% Mizar problem: t57_polyred,polyred,4261,35 fof(t57_polyred,conjecture,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( v2_group_1(C) & v4_group_1(C) & v7_group_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k30_polynom1(A,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k30_polynom1(A,C))) => ( r2_rewrite1(k3_polyred(A,B,C,D),E,F) => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),E,F) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc10_rewrite1,cc11_rewrite1,cc12_rewrite1,cc13_rewrite1,cc14_rewrite1,cc15_rewrite1,cc1_algstr_1,cc1_binom,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_gcd_1,cc1_ideal_1,cc1_polynom4,cc1_polynom7,cc1_relat_1,cc1_relset_1,cc1_rewrite1,cc1_vectsp_1,cc1_xreal_0,cc2_algstr_1,cc2_binom,cc2_card_1,cc2_finset_1,cc2_finsub_1,cc2_gcd_1,cc2_ideal_1,cc2_rewrite1,cc2_vectsp_1,cc2_xreal_0,cc3_algstr_1,cc3_binom,cc3_card_1,cc3_gcd_1,cc3_polynom1,cc3_polynom7,cc3_rewrite1,cc3_vectsp_1,cc3_xreal_0,cc4_algstr_1,cc4_binom,cc4_gcd_1,cc4_polynom1,cc4_polynom7,cc4_rewrite1,cc4_vectsp_1,cc4_xreal_0,cc5_binom,cc5_gcd_1,cc5_polynom1,cc5_rewrite1,cc5_vectsp_1,cc5_xreal_0,cc6_rewrite1,cc6_xreal_0,cc7_rewrite1,cc7_xreal_0,cc8_rewrite1,cc8_xreal_0,cc9_rewrite1,commutativity_k1_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,connectedness_r1_xreal_0,d13_polyred,d14_polyred,d1_mcart_1,d1_tarski,d27_polynom1,d2_mcart_1,d2_polynom7,d2_rewrite1,d2_xboole_0,d3_finseq_1,d3_rewrite1,d4_rewrite1,d4_xboole_0,d7_relat_1,dt_g3_vectsp_1,dt_k13_polynom1,dt_k14_polynom1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_group_1,dt_k1_mcart_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_rlvect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_polynom1,dt_k26_polynom1,dt_k27_polynom1,dt_k28_polynom1,dt_k2_finseq_1,dt_k2_mcart_1,dt_k2_rlvect_1,dt_k2_vectsp_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k30_polynom1,dt_k3_finseq_1,dt_k3_polyred,dt_k3_xboole_0,dt_k4_finseq_1,dt_k4_relat_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k6_relset_1,dt_k6_rlvect_1,dt_k7_ideal_1,dt_k7_relat_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_relset_1,dt_m1_rewrite1,dt_m1_subset_1,dt_m2_relset_1,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_relset_1,existence_m1_rewrite1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_finset_1,fc10_xreal_0,fc11_finset_1,fc11_relat_1,fc11_xreal_0,fc12_finset_1,fc12_relat_1,fc12_xreal_0,fc13_relat_1,fc14_finset_1,fc14_polynom1,fc15_ideal_1,fc16_ideal_1,fc17_finseq_1,fc17_ideal_1,fc18_ideal_1,fc1_bagorder,fc1_finseq_1,fc1_finset_1,fc1_finsub_1,fc1_ideal_1,fc1_ordinal2,fc1_polynom1,fc1_polynom7,fc1_polyred,fc1_relat_1,fc1_struct_0,fc1_termord,fc20_polynom1,fc25_polynom1,fc2_bagorder,fc2_card_1,fc2_finseq_1,fc2_ideal_1,fc2_polynom7,fc2_relat_1,fc2_termord,fc31_ideal_1,fc32_polynom1,fc33_ideal_1,fc35_polynom1,fc36_polynom1,fc37_polynom1,fc38_polynom1,fc39_polynom1,fc3_ideal_1,fc3_polynom1,fc3_polynom2,fc3_relat_1,fc3_xreal_0,fc40_polynom1,fc41_polynom1,fc42_polynom1,fc43_polynom1,fc44_polynom1,fc4_relat_1,fc5_polynom1,fc5_relat_1,fc7_relat_1,fc7_xreal_0,fc8_xreal_0,fc9_finset_1,fc9_xreal_0,free_g3_vectsp_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,involutiveness_k4_relat_1,involutiveness_k6_relset_1,l89_polyred,rc11_polynom1,rc12_polynom1,rc14_ideal_1,rc14_polynom1,rc1_binom,rc1_card_1,rc1_finseq_1,rc1_finset_1,rc1_ideal_1,rc1_polynom2,rc1_polynom7,rc1_polyred,rc1_relat_1,rc1_rewrite1,rc1_termord,rc1_xreal_0,rc2_binom,rc2_card_1,rc2_finseq_1,rc2_finset_1,rc2_ideal_1,rc2_polynom1,rc2_polynom7,rc2_relat_1,rc2_rewrite1,rc2_termord,rc2_xreal_0,rc3_binom,rc3_finseq_1,rc3_finset_1,rc3_gcd_1,rc3_ideal_1,rc3_relat_1,rc3_rewrite1,rc3_struct_0,rc3_xreal_0,rc4_binom,rc4_finset_1,rc4_gcd_1,rc4_ideal_1,rc4_polynom7,rc4_rewrite1,rc4_struct_0,rc4_xreal_0,rc5_ideal_1,rc5_polynom7,rc5_struct_0,rc6_finseq_1,rc6_ideal_1,rc6_polynom1,rc6_vectsp_1,rc7_finseq_1,rc7_ideal_1,rc7_polynom1,rc7_polynom7,rc7_vectsp_1,rc8_finseq_1,rc8_ideal_1,rc8_polynom7,rc8_vectsp_1,rc9_vectsp_1,redefinition_k14_polynom1,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k6_relset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_binom__e4_94__polyred,spc0_boole,spc1_boole,spc1_numerals,t19_finseq_1,t1_boole,t1_numerals,t1_real,t1_subset,t21_finseq_1,t28_rlvect_1,t29_nat_1,t2_boole,t2_real,t2_subset,t2_xreal_1,t39_nat_1,t3_boole,t3_finseq_1,t3_ideal_1,t3_real,t3_subset,t4_boole,t4_real,t4_subset,t53_polyred,t54_polyred,t5_real,t5_subset,t68_funct_1,t6_boole,t6_finseq_1,t6_real,t6_relset_1,t7_boole,t7_real,t8_boole,t8_real]), [file(polyred,t57_polyred)]). 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_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) ) ) ), file(rewrite1,cc10_rewrite1), []). fof(cc11_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_rewrite1(A) & v4_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) ) ) ), file(rewrite1,cc11_rewrite1), []). fof(cc12_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc12_rewrite1), []). fof(cc13_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v9_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc13_rewrite1), []). fof(cc14_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v10_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc14_rewrite1), []). fof(cc15_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v10_rewrite1(A) ) ) ), file(rewrite1,cc15_rewrite1), []). 