% Mizar problem: t28_hilbasis,hilbasis,1044,76 fof(t28_hilbasis,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & ~ v3_realset2(A) & l3_vectsp_1(A) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k30_polynom1(0,A))) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k30_polynom1(0,A))) & v4_quofield(B,A,k30_polynom1(0,A)) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_algstr_1,cc1_binom,cc1_card_1,cc1_card_5,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_funct_7,cc1_membered,cc1_ordinal1,cc1_polynom1,cc1_polynom3,cc1_relat_1,cc1_relset_1,cc1_vectsp_1,cc1_xreal_0,cc20_membered,cc2_algstr_1,cc2_binom,cc2_card_1,cc2_card_5,cc2_finset_1,cc2_funct_1,cc2_funct_7,cc2_gobrd13,cc2_int_1,cc2_membered,cc2_ordinal1,cc2_vectsp_1,cc2_xreal_0,cc3_algstr_1,cc3_binom,cc3_card_1,cc3_int_1,cc3_membered,cc3_ordinal1,cc3_polynom1,cc3_vectsp_1,cc3_xreal_0,cc4_algstr_1,cc4_binom,cc4_gcd_1,cc4_int_1,cc4_membered,cc4_polynom1,cc4_vectsp_1,cc4_xreal_0,cc5_binom,cc5_polynom1,cc5_xreal_0,cc6_membered,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k23_polynom1,commutativity_k4_rlvect_1,connectedness_r1_xreal_0,d10_polynom1,d13_grcat_1,d14_polynom1,d15_polynom1,d1_funct_2,d1_tarski,d21_polynom1,d21_quofield,d22_quofield,d23_quofield,d24_polynom1,d24_quofield,d25_polynom1,d26_polynom1,d27_polynom1,d2_cqc_lang,d3_funct_7,d4_finseq_4,d5_funct_1,d7_group_6,d8_endalg,d8_funct_1,dt_g3_vectsp_1,dt_k10_finseq_1,dt_k12_finseq_1,dt_k12_polynom1,dt_k13_binarith,dt_k13_polynom1,dt_k14_polynom1,dt_k15_polynom1,dt_k16_polynom1,dt_k1_borsuk_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_group_1,dt_k1_numbers,dt_k1_polynom1,dt_k1_relat_1,dt_k1_rlvect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_polynom1,dt_k22_polynom1,dt_k23_polynom1,dt_k26_polynom1,dt_k27_polynom1,dt_k28_polynom1,dt_k2_funcop_1,dt_k2_funct_7,dt_k2_group_1,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_rlvect_1,dt_k2_vectsp_1,dt_k2_zfmisc_1,dt_k30_polynom1,dt_k3_cqc_lang,dt_k3_finseq_1,dt_k3_polynom1,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_finseq_4,dt_k4_partfun1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k4_rlvect_1,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relset_1,dt_k5_rfunct_3,dt_k8_funct_2,dt_k9_finseq_1,dt_k9_rlvect_1,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_polynom1,dt_m1_relset_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_rfunct_3,dt_m2_subset_1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_struct_0,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_polynom1,existence_m1_relset_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_rfunct_3,existence_m2_subset_1,fc10_funct_7,fc10_membered,fc11_membered,fc11_polynom1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc15_polynom1,fc16_polynom1,fc1_finseq_5,fc1_finset_1,fc1_funct_7,fc1_ideal_1,fc1_ordinal2,fc1_polynom1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc20_polynom1,fc22_polynom1,fc25_polynom1,fc2_card_1,fc2_finseq_5,fc2_ideal_1,fc2_membered,fc2_ordinal1,fc2_polynom2,fc2_subset_1,fc30_polynom1,fc31_polynom1,fc32_polynom1,fc35_polynom1,fc36_polynom1,fc37_polynom1,fc38_polynom1,fc39_polynom1,fc3_funct_7,fc3_ideal_1,fc3_polynom1,fc3_polynom2,fc40_polynom1,fc41_polynom1,fc43_polynom1,fc44_polynom1,fc4_funct_7,fc4_ordinal2,fc4_relat_1,fc4_subset_1,fc5_funct_7,fc5_membered,fc5_polynom1,fc5_relat_1,fc6_membered,fc6_relat_1,fc7_membered,fc7_relat_1,fc8_membered,fc8_relat_1,fc9_funct_7,fc9_membered,free_g3_vectsp_1,idempotence_k1_funct_4,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc14_polynom1,rc1_binom,rc1_card_1,rc1_card_5,rc1_finseq_5,rc1_finset_1,rc1_funct_1,rc1_ideal_1,rc1_int_1,rc1_membered,rc1_ordinal1,rc1_pre_circ,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc2_binom,rc2_card_1,rc2_card_5,rc2_finseq_5,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_ordinal1,rc2_polynom1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc2_xreal_0,rc3_binom,rc3_finset_1,rc3_funct_1,rc3_ideal_1,rc3_ordinal1,rc3_polynom1,rc3_relat_1,rc3_struct_0,rc3_xreal_0,rc4_finset_1,rc4_funct_1,rc4_ideal_1,rc4_polynom1,rc4_struct_0,rc4_xreal_0,rc5_ideal_1,rc5_struct_0,rc6_ideal_1,rc6_vectsp_1,rc7_ideal_1,rc7_polynom1,rc7_vectsp_1,rc8_ideal_1,rc8_polynom1,rc9_polynom1,redefinition_k12_finseq_1,redefinition_k13_binarith,redefinition_k14_polynom1,redefinition_k15_polynom1,redefinition_k1_borsuk_1,redefinition_k1_polynom1,redefinition_k23_polynom1,redefinition_k2_pre_circ,redefinition_k3_finseq_1,redefinition_k3_polynom1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k5_rfunct_3,redefinition_k8_funct_2,redefinition_k9_finseq_1,redefinition_m1_polynom1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s3_funct_1__e1_34__hilbasis,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t13_finset_1,t13_funcop_1,t14_funct_1,t15_funcop_1,t16_funcop_1,t1_numerals,t1_real,t1_subset,t1_xreal_1,t20_funct_4,t27_finseq_3,t2_hilbasis,t2_real,t2_subset,t2_tarski,t3_funct_2,t3_real,t3_subset,t4_real,t4_subset,t55_polynom1,t56_finseq_1,t57_finseq_1,t5_real,t5_subset,t61_rlvect_1,t64_relat_1,t6_boole,t6_real,t7_boole,t7_funct_4,t7_real,t8_boole,t8_real,t90_polynom1]), [file(hilbasis,t28_hilbasis)]). fof(abstractness_v3_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( v3_vectsp_1(A) => A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) ), file(vectsp_1,v3_vectsp_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_algstr_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v6_algstr_1(A) ) => ( ~ v3_struct_0(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) ) ) ) ), file(algstr_1,cc1_algstr_1), []). fof(cc1_binom,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v2_algstr_1(A) & v3_algstr_1(A) ) => ( ~ v3_struct_0(A) & v1_binom(A) ) ) ) ), file(binom,cc1_binom), []). fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(card_1,cc1_card_1), []). fof(cc1_card_5,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_xboole_0(A) ) ), file(card_5,cc1_card_5), []). fof(cc1_finseq_5,axiom,( ! [A] : ( v1_xboole_0(A) => v1_realset1(A) ) ), file(finseq_5,cc1_finseq_5), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) ), file(ordinal1,cc1_ordinal1), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). fof(cc1_polynom3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) ) => ! [C] : ( m1_finseq_1(C,k4_finseq_2(B,A)) => v1_matrlin(C) ) ) ), file(polynom3,cc1_polynom3), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_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_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) ) ) ), file(vectsp_1,cc1_vectsp_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_algstr_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) ) => ( ~ v3_struct_0(A) & v6_algstr_1(A) ) ) ) ), file(algstr_1,cc2_algstr_1), []). fof(cc2_binom,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v1_binom(A) ) => ( ~ v3_struct_0(A) & v2_algstr_1(A) & v3_algstr_1(A) ) ) ) ), file(binom,cc2_binom), []). fof(cc2_card_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_card_1(A) ) ) ), file(card_1,cc2_card_1), []). fof(cc2_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(card_5,cc2_card_5), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). fof(cc2_gobrd13,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_matrlin(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) ), file(gobrd13,cc2_gobrd13), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_ordinal1,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) ), file(ordinal1,cc2_ordinal1), []). fof(cc2_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) ) ) ), file(vectsp_1,cc2_vectsp_1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_algstr_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v6_algstr_1(A) ) => ( ~ v3_struct_0(A) & v6_rlvect_1(A) ) ) ) ), file(algstr_1,cc3_algstr_1), []). fof(cc3_binom,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v3_algstr_1(A) ) => ( ~ v3_struct_0(A) & v2_algstr_1(A) ) ) ) ), file(binom,cc3_binom), []). fof(cc3_card_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_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(ordinal1,cc3_ordinal1), []). fof(cc3_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ) ), file(polynom1,cc3_polynom1), []). fof(cc3_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v2_group_1(A) ) => ( ~ v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) ) ) ), file(vectsp_1,cc3_vectsp_1), []). 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_algstr_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) => ( ~ v3_struct_0(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) & v6_algstr_1(A) ) ) ) ), file(algstr_1,cc4_algstr_1), []). fof(cc4_binom,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v2_algstr_1(A) ) => ( ~ v3_struct_0(A) & v3_algstr_1(A) ) ) ) ), file(binom,cc4_binom), []). fof(cc4_gcd_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) ) ) ) ), file(gcd_1,cc4_gcd_1), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_polynom1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k5_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v7_seqm_3(B) ) ) ) ), file(polynom1,cc4_polynom1), []). fof(cc4_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) ) ) ) ), file(vectsp_1,cc4_vectsp_1), []). 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_binom,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) => ( ~ v3_struct_0(A) & v3_algstr_1(A) ) ) ) ), file(binom,cc5_binom), []). fof(cc5_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) ) ), file(polynom1,cc5_polynom1), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_polynom1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_pboole(B,A) => v1_polynom1(B) ) ) ), file(polynom1,cc6_polynom1), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k23_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => k23_polynom1(A,B,C,D) = k23_polynom1(A,B,D,C) ) ), file(polynom1,k23_polynom1), []). fof(commutativity_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_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_polynom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( l2_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m2_relset_1(C,A,u1_struct_0(B)) ) => ( v2_polynom1(C,A,B) <=> v1_finset_1(k12_polynom1(A,B,C)) ) ) ) ) ), file(polynom1,d10_polynom1), []). fof(d13_grcat_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_grcat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ), file(grcat_1,d13_grcat_1), []). fof(d14_polynom1,axiom,( ! [A,B] : ( B = k13_polynom1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) ) ) ), file(polynom1,d14_polynom1), []). fof(d15_polynom1,axiom,( ! [A] : k16_polynom1(A) = k2_funcop_1(A,0) ), file(polynom1,d15_polynom1), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d21_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) ) => ( E = k22_polynom1(A,B,C,D) <=> ! [F] : ( ( v7_seqm_3(F) & v1_polynom1(F) & m1_pboole(F,A) ) => k15_polynom1(A,B,E,F) = k2_rlvect_1(B,k15_polynom1(A,B,C,F),k15_polynom1(A,B,D,F)) ) ) ) ) ) ) ), file(polynom1,d21_polynom1), []). fof(d21_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_quofield(C,A,B) <=> ( v1_grcat_1(C,A,B) & v1_group_6(C,A,B) & v1_endalg(C,A,B) ) ) ) ) ) ), file(quofield,d21_quofield), []). fof(d22_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v2_quofield(C,A,B) <=> ( v1_quofield(C,A,B) & k2_relat_1(C) = u1_struct_0(B) ) ) ) ) ) ), file(quofield,d22_quofield), []). fof(d23_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v3_quofield(C,A,B) <=> ( v1_quofield(C,A,B) & v2_funct_1(C) ) ) ) ) ) ), file(quofield,d23_quofield), []). fof(d24_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => k26_polynom1(A,B) = k5_rfunct_3(k13_polynom1(A),u1_struct_0(B),k14_polynom1(A),k1_rlvect_1(B)) ) ), file(polynom1,d24_polynom1), []). fof(d24_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v4_quofield(C,A,B) <=> ( v3_quofield(C,A,B) & v2_quofield(C,A,B) ) ) ) ) ) ), file(quofield,d24_quofield), []). fof(d25_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_group_1(B) & l2_vectsp_1(B) ) => k27_polynom1(A,B) = k1_polynom1(k14_polynom1(A),u1_struct_0(B),k26_polynom1(A,B),k16_polynom1(A),k2_group_1(B)) ) ), file(polynom1,d25_polynom1), []). fof(d26_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) ) => ( E = k28_polynom1(A,B,C,D) <=> ! [F] : ( ( v7_seqm_3(F) & v1_polynom1(F) & m1_pboole(F,A) ) => ? [G] : ( m2_finseq_1(G,u1_struct_0(B)) & k15_polynom1(A,B,E,F) = k9_rlvect_1(B,G) & k3_finseq_1(G) = k3_finseq_1(k21_polynom1(A,F)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( r2_hidden(H,k4_finseq_1(G)) & ! [I] : ( ( v7_seqm_3(I) & v1_polynom1(I) & m1_pboole(I,A) ) => ! [J] : ( ( v7_seqm_3(J) & v1_polynom1(J) & m1_pboole(J,A) ) => ~ ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,F),H) = k10_finseq_1(I,J) & k4_finseq_4(k5_numbers,u1_struct_0(B),G,H) = k1_group_1(B,k15_polynom1(A,B,C,I),k15_polynom1(A,B,D,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(polynom1,d26_polynom1), []). fof(d27_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_vectsp_1(C) & l3_vectsp_1(C) ) => ( C = k30_polynom1(A,B) <=> ( ! [D] : ( r2_hidden(D,u1_struct_0(C)) <=> ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(F,k14_polynom1(A),B) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(B)) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(G,k14_polynom1(A),B) & m2_relset_1(G,k14_polynom1(A),u1_struct_0(B)) ) => ( ( D = F & E = G ) => k2_rlvect_1(C,D,E) = k22_polynom1(A,B,F,G) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(F,k14_polynom1(A),B) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(B)) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(G,k14_polynom1(A),B) & m2_relset_1(G,k14_polynom1(A),u1_struct_0(B)) ) => ( ( D = F & E = G ) => k1_group_1(C,D,E) = k28_polynom1(A,B,F,G) ) ) ) ) ) & k1_rlvect_1(C) = k26_polynom1(A,B) & k2_vectsp_1(C) = k27_polynom1(A,B) ) ) ) ) ) ), file(polynom1,d27_polynom1), []). fof(d2_cqc_lang,axiom,( ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ), file(cqc_lang,d2_cqc_lang), []). fof(d3_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) => k2_funct_7(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) & ( ~ r2_hidden(B,k1_relat_1(A)) => k2_funct_7(A,B,C) = A ) ) ) ), file(funct_7,d3_funct_7), []). 