), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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_jordan1g,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_goboard1(u1_struct_0(k15_euclid(2)),k1_jordan1e(B,A),k1_jordan8(B,A)) ) ) ), file(jordan1g,t4_jordan1g), []). 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(t4_topreal1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_topreal1(A,C,D,B) => ( r2_hidden(C,B) & r2_hidden(D,B) ) ) ) ) ) ) ), file(topreal1,t4_topreal1), []). fof(t4_xboole_1,axiom,( ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ), file(xboole_1,t4_xboole_1), []). 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(t51_jordan1j,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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_goboard1(u1_struct_0(k15_euclid(2)),k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),A) ) => ( r1_xreal_0(k3_finseq_1(B),D) | ( k4_gobrd13(k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),A,D) = k4_gobrd13(B,A,D) & k3_gobrd13(k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ), file(jordan1j,t51_jordan1j), []). 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_jordan1h,axiom,( ! [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)))) ) => ( v2_connsp_1(B,k15_euclid(2)) => k3_goboard2(k1_jordan9(B,A)) = k1_jordan8(B,A) ) ) ) ), file(jordan1h,t52_jordan1h), []). fof(t52_jordan1j,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] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) & r2_hidden(C,k2_relat_1(B)) ) => ( r1_xreal_0(k5_finseq_4(B,C),D) | ( k4_gobrd13(k4_jordan3(B,C),A,D) = k4_gobrd13(B,A,D) & k3_gobrd13(k4_jordan3(B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ), file(jordan1j,t52_jordan1j), []). 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_jordan1j,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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) ) => ( r1_xreal_0(k5_finseq_4(B,C),D) | ( k4_gobrd13(k1_finseq_5(u1_struct_0(k15_euclid(2)),B,C),A,D) = k4_gobrd13(B,A,D) & k3_gobrd13(k1_finseq_5(u1_struct_0(k15_euclid(2)),B,C),A,D) = k3_gobrd13(B,A,D) ) ) ) ) ) ) ) ), file(jordan1j,t53_jordan1j), []). fof(t54_jordan1j,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) & v3_topreal1(A) & v2_funct_1(A) & v2_topreal1(B) & v3_topreal1(B) & v2_funct_1(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)),k5_topreal1(2,A),k5_topreal1(2,B)) = k1_struct_0(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,1)) ) => v3_topreal1(k4_graph_2(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ), file(jordan1j,t54_jordan1j), []). fof(t55_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( ( v2_funct_1(A) & v2_funct_1(B) & r1_tarski(k3_xboole_0(k2_relat_1(A),k2_relat_1(B)),k1_struct_0(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,1))) ) => v2_funct_1(k4_graph_2(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ), file(jordan1j,t55_jordan1j), []). fof(t56_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( v4_topreal1(A) & r2_hidden(B,k2_relat_1(A)) ) => ( B = k1_funct_1(A,1) | k1_nat_1(k2_jordan3(A,B),1) = k5_finseq_4(A,B) ) ) ) ) ), file(jordan1j,t56_jordan1j), []). fof(t57_jordan1g,axiom,( ! [A] : ( ( v4_topreal1(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,k2_relat_1(A)) => k4_jordan3(A,B) = k1_jordan3(u1_struct_0(k15_euclid(2)),A,1,k5_finseq_4(A,B)) ) ) ) ), file(jordan1g,t57_jordan1g), []). fof(t57_jordan1j,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) => ~ ( ~ r1_xreal_0(C,1) & ~ r1_xreal_0(k3_finseq_1(k1_jordan8(B,A)),C) & r1_xreal_0(1,D) & r1_xreal_0(E,k1_matrix_1(k1_jordan8(B,A))) & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k5_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k5_topreal1(2,k2_jordan1e(B,A))) & D = E ) ) ) ) ) ) ), file(jordan1j,t57_jordan1j), []). fof(t58_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)) => ( k1_funct_1(k3_jordan3(A,B),1) = B & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(C,k3_finseq_1(k3_jordan3(A,B))) => ( r1_xreal_0(C,1) | ( ( B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),1)) => k1_funct_1(k3_jordan3(A,B),C) = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),C)) ) & ( B != k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),1)) => k1_funct_1(k3_jordan3(A,B),C) = k1_funct_1(A,k5_real_1(k1_nat_1(k2_jordan3(A,B),C),1)) ) ) ) ) ) ) ) ) ) ), file(jordan3,t58_jordan3), []). fof(t59_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)) => ( k1_funct_1(k4_jordan3(A,B),k3_finseq_1(k4_jordan3(A,B))) = B & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k2_jordan3(A,B)) ) => k1_funct_1(k4_jordan3(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) ) ), file(jordan3,t59_jordan3), []). fof(t5_amistd_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),1) = k4_finseq_4(k5_numbers,A,B,1) ) ) ) ), file(amistd_1,t5_amistd_1), []). fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). fof(t5_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))) => ( ( r2_hidden(A,k3_topreal1(2,B,C)) & k21_euclid(B) = k21_euclid(C) ) => k21_euclid(A) = k21_euclid(C) ) ) ) ) ), file(goboard7,t5_goboard7), []). fof(t5_goboard9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_tarski(B,C) & v2_connsp_1(B,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r4_connsp_1(A,C,D) & r1_tarski(B,D) ) ) ) ) ) ) ), file(goboard9,t5_goboard9), []). fof(t5_jordan10,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_subset_1(B,k5_topreal1(2,k1_jordan9(B,A))) ) ) ), file(jordan10,t5_jordan10), []). fof(t5_jordan1f,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),1) = k30_pscomp_1(k5_topreal1(2,k1_jordan9(A,B))) ) ) ), file(jordan1f,t5_jordan1f), []). fof(t5_jordan1g,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_goboard1(u1_struct_0(k15_euclid(2)),k2_jordan1e(B,A),k1_jordan8(B,A)) ) ) ), file(jordan1g,t5_jordan1g), []). 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(t61_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)) => ( ( B = k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),1)) => k3_finseq_1(k3_jordan3(A,B)) = k5_real_1(k3_finseq_1(A),k2_jordan3(A,B)) ) & ( B != k1_funct_1(A,k1_nat_1(k2_jordan3(A,B),1)) => k3_finseq_1(k3_jordan3(A,B)) = k3_real_1(k5_real_1(k3_finseq_1(A),k2_jordan3(A,B)),1) ) ) ) ) ) ), file(jordan3,t61_jordan3), []). fof(t62_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xreal_0(k21_euclid(A),k21_euclid(B)) => k18_pscomp_1(k3_topreal1(2,A,B)) = k21_euclid(A) ) ) ) ), file(sprect_1,t62_sprect_1), []). fof(t63_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_xboole_0(B,C) ) => r1_xboole_0(A,C) ) ), file(xboole_1,t63_xboole_1), []). fof(t69_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( v4_topreal1(A) & r2_hidden(B,k5_topreal1(2,A)) ) => ( B = k1_funct_1(A,k3_finseq_1(A)) | v4_topreal1(k3_jordan3(A,B)) ) ) ) ) ), file(jordan3,t69_jordan3), []). fof(t6_amistd_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( ~ v1_realset1(C) & m2_finseq_1(C,A) ) => k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),k3_finseq_1(k4_graph_2(A,B,C))) = k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) ) ) ) ), file(amistd_1,t6_amistd_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_jordan1f,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k2_jordan1e(A,B),1) = k34_pscomp_1(k5_topreal1(2,k1_jordan9(A,B))) ) ) ), file(jordan1f,t6_jordan1f), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t6_topreal1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k1_topreal1(A,B,C)) & r2_hidden(C,k1_topreal1(A,B,C)) ) ) ) ) ), file(topreal1,t6_topreal1), []). fof(t70_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( v4_topreal1(A) & r2_hidden(B,k5_topreal1(2,A)) ) => ( B = k1_funct_1(A,1) | v4_topreal1(k4_jordan3(A,B)) ) ) ) ) ), file(jordan3,t70_jordan3), []). fof(t70_xboole_1,axiom,( ! [A,B,C] : ( ~ ( ~ r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,B) & r1_xboole_0(A,C) ) & ~ ( ~ ( r1_xboole_0(A,B) & r1_xboole_0(A,C) ) & r1_xboole_0(A,k2_xboole_0(B,C)) ) ) ), file(xboole_1,t70_xboole_1), []). fof(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(t76_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_tarski(k5_topreal1(2,k4_jordan3(A,B)),k5_topreal1(2,A)) ) ) ) ), file(jordan3,t76_jordan3), []). fof(t77_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_tarski(k5_topreal1(2,k3_jordan3(A,B)),k5_topreal1(2,A)) ) ) ) ), file(jordan3,t77_jordan3), []). 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_jordan1f,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),k3_finseq_1(k1_jordan1e(A,B))) = k34_pscomp_1(k5_topreal1(2,k1_jordan9(A,B))) ) ) ), file(jordan1f,t7_jordan1f), []). 