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_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_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_finsub_1,axiom,( ! [A] : ( v4_finsub_1(A) => ( v1_finsub_1(A) & v3_finsub_1(A) ) ) ), file(finsub_1,cc1_finsub_1), []). fof(cc1_gcd_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_group_1(A) & v6_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v8_vectsp_1(A) ) ) ) ), file(gcd_1,cc1_gcd_1), []). fof(cc1_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v7_group_1(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) ) => ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) ) ) ) ) ), file(ideal_1,cc1_ideal_1), []). fof(cc1_polynom4,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & v1_algstr_1(A) & v3_algstr_1(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v2_vectsp_2(A) & v1_algstr_1(A) & v3_algstr_1(A) ) ) ) ), file(polynom4,cc1_polynom4), []). fof(cc1_polynom7,axiom,( ! [A] : ( l2_struct_0(A) => ( ~ v3_realset2(A) => ~ v3_struct_0(A) ) ) ), file(polynom7,cc1_polynom7), []). 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_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ v1_xboole_0(B) ) ) ), file(rewrite1,cc1_rewrite1), []). 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(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_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_finsub_1,axiom,( ! [A] : ( ( v1_finsub_1(A) & v3_finsub_1(A) ) => v4_finsub_1(A) ) ), file(finsub_1,cc2_finsub_1), []). fof(cc2_gcd_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_group_1(A) & v4_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v7_vectsp_1(A) ) ) ) ), file(gcd_1,cc2_gcd_1), []). fof(cc2_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v7_group_1(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) ) => ( ~ v1_xboole_0(B) & v2_ideal_1(B,A) ) ) ) ) ), file(ideal_1,cc2_ideal_1), []). fof(cc2_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) ) ), file(rewrite1,cc2_rewrite1), []). 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_gcd_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_group_1(A) & v5_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v7_vectsp_1(A) ) ) ) ), file(gcd_1,cc3_gcd_1), []). 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_polynom7,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v3_polynom7(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) ) ) ) ) ), file(polynom7,cc3_polynom7), []). fof(cc3_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) => ( v1_relat_1(A) & v3_rewrite1(A) ) ) ), file(rewrite1,cc3_rewrite1), []). 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_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_polynom7,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v4_polynom7(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) & v3_polynom7(C,A,B) ) ) ) ) ), file(polynom7,cc4_polynom7), []). fof(cc4_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ) ), file(rewrite1,cc4_rewrite1), []). 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_gcd_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & v3_gcd_1(A) ) ) ) ), file(gcd_1,cc5_gcd_1), []). 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_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_rewrite1(A) ) ) ), file(rewrite1,cc5_rewrite1), []). fof(cc5_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_group_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v6_vectsp_1(A) ) ) ) ), file(vectsp_1,cc5_vectsp_1), []). 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_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) ), file(rewrite1,cc6_rewrite1), []). 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_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc7_rewrite1), []). 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_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v6_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) ), file(rewrite1,cc8_rewrite1), []). 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_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v5_rewrite1(A) ) ) ), file(rewrite1,cc9_rewrite1), []). 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_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_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). 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(d13_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( v2_group_1(C) & v4_group_1(C) & v7_group_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) => ! [E] : ( m2_relset_1(E,k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C))) => ( E = k3_polyred(A,B,C,D) <=> ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(F,k14_polynom1(A),C) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(G,k14_polynom1(A),C) & m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) ) => ( r2_hidden(k4_tarski(F,G),E) <=> r5_polyred(A,B,C,F,G,D) ) ) ) ) ) ) ) ) ) ), file(polyred,d13_polyred), []). fof(d14_polyred,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(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)) => ( r11_polyred(A,B,C,D) <=> r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) ), file(polyred,d14_polyred), []). fof(d1_mcart_1,axiom,( ! [A] : ( ? [B,C] : A = k4_tarski(B,C) => ! [B] : ( B = k1_mcart_1(A) <=> ! [C,D] : ( A = k4_tarski(C,D) => B = C ) ) ) ), file(mcart_1,d1_mcart_1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). 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_mcart_1,axiom,( ! [A] : ( ? [B,C] : A = k4_tarski(B,C) => ! [B] : ( B = k2_mcart_1(A) <=> ! [C,D] : ( A = k4_tarski(C,D) => B = D ) ) ) ), file(mcart_1,d2_mcart_1), []). fof(d2_polynom7,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(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)) ) => ( v1_polynom7(C,A,B) <=> C != k26_polynom1(A,B) ) ) ) ), file(polynom7,d2_polynom7), []). fof(d2_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_rewrite1(B,A) <=> ( ~ r1_xreal_0(k3_finseq_1(B),0) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) ) => r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))),A) ) ) ) ) ) ) ), file(rewrite1,d2_rewrite1), []). 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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r1_rewrite1(A,B,C) <=> ? [D] : ( m1_rewrite1(D,A) & k1_funct_1(D,1) = B & k1_funct_1(D,k3_finseq_1(D)) = C ) ) ) ), file(rewrite1,d3_rewrite1), []). fof(d4_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_rewrite1(A,B,C) <=> r1_rewrite1(k2_xboole_0(A,k4_relat_1(A)),B,C) ) ) ), file(rewrite1,d4_rewrite1), []). 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(d7_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( B = k4_relat_1(A) <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),B) <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ), file(relat_1,d7_relat_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_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_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). 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_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_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_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_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_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_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_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_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_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_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_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_polyred,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & v2_group_1(C) & v4_group_1(C) & v7_group_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) ) => m2_relset_1(k3_polyred(A,B,C,D),k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C))) ) ), file(polyred,k3_polyred), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k4_relat_1(A)) ) ), file(relat_1,k4_relat_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). 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_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m2_relset_1(k6_relset_1(A,B,C),B,A) ) ), file(relset_1,k6_relset_1), []). fof(dt_k6_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(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k6_rlvect_1), []). fof(dt_k7_ideal_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(k7_ideal_1(A,B)) & v1_ideal_1(k7_ideal_1(A,B),A) & v2_ideal_1(k7_ideal_1(A,B),A) & v3_ideal_1(k7_ideal_1(A,B),A) & m1_subset_1(k7_ideal_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(ideal_1,k7_ideal_1), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_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_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ), file(rewrite1,m1_rewrite1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_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_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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ? [B] : m1_rewrite1(B,A) ) ), file(rewrite1,m1_rewrite1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)) ) ) ), file(relat_1,fc11_relat_1), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). 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(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_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)) ) ) ), file(relat_1,fc13_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_ideal_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v5_rlvect_1(A) & v5_vectsp_1(A) & v2_algstr_1(A) & l3_vectsp_1(A) & ~ v1_xboole_0(B) & v2_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k3_xboole_0(B,C)) ) ), file(ideal_1,fc15_ideal_1), []). fof(fc16_ideal_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & v1_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v1_ideal_1(k3_xboole_0(B,C),A) ) ), file(ideal_1,fc16_ideal_1), []). 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_ideal_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_vectsp_1(A) & v2_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v2_ideal_1(k3_xboole_0(B,C),A) ) ), file(ideal_1,fc17_ideal_1), []). fof(fc18_ideal_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_vectsp_1(A) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v3_ideal_1(k3_xboole_0(B,C),A) ) ), file(ideal_1,fc18_ideal_1), []). fof(fc1_bagorder,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) & v7_seqm_3(k7_relat_1(A,B)) ) ) ), file(bagorder,fc1_bagorder), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). 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_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) ) ), file(finsub_1,fc1_finsub_1), []). 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_polynom7,axiom,( ! [A,B] : ( ( ~ 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) & v3_polynom7(k26_polynom1(A,B),A,B) & v4_polynom7(k26_polynom1(A,B),A,B) ) ) ), file(polynom7,fc1_polynom7), []). fof(fc1_polyred,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v2_group_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_vectsp_1(B) & v2_vectsp_2(B) & v1_algstr_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) & v1_polynom7(C,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) & v1_polynom7(D,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) & v1_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) ), file(polyred,fc1_polyred), []). fof(fc1_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_1), []). 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_termord,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)) & v3_polynom7(C,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)) & v3_polynom7(D,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) & v3_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) ), file(termord,fc1_termord), []). 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(fc25_polynom1,axiom,( ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ), file(polynom1,fc25_polynom1), []). fof(fc2_bagorder,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_polynom1(k7_relat_1(A,B)) ) ) ), file(bagorder,fc2_bagorder), []). 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_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_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_polynom7,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_group_1(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) & v3_polynom7(k27_polynom1(A,B),A,B) & v4_polynom7(k27_polynom1(A,B),A,B) ) ) ), file(polynom7,fc2_polynom7), []). fof(fc2_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) ), file(relat_1,fc2_relat_1), []). fof(fc2_termord,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_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)) & v4_polynom7(C,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)) & v4_polynom7(D,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) & v3_polynom7(k28_polynom1(A,B,C,D),A,B) & v4_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) ), file(termord,fc2_termord), []). fof(fc31_ideal_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(k7_ideal_1(A,B)) & v1_ideal_1(k7_ideal_1(A,B),A) & v2_ideal_1(k7_ideal_1(A,B),A) & v3_ideal_1(k7_ideal_1(A,B),A) & v6_ideal_1(k7_ideal_1(A,B),A) ) ) ), file(ideal_1,fc31_ideal_1), []). 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(fc33_ideal_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(k7_relat_1(C,D)) & v1_relat_1(k7_relat_1(C,D)) ) ) ), file(ideal_1,fc33_ideal_1), []). 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_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(fc3_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k4_xboole_0(A,B)) ) ), file(relat_1,fc3_relat_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(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(fc42_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_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)) & v7_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,fc42_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_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). 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(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(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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_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_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_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(involutiveness_k4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k4_relat_1(k4_relat_1(A)) = A ) ), file(relat_1,k4_relat_1), []). fof(involutiveness_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k6_relset_1(A,B,k6_relset_1(A,B,C)) = C ) ), file(relset_1,k6_relset_1), []). fof(l89_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( v2_group_1(C) & v4_group_1(C) & v7_group_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(E,k14_polynom1(A),C) & v1_polynom7(E,A,C) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(F,k14_polynom1(A),C) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k30_polynom1(A,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k30_polynom1(A,C))) => ( ( E = G & F = H & r5_polyred(A,B,C,E,F,D) ) => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),G,H) ) ) ) ) ) ) ) ) ) ), file(polyred,l89_polyred), []). 