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(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d7_group_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_group_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_group_6(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_group_1(A,D,E)) = k1_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ), file(group_6,d7_group_6), []). fof(d8_endalg,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_endalg(C,A,B) <=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_group_1(A)) = k2_group_1(B) ) ) ) ) ), file(endalg,d8_endalg), []). fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), []). fof(dt_g3_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ), file(vectsp_1,g3_vectsp_1), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k12_polynom1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & l2_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => m1_subset_1(k12_polynom1(A,B,C),k1_zfmisc_1(A)) ) ), file(polynom1,k12_polynom1), []). fof(dt_k13_binarith,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k13_binarith(A,B),A,k4_finseq_2(1,A)) ) ), file(binarith,k13_binarith), []). fof(dt_k13_polynom1,axiom,( $true ), file(polynom1,k13_polynom1), []). fof(dt_k14_polynom1,axiom,( ! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ), file(polynom1,k14_polynom1), []). fof(dt_k15_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => m1_subset_1(k15_polynom1(A,B,C,D),u1_struct_0(B)) ) ), file(polynom1,k15_polynom1), []). fof(dt_k16_polynom1,axiom,( ! [A] : m1_polynom1(k16_polynom1(A),A,k14_polynom1(A)) ), file(polynom1,k16_polynom1), []). fof(dt_k1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => ( v1_funct_1(k1_borsuk_1(A,B,C)) & v1_funct_2(k1_borsuk_1(A,B,C),B,A) & m2_relset_1(k1_borsuk_1(A,B,C),B,A) ) ) ), file(borsuk_1,k1_borsuk_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k1_group_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_polynom1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(E,B) ) => ( v1_funct_1(k1_polynom1(A,B,C,D,E)) & v1_funct_2(k1_polynom1(A,B,C,D,E),A,B) & m2_relset_1(k1_polynom1(A,B,C,D,E),A,B) ) ) ), file(polynom1,k1_polynom1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_rlvect_1,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ), file(rlvect_1,k1_rlvect_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k21_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => m2_finseq_1(k21_polynom1(A,B),k4_finseq_2(2,k14_polynom1(A))) ) ), file(polynom1,k21_polynom1), []). fof(dt_k22_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_funct_1(k22_polynom1(A,B,C,D)) & v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k22_polynom1), []). fof(dt_k23_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_funct_1(k23_polynom1(A,B,C,D)) & v1_funct_2(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k23_polynom1), []). fof(dt_k26_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => ( v1_funct_1(k26_polynom1(A,B)) & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k26_polynom1), []). fof(dt_k27_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_group_1(B) & l2_vectsp_1(B) ) => ( v1_funct_1(k27_polynom1(A,B)) & v1_funct_2(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k27_polynom1), []). fof(dt_k28_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l3_vectsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_funct_1(k28_polynom1(A,B,C,D)) & v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k28_polynom1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_funct_7,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) ) ) ), file(funct_7,k2_funct_7), []). fof(dt_k2_group_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ), file(group_1,k2_group_1), []). fof(dt_k2_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), []). fof(dt_k2_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)) ) ), file(vectsp_1,k2_vectsp_1), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k30_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) & l3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,k30_polynom1), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). 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_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => m2_finseq_2(k3_polynom1(A,B,C,D,E),A,C) ) ), file(polynom1,k3_polynom1), []). 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_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_partfun1,axiom,( $true ), file(partfun1,k4_partfun1), []). 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_rfunct_3,axiom,( ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ), file(rfunct_3,k4_rfunct_3), []). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). 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_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_1), []). fof(dt_k5_rfunct_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,B) ) => m2_rfunct_3(k5_rfunct_3(A,B,C,D),A,B,k4_rfunct_3(A,B)) ) ), file(rfunct_3,k5_rfunct_3), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_k9_rlvect_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) ) => m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)) ) ), file(rlvect_1,k9_rlvect_1), []). fof(dt_l1_group_1,axiom,( ! [A] : ( l1_group_1(A) => l1_struct_0(A) ) ), file(group_1,l1_group_1), []). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => l1_group_1(A) ) ), file(vectsp_1,l1_vectsp_1), []). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), []). fof(dt_l2_vectsp_1,axiom,( ! [A] : ( l2_vectsp_1(A) => ( l1_vectsp_1(A) & l2_struct_0(A) ) ) ), file(vectsp_1,l2_vectsp_1), []). fof(dt_l3_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( l1_rlvect_1(A) & l2_vectsp_1(A) ) ) ), file(vectsp_1,l3_vectsp_1), []). 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_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ! [C] : ( m1_polynom1(C,A,B) => ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) ) ) ), file(polynom1,m1_polynom1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rfunct_3,axiom,( $true ), file(rfunct_3,m1_rfunct_3), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). 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_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) => ( v1_funct_1(D) & m2_relset_1(D,A,B) ) ) ) ), file(rfunct_3,m2_rfunct_3), []). 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_group_1,axiom,( ! [A] : ( l1_group_1(A) => ( v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(group_1,u1_group_1), []). fof(dt_u1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( v1_funct_1(u1_rlvect_1(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u1_rlvect_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u1_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)) ) ), file(vectsp_1,u1_vectsp_1), []). fof(dt_u2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ), file(struct_0,u2_struct_0), []). fof(existence_l1_group_1,axiom,( ? [A] : l1_group_1(A) ), file(group_1,l1_group_1), []). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_vectsp_1,axiom,( ? [A] : l1_vectsp_1(A) ), file(vectsp_1,l1_vectsp_1), []). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), []). fof(existence_l2_vectsp_1,axiom,( ? [A] : l2_vectsp_1(A) ), file(vectsp_1,l2_vectsp_1), []). fof(existence_l3_vectsp_1,axiom,( ? [A] : l3_vectsp_1(A) ), file(vectsp_1,l3_vectsp_1), []). 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_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ? [C] : m1_polynom1(C,A,B) ) ), file(polynom1,m1_polynom1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rfunct_3,axiom,( ! [A,B] : ? [C] : m1_rfunct_3(C,A,B) ), file(rfunct_3,m1_rfunct_3), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ? [D] : m2_rfunct_3(D,A,B,C) ) ), file(rfunct_3,m2_rfunct_3), []). 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_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_funct_7(k5_finseq_1(A)) ) ) ), file(funct_7,fc10_funct_7), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_matrlin(k5_finseq_1(A)) ) ) ), file(polynom1,fc11_polynom1), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) ), file(polynom1,fc14_polynom1), []). fof(fc15_polynom1,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & m1_subset_1(C,k5_numbers) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_seq_1(k2_funct_7(A,B,C)) & v7_seqm_3(k2_funct_7(A,B,C)) ) ) ), file(polynom1,fc15_polynom1), []). fof(fc16_polynom1,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & m1_subset_1(C,k5_numbers) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_seq_1(k2_funct_7(A,B,C)) ) ) ), file(polynom1,fc16_polynom1), []). fof(fc1_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_realset1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_5,fc1_finseq_5), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_funct_7,axiom,( ! [A,B] : ( ~ v1_xboole_0(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) ) ), file(funct_7,fc1_funct_7), []). fof(fc1_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) ) => v1_ideal_1(k1_tarski(k1_rlvect_1(A)),A) ) ), file(ideal_1,fc1_ideal_1), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( ~ v3_struct_0(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ), file(polynom1,fc1_polynom1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_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_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) & v1_polynom1(k1_xboole_0) ), file(polynom1,fc20_polynom1), []). fof(fc22_polynom1,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_polynom1(k2_funct_7(A,B,C)) ) ) ), file(polynom1,fc22_polynom1), []). fof(fc25_polynom1,axiom,( ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ), file(polynom1,fc25_polynom1), []). fof(fc2_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) ), file(card_1,fc2_card_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_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v1_algstr_1(A) & v3_algstr_1(A) & l3_vectsp_1(A) ) => v2_ideal_1(k1_tarski(k1_rlvect_1(A)),A) ) ), file(ideal_1,fc2_ideal_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_ordinal1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) & v3_ordinal1(k1_xboole_0) ), file(ordinal1,fc2_ordinal1), []). fof(fc2_polynom2,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) ) => v1_finset_1(k12_polynom1(k14_polynom1(A),B,C)) ) ), file(polynom2,fc2_polynom2), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc30_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k21_polynom1(A,B)) & v1_funct_1(k21_polynom1(A,B)) & v2_funct_1(k21_polynom1(A,B)) & ~ v1_xboole_0(k21_polynom1(A,B)) & v1_finset_1(k21_polynom1(A,B)) & v1_finseq_1(k21_polynom1(A,B)) & v1_funcop_1(k21_polynom1(A,B)) & v1_matrlin(k21_polynom1(A,B)) & v1_polynom1(k21_polynom1(A,B)) ) ) ), file(polynom1,fc30_polynom1), []). fof(fc31_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & m1_subset_1(B,k14_polynom1(A)) ) => ( v1_relat_1(k21_polynom1(A,B)) & v1_funct_1(k21_polynom1(A,B)) & v2_funct_1(k21_polynom1(A,B)) & ~ v1_xboole_0(k21_polynom1(A,B)) & v1_finset_1(k21_polynom1(A,B)) & v1_finseq_1(k21_polynom1(A,B)) & v1_funcop_1(k21_polynom1(A,B)) & v1_matrlin(k21_polynom1(A,B)) & v1_polynom1(k21_polynom1(A,B)) ) ) ), file(polynom1,fc31_polynom1), []). fof(fc32_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_relat_1(k22_polynom1(A,B,C,D)) & v1_funct_1(k22_polynom1(A,B,C,D)) & v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k22_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ), file(polynom1,fc32_polynom1), []). fof(fc35_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & l2_struct_0(B) ) => ( v1_relat_1(k26_polynom1(A,B)) & v1_funct_1(k26_polynom1(A,B)) & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B) ) ) ), file(polynom1,fc35_polynom1), []). fof(fc36_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( v1_relat_1(k27_polynom1(A,B)) & v1_funct_1(k27_polynom1(A,B)) & v1_funct_2(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k27_polynom1(A,B),k14_polynom1(A),B) ) ) ), file(polynom1,fc36_polynom1), []). fof(fc37_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & l3_vectsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_relat_1(k28_polynom1(A,B,C,D)) & v1_funct_1(k28_polynom1(A,B,C,D)) & v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k28_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ), file(polynom1,fc37_polynom1), []). fof(fc38_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_rlvect_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc38_polynom1), []). fof(fc39_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc39_polynom1), []). fof(fc3_funct_7,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). fof(fc3_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v5_rlvect_1(A) & v5_vectsp_1(A) & v2_algstr_1(A) & l3_vectsp_1(A) ) => v3_ideal_1(k1_tarski(k1_rlvect_1(A)),A) ) ), file(ideal_1,fc3_ideal_1), []). fof(fc3_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_matrlin(k1_xboole_0) ), file(polynom1,fc3_polynom1), []). fof(fc3_polynom2,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_rlvect_1(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v5_rlvect_1(k30_polynom1(A,B)) & v6_rlvect_1(k30_polynom1(A,B)) & v2_group_1(k30_polynom1(A,B)) & v4_group_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) & v4_vectsp_1(k30_polynom1(A,B)) & v6_vectsp_1(k30_polynom1(A,B)) & v8_vectsp_1(k30_polynom1(A,B)) & v1_algstr_1(k30_polynom1(A,B)) & v2_algstr_1(k30_polynom1(A,B)) & v3_algstr_1(k30_polynom1(A,B)) & v4_algstr_1(k30_polynom1(A,B)) & v5_algstr_1(k30_polynom1(A,B)) & v6_algstr_1(k30_polynom1(A,B)) ) ) ), file(polynom2,fc3_polynom2), []). fof(fc40_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v5_rlvect_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc40_polynom1), []). fof(fc41_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v5_rlvect_1(k30_polynom1(A,B)) & v6_rlvect_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) & v1_algstr_1(k30_polynom1(A,B)) & v2_algstr_1(k30_polynom1(A,B)) & v3_algstr_1(k30_polynom1(A,B)) & v4_algstr_1(k30_polynom1(A,B)) & v5_algstr_1(k30_polynom1(A,B)) & v6_algstr_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc41_polynom1), []). fof(fc43_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_rlvect_1(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v5_rlvect_1(k30_polynom1(A,B)) & v6_rlvect_1(k30_polynom1(A,B)) & v4_group_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) & v1_algstr_1(k30_polynom1(A,B)) & v2_algstr_1(k30_polynom1(A,B)) & v3_algstr_1(k30_polynom1(A,B)) & v4_algstr_1(k30_polynom1(A,B)) & v5_algstr_1(k30_polynom1(A,B)) & v6_algstr_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc43_polynom1), []). fof(fc44_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_rlvect_1(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v5_rlvect_1(k30_polynom1(A,B)) & v6_rlvect_1(k30_polynom1(A,B)) & v2_group_1(k30_polynom1(A,B)) & v4_group_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) & v4_vectsp_1(k30_polynom1(A,B)) & v6_vectsp_1(k30_polynom1(A,B)) & v8_vectsp_1(k30_polynom1(A,B)) & v1_algstr_1(k30_polynom1(A,B)) & v2_algstr_1(k30_polynom1(A,B)) & v3_algstr_1(k30_polynom1(A,B)) & v4_algstr_1(k30_polynom1(A,B)) & v5_algstr_1(k30_polynom1(A,B)) & v6_algstr_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc44_polynom1), []). fof(fc4_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) ) ) ), file(funct_7,fc4_funct_7), []). fof(fc4_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_funct_7,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funcop_1(k10_finseq_1(A,B)) ) ) ), file(funct_7,fc5_funct_7), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & v1_finset_1(k1_funct_1(A,B)) & v1_finseq_1(k1_funct_1(A,B)) ) ) ), file(polynom1,fc5_polynom1), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc9_funct_7,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_finset_1(k2_funct_7(A,B,C)) & v1_finseq_1(k2_funct_7(A,B,C)) ) ) ), file(funct_7,fc9_funct_7), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(free_g3_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ! [F,G,H,I,J] : ( g3_vectsp_1(A,B,C,D,E) = g3_vectsp_1(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) ), file(vectsp_1,g3_vectsp_1), []). fof(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(rc10_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc10_polynom1), []). fof(rc11_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_seq_1(A) & v7_seqm_3(A) & v1_polynom1(A) ) ), file(polynom1,rc11_polynom1), []). fof(rc12_polynom1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc12_polynom1), []). fof(rc13_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc13_polynom1), []). fof(rc14_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) ) ) ), file(polynom1,rc14_polynom1), []). fof(rc1_binom,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v2_algstr_1(A) ) ), file(binom,rc1_binom), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_card_5,axiom,( ? [A] : ~ v1_finset_1(A) ), file(card_5,rc1_card_5), []). 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_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_ideal_1,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v1_algstr_1(A) ) ), file(ideal_1,rc1_ideal_1), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_ordinal1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc1_ordinal1), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_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_binom,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v3_algstr_1(A) ) ), file(binom,rc2_binom), []). fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) ), file(card_1,rc2_card_1), []). fof(rc2_card_5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) ) ), file(card_5,rc2_card_5), []). 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_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc2_ordinal1), []). fof(rc2_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_matrlin(A) ) ), file(polynom1,rc2_polynom1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_binom,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v1_binom(A) ) ), file(binom,rc3_binom), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) ) ) ), file(ideal_1,rc3_ideal_1), []). fof(rc3_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc3_ordinal1), []). fof(rc3_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc3_polynom1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_ideal_1(B,A) ) ) ), file(ideal_1,rc4_ideal_1), []). fof(rc4_polynom1,axiom,( ? [A] : ( m1_finseq_1(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc4_polynom1), []). fof(rc4_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_ideal_1(B,A) ) ) ), file(ideal_1,rc5_ideal_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v2_ideal_1(B,A) & v3_ideal_1(B,A) ) ) ), file(ideal_1,rc6_ideal_1), []). fof(rc6_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc6_vectsp_1), []). fof(rc7_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v3_ideal_1(B,A) ) ) ), file(ideal_1,rc7_ideal_1), []). fof(rc7_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v7_seqm_3(A) ) ), file(polynom1,rc7_polynom1), []). fof(rc7_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc7_vectsp_1), []). fof(rc8_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v2_ideal_1(B,A) ) ) ), file(ideal_1,rc8_ideal_1), []). fof(rc8_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) ) ), file(polynom1,rc8_polynom1), []). fof(rc9_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc9_polynom1), []). fof(redefinition_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k13_binarith,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k13_binarith(A,B) = k5_finseq_1(B) ) ), file(binarith,k13_binarith), []). fof(redefinition_k14_polynom1,axiom,( ! [A] : k14_polynom1(A) = k13_polynom1(A) ), file(polynom1,k14_polynom1), []). fof(redefinition_k15_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => k15_polynom1(A,B,C,D) = k1_funct_1(C,D) ) ), file(polynom1,k15_polynom1), []). fof(redefinition_k1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k1_borsuk_1(A,B,C) = k2_funcop_1(B,C) ) ), file(borsuk_1,k1_borsuk_1), []). fof(redefinition_k1_polynom1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(E,B) ) => k1_polynom1(A,B,C,D,E) = k2_funct_7(C,D,E) ) ), file(polynom1,k1_polynom1), []). fof(redefinition_k23_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => k23_polynom1(A,B,C,D) = k22_polynom1(A,B,C,D) ) ), file(polynom1,k23_polynom1), []). fof(redefinition_k2_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). 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_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => k3_polynom1(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) ), file(polynom1,k3_polynom1), []). 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_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_rfunct_3,axiom,( ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ), file(rfunct_3,k4_rfunct_3), []). fof(redefinition_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), []). fof(redefinition_k5_rfunct_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,B) ) => k5_rfunct_3(A,B,C,D) = k2_funcop_1(C,D) ) ), file(rfunct_3,k5_rfunct_3), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). fof(redefinition_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ! [C] : ( m1_polynom1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(polynom1,m1_polynom1), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). 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_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(rfunct_3,m2_rfunct_3), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s3_funct_1__e1_34__hilbasis,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & ~ v3_realset2(A) & l3_vectsp_1(A) ) => ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k1_relat_1(B) = u1_struct_0(A) & ! [C] : ( r2_hidden(C,u1_struct_0(A)) => k1_funct_1(B,C) = k2_pre_circ(k14_polynom1(k1_xboole_0),C) ) ) ) ), file(hilbasis,s3_funct_1__e1_34__hilbasis), []). 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(t13_finset_1,axiom,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t14_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k1_relat_1(B) = k1_tarski(A) => k2_relat_1(B) = k1_tarski(k1_funct_1(B,A)) ) ) ), file(funct_1,t14_funct_1), []). fof(t15_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( k2_relat_1(A) = k1_tarski(B) => A = k2_funcop_1(k1_relat_1(A),B) ) ) ), file(funcop_1,t15_funcop_1), []). fof(t16_funcop_1,axiom,( ! [A] : ( k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 ) ), file(funcop_1,t16_funcop_1), []). 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_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_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) => k1_funct_4(A,B) = B ) ) ) ), file(funct_4,t20_funct_4), []). 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(t2_hilbasis,axiom,( ! [A] : ( ( v7_seqm_3(A) & v1_polynom1(A) & m1_pboole(A,0) ) => k21_polynom1(0,A) = k9_finseq_1(k10_finseq_1(k1_xboole_0,k1_xboole_0)) ) ), file(hilbasis,t2_hilbasis), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t3_funct_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ), file(funct_2,t3_funct_2), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(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(t55_polynom1,axiom,( k14_polynom1(k1_xboole_0) = k1_tarski(k1_xboole_0) ), file(polynom1,t55_polynom1), []). fof(t56_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k3_finseq_1(B) = 1 & k2_relat_1(B) = k1_tarski(A) ) ) ) ), file(finseq_1,t56_finseq_1), []). fof(t57_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k3_finseq_1(B) = 1 & k1_funct_1(B,1) = A ) ) ) ), file(finseq_1,t57_finseq_1), []). 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_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) ), file(rlvect_1,t61_rlvect_1), []). fof(t64_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ( k1_relat_1(A) = k1_xboole_0 | k2_relat_1(A) = k1_xboole_0 ) => A = k1_xboole_0 ) ) ), file(relat_1,t64_relat_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_funct_4,axiom,( ! [A,B,C,D] : ( r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) => ( A = k1_xboole_0 | B = D ) ) ), file(funct_4,t7_funct_4), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t90_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => k2_group_1(k30_polynom1(A,B)) = k27_polynom1(A,B) ) ) ), file(polynom1,t90_polynom1), []).