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_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(t7_topreal8,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_xreal_0(k3_finseq_1(A),k3_finseq_1(k3_graph_2(A,B))) ) ) ), file(topreal8,t7_topreal8), []). fof(t7_xboole_1,axiom,( ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ), file(xboole_1,t7_xboole_1), []). fof(t84_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( k21_euclid(k30_pscomp_1(A)) = k18_pscomp_1(A) & k21_euclid(k31_pscomp_1(A)) = k18_pscomp_1(A) ) ) ), file(pscomp_1,t84_pscomp_1), []). fof(t85_finseq_4,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v4_ordinal2(B) => ! [C,D] : ( m2_finseq_1(D,C) => ( r2_hidden(B,k4_finseq_1(k16_finseq_1(C,D,A))) => k4_finseq_4(k5_numbers,C,k16_finseq_1(C,D,A),B) = k4_finseq_4(k5_numbers,C,D,B) ) ) ) ) ), file(finseq_4,t85_finseq_4), []). fof(t88_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,k26_pscomp_1(B)) => ( k21_euclid(A) = k21_euclid(k30_pscomp_1(B)) & ( v6_compts_1(B,k15_euclid(2)) => ( r1_xreal_0(k22_euclid(k30_pscomp_1(B)),k22_euclid(A)) & r1_xreal_0(k22_euclid(A),k22_euclid(k31_pscomp_1(B))) ) ) ) ) ) ) ), file(pscomp_1,t88_pscomp_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( k21_euclid(A) = k21_euclid(B) & k21_euclid(B) = k21_euclid(C) & r1_xreal_0(k22_euclid(A),k22_euclid(B)) & r1_xreal_0(k22_euclid(B),k22_euclid(C)) ) => r2_hidden(B,k3_topreal1(2,A,C)) ) ) ) ) ), file(goboard7,t8_goboard7), []). fof(t8_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_jordan1f,axiom,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),k2_jordan1e(A,B),k3_finseq_1(k2_jordan1e(A,B))) = k30_pscomp_1(k5_topreal1(2,k1_jordan9(A,B))) ) ) ), file(jordan1f,t8_jordan1f), []). fof(t8_jordan1i,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k30_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k30_pscomp_1(k5_topreal1(2,k1_jordan9(B,A)))),1)) ) ) ), file(jordan1i,t8_jordan1i), []). fof(t8_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_xreal_0(2,k3_finseq_1(B)) & r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) & v5_seqm_3(B) ) ) ) ), file(jordan8,t8_jordan8), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t8_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(C,B) ) => r1_tarski(k2_xboole_0(A,C),B) ) ), file(xboole_1,t8_xboole_1), []). fof(t92_jordan1a,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v2_connsp_1(C,k15_euclid(2)) & v6_compts_1(C,k15_euclid(2)) & ~ v1_sppol_1(C) & ~ v2_sppol_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) ) => k20_pscomp_1(k5_topreal1(2,k1_jordan9(C,B))) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),k3_finseq_1(k1_jordan8(C,B)),A)) ) ) ) ) ), file(jordan1a,t92_jordan1a), []). fof(t94_jordan1a,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v2_connsp_1(C,k15_euclid(2)) & v6_compts_1(C,k15_euclid(2)) & ~ v1_sppol_1(C) & ~ v2_sppol_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xreal_0(1,A) & r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) ) => k18_pscomp_1(k5_topreal1(2,k1_jordan9(C,B))) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),1,A)) ) ) ) ) ), file(jordan1a,t94_jordan1a), []). fof(t95_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k1_finseq_6(A,B,k4_finseq_4(k5_numbers,A,B,1)) = B ) ) ), file(finseq_6,t95_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), []). 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), []). fof(t9_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_jordan2c(k3_jordan1a(A),2) ) ), file(jordan1c,t9_jordan1c), []). fof(t9_jordan1i,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_connsp_1(B,k15_euclid(2)) & v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k34_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(2)),k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(2,k1_jordan9(B,A)))),1)) ) ) ), file(jordan1i,t9_jordan1i), []). fof(t9_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) => ( r1_xreal_0(k1_nat_1(C,1),k3_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B))) => k4_topreal1(2,k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B),C) = k4_topreal1(2,A,C) ) ) ) ) ), file(sppol_2,t9_sppol_2), []). fof(t9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ), file(xreal_1,t9_xreal_1), []).