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(rc14_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) & v6_ideal_1(B,A) ) ) ), file(ideal_1,rc14_ideal_1), []). 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_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_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_polynom2,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) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(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) & ~ v3_realset2(A) ) ), file(polynom2,rc1_polynom2), []). fof(rc1_polynom7,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) ) ), file(polynom7,rc1_polynom7), []). fof(rc1_polyred,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_realset2(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) & v1_polynom7(C,A,B) & v3_polynom7(C,A,B) ) ) ), file(polyred,rc1_polyred), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ), file(rewrite1,rc1_rewrite1), []). fof(rc1_termord,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) ) ), file(termord,rc1_termord), []). 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_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_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_ideal_1,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_binom(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & ~ v3_realset2(A) ) ), file(ideal_1,rc2_ideal_1), []). 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_polynom7,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) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(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) & v2_vectsp_2(A) & v1_binom(A) & ~ v3_realset2(A) ) ), file(polynom7,rc2_polynom7), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ), file(rewrite1,rc2_rewrite1), []). fof(rc2_termord,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(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) & ~ v3_realset2(A) ) ), file(termord,rc2_termord), []). 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_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_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_gcd_1,axiom,( ? [A] : ( l1_vectsp_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v3_gcd_1(A) ) ), file(gcd_1,rc3_gcd_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_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) & v10_rewrite1(A) ) ), file(rewrite1,rc3_rewrite1), []). 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_binom,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v1_binom(A) ) ), file(binom,rc4_binom), []). 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_gcd_1,axiom,( ? [A] : ( l2_vectsp_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v3_gcd_1(A) ) ), file(gcd_1,rc4_gcd_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_polynom7,axiom,( ! [A,B] : ( ( ~ v3_realset2(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)) & v1_polynom7(C,A,B) ) ) ), file(polynom7,rc4_polynom7), []). fof(rc4_rewrite1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) & v10_rewrite1(A) ) ), file(rewrite1,rc4_rewrite1), []). 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_polynom7,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_realset2(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) & v1_polynom7(C,A,B) ) ) ), file(polynom7,rc5_polynom7), []). 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_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(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_polynom1,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) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v3_realset2(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(polynom1,rc6_polynom1), []). fof(rc6_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc6_vectsp_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(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_polynom7,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)) & v3_polynom7(C,A,B) ) ) ), file(polynom7,rc7_polynom7), []). 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_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(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_polynom7,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)) & v4_polynom7(C,A,B) ) ) ), file(polynom7,rc8_polynom7), []). fof(rc8_vectsp_1,axiom,( ? [A] : ( l1_group_1(A) & ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) ) ), file(vectsp_1,rc8_vectsp_1), []). fof(rc9_vectsp_1,axiom,( ? [A] : ( l1_vectsp_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) ), file(vectsp_1,rc9_vectsp_1), []). fof(redefinition_k14_polynom1,axiom,( ! [A] : k14_polynom1(A) = k13_polynom1(A) ), file(polynom1,k14_polynom1), []). 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_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k6_relset_1(A,B,C) = k4_relat_1(C) ) ), file(relset_1,k6_relset_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s1_binom__e4_94__polyred,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & v2_group_1(C) & v4_group_1(C) & v7_group_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(k30_polynom1(A,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k30_polynom1(A,C))) => ( r1_rewrite1(k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D))),E,F) => ! [G] : ( m1_rewrite1(G,k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D)))) => ( ( k1_funct_1(G,1) = E & k1_funct_1(G,k3_finseq_1(G)) = F & k3_finseq_1(G) = 1 ) => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),E,F) ) ) ) ) ) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,H) & ! [I] : ( m1_subset_1(I,u1_struct_0(k30_polynom1(A,C))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k30_polynom1(A,C))) => ( r1_rewrite1(k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D))),I,J) => ! [K] : ( m1_rewrite1(K,k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D)))) => ( ( k1_funct_1(K,1) = I & k1_funct_1(K,k3_finseq_1(K)) = J & k3_finseq_1(K) = H ) => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),I,J) ) ) ) ) ) ) => ! [L] : ( m1_subset_1(L,u1_struct_0(k30_polynom1(A,C))) => ! [M] : ( m1_subset_1(M,u1_struct_0(k30_polynom1(A,C))) => ( r1_rewrite1(k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D))),L,M) => ! [N] : ( m1_rewrite1(N,k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D)))) => ( ( k1_funct_1(N,1) = L & k1_funct_1(N,k3_finseq_1(N)) = M & k3_finseq_1(N) = k1_nat_1(H,1) ) => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),L,M) ) ) ) ) ) ) ) ) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r1_xreal_0(1,H) => ! [O] : ( m1_subset_1(O,u1_struct_0(k30_polynom1(A,C))) => ! [P] : ( m1_subset_1(P,u1_struct_0(k30_polynom1(A,C))) => ( r1_rewrite1(k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D))),O,P) => ! [Q] : ( m1_rewrite1(Q,k2_xboole_0(k3_polyred(A,B,C,D),k6_relset_1(k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)),k3_polyred(A,B,C,D)))) => ( ( k1_funct_1(Q,1) = O & k1_funct_1(Q,k3_finseq_1(Q)) = P & k3_finseq_1(Q) = H ) => r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),O,P) ) ) ) ) ) ) ) ) ) ), file(polyred,s1_binom__e4_94__polyred), []). 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(t19_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) ) ) ) ), file(finseq_1,t19_finseq_1), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t21_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( r1_xreal_0(A,k3_finseq_1(B)) & C = k7_relat_1(B,k2_finseq_1(A)) ) => ( k3_finseq_1(C) = A & k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ) ) ), file(finseq_1,t21_finseq_1), []). fof(t28_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)) => k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) ), file(rlvect_1,t28_rlvect_1), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_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(t39_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( ~ r1_xreal_0(1,A) => A = 0 ) ) ), file(nat_1,t39_nat_1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xreal_0(1,A) & r1_xreal_0(A,B) ) ) ) ) ), file(finseq_1,t3_finseq_1), []). fof(t3_ideal_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v1_algstr_1(A) & v3_algstr_1(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_hidden(k1_rlvect_1(A),B) ) ) ), file(ideal_1,t3_ideal_1), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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(t53_polyred,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & 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)) => ( r11_polyred(A,B,C,D) => r11_polyred(A,B,D,C) ) ) ) ) ) ), file(polyred,t53_polyred), []). fof(t54_polyred,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_ideal_1(B,A) & 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)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r11_polyred(A,B,C,D) & r11_polyred(A,B,D,E) ) => r11_polyred(A,B,C,E) ) ) ) ) ) ) ), file(polyred,t54_polyred), []). 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(t68_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( B = k7_relat_1(C,A) <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A) & ! [D] : ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ), file(funct_1,t68_funct_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => r2_hidden(k2_xcmplx_0(A,1),k2_finseq_1(k2_xcmplx_0(A,1))) ) ), file(finseq_1,t6_finseq_1), []). 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_relset_1,axiom,( ! [A,B,C,D] : ( m2_relset_1(D,A,B) => ~ ( r2_hidden(C,D) & ! [E,F] : ~ ( C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B) ) ) ) ), file(relset_1,t6_relset_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).