% Mizar problem: t51_groeb_3,groeb_3,2406,39 fof(t51_groeb_3,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)) & v2_bagorder(B,A) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v4_group_1(C) & v7_group_1(C) & v6_vectsp_1(C) & v7_vectsp_1(C) & v8_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & v1_polynom7(D,A,C) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(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)) ) => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,E)),k29_polynom1(A,C,D,E),k26_polynom1(A,C)) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc1_algstr_1,cc1_binom,cc1_card_1,cc1_finset_1,cc1_polynom4,cc1_polynom7,cc1_relset_1,cc1_termord,cc1_vectsp_1,cc1_xreal_0,cc2_algstr_1,cc2_binom,cc2_card_1,cc2_finset_1,cc2_int_1,cc2_vectsp_1,cc2_xreal_0,cc3_algstr_1,cc3_binom,cc3_card_1,cc3_int_1,cc3_polynom1,cc3_polynom7,cc3_vectsp_1,cc3_xreal_0,cc4_algstr_1,cc4_binom,cc4_int_1,cc4_polynom1,cc4_polynom7,cc4_vectsp_1,cc4_xreal_0,cc5_binom,cc5_polynom1,cc5_vectsp_1,cc5_xreal_0,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k29_polynom1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,d13_polyred,d1_tarski,d2_polynom7,d3_tarski,d5_card_1,d5_tarski,d6_termord,dt_g3_vectsp_1,dt_k12_polynom1,dt_k13_polynom1,dt_k14_polynom1,dt_k16_polynom1,dt_k1_card_1,dt_k1_groeb_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k26_polynom1,dt_k28_polynom1,dt_k29_polynom1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k30_polynom1,dt_k3_polyred,dt_k3_termord,dt_k4_card_1,dt_k4_ordinal2,dt_k4_tarski,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k6_termord,dt_k6_xcmplx_0,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_pboole,dt_m1_polynom1,dt_m1_relset_1,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_pboole,existence_m1_polynom1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_xreal_0,fc12_finset_1,fc12_xreal_0,fc14_finset_1,fc14_polynom1,fc15_xreal_0,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_xreal_0,fc1_finset_1,fc1_groeb_3,fc1_int_1,fc1_polynom1,fc1_polynom7,fc1_polyred,fc1_struct_0,fc1_termord,fc20_polynom1,fc20_xreal_0,fc25_polynom1,fc2_card_1,fc2_finset_1,fc2_polynom2,fc2_termord,fc35_polynom1,fc37_polynom1,fc38_polynom1,fc39_polynom1,fc3_polynom1,fc3_polynom2,fc3_xreal_0,fc40_polynom1,fc41_polynom1,fc42_polynom1,fc43_polynom1,fc44_polynom1,fc4_int_1,fc5_xreal_0,fc6_int_1,fc7_xreal_0,fc8_int_1,fc8_xreal_0,fc9_int_1,fc9_xreal_0,free_g3_vectsp_1,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc14_polynom1,rc1_binom,rc1_card_1,rc1_finset_1,rc1_int_1,rc1_polynom2,rc1_polynom7,rc1_polyred,rc1_termord,rc1_xreal_0,rc2_binom,rc2_card_1,rc2_finset_1,rc2_int_1,rc2_polynom1,rc2_polynom7,rc2_termord,rc2_xreal_0,rc3_binom,rc3_finset_1,rc3_struct_0,rc3_termord,rc3_xreal_0,rc4_binom,rc4_finset_1,rc4_polynom7,rc4_struct_0,rc4_xreal_0,rc5_polynom7,rc5_struct_0,rc6_polynom1,rc6_vectsp_1,rc7_polynom1,rc7_polynom7,rc7_vectsp_1,rc8_polynom1,rc8_polynom7,rc8_vectsp_1,rc9_polynom1,rc9_vectsp_1,redefinition_k14_polynom1,redefinition_k1_groeb_1,redefinition_k1_nat_1,redefinition_k29_polynom1,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_m1_polynom1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r2_wellord2,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_wellord2,reflexivity_r6_pboole,s1_nat_1__e4_63__groeb_3,spc0_boole,spc1_boole,spc1_numerals,symmetry_r2_wellord2,symmetry_r6_pboole,t13_rewrite1,t16_rewrite1,t17_rewrite1,t1_arithm,t1_numerals,t1_polynom7,t1_subset,t20_card_2,t2_subset,t36_termord,t3_boole,t3_subset,t46_card_1,t47_groeb_3,t4_arithm,t4_boole,t4_subset,t50_card_1,t5_polyred,t5_subset,t63_card_2,t6_boole,t7_boole,t8_boole]), [file(groeb_3,t51_groeb_3)]). 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(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_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_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_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_termord,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) => ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v2_bagorder(B,A) ) => ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v2_bagorder(B,A) & v1_wellord1(B) ) ) ) ) ), file(termord,cc1_termord), []). 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_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_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_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_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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_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_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_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_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(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_k29_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_group_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)) ) => k29_polynom1(A,B,C,D) = k29_polynom1(A,B,D,C) ) ), file(polynom1,k29_polynom1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(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(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). 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(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d5_card_1,axiom,( ! [A,B] : ( v1_card_1(B) => ( B = k1_card_1(A) <=> r2_wellord2(A,B) ) ) ), file(card_1,d5_card_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( ~ v3_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) ) => ! [E] : ( m1_polynom1(E,A,k14_polynom1(A)) => ( E = k3_termord(A,B,C,D) <=> ( ( k12_polynom1(k14_polynom1(A),C,D) = k1_xboole_0 & r6_pboole(A,E,k16_polynom1(A)) ) | ( r2_hidden(E,k12_polynom1(k14_polynom1(A),C,D)) & ! [F] : ( ( v7_seqm_3(F) & v1_polynom1(F) & m1_pboole(F,A) ) => ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D)) => r1_termord(A,B,F,E) ) ) ) ) ) ) ) ) ) ) ), file(termord,d6_termord), []). 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_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_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_k16_polynom1,axiom,( ! [A] : m1_polynom1(k16_polynom1(A),A,k14_polynom1(A)) ), file(polynom1,k16_polynom1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_groeb_1,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & v2_group_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_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_xboole_0(k1_groeb_1(A,B,C)) & v1_finset_1(k1_groeb_1(A,B,C)) & m1_subset_1(k1_groeb_1(A,B,C),k1_zfmisc_1(u1_struct_0(k30_polynom1(A,B)))) ) ) ), file(groeb_1,k1_groeb_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_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_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_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_k29_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_group_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(k29_polynom1(A,B,C,D)) & v1_funct_2(k29_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k29_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k29_polynom1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_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_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_termord,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & ~ v3_struct_0(C) & l2_struct_0(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) ) => m1_polynom1(k3_termord(A,B,C,D),A,k14_polynom1(A)) ) ), file(termord,k3_termord), []). fof(dt_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). fof(dt_k4_ordinal2,axiom, ( v3_ordinal1(k4_ordinal2) & ~ v1_xboole_0(k4_ordinal2) ), file(ordinal2,k4_ordinal2), []). 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_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k6_termord,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & ~ v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) ) => ( v1_funct_1(k6_termord(A,B,C,D)) & v1_funct_2(k6_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(k6_termord(A,B,C,D),k14_polynom1(A),C) & m2_relset_1(k6_termord(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) ), file(termord,k6_termord), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). 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_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_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_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_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_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_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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). fof(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_groeb_3,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_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_finset_1(k12_polynom1(k14_polynom1(A),B,C)) ) ), file(groeb_3,fc1_groeb_3), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_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_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(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(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_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_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_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(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(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_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_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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc5_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), []). fof(fc8_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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(free_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(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_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_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_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_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_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_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_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_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_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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_1(B) & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v2_bagorder(B,A) ) ) ), file(termord,rc3_termord), []). 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_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_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_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_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_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_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(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_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(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_groeb_1,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & v2_group_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_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)) ) => k1_groeb_1(A,B,C) = k1_tarski(C) ) ), file(groeb_1,k1_groeb_1), []). 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_k29_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_group_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)) ) => k29_polynom1(A,B,C,D) = k28_polynom1(A,B,C,D) ) ), file(polynom1,k29_polynom1), []). fof(redefinition_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_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_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r2_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) <=> r2_tarski(A,B) ) ), file(wellord2,r2_wellord2), []). fof(redefinition_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r2_wellord2,axiom,( ! [A,B] : r2_wellord2(A,A) ), file(wellord2,r2_wellord2), []). fof(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(s1_nat_1__e4_63__groeb_3,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)) & v2_bagorder(B,A) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v4_group_1(C) & v7_group_1(C) & v6_vectsp_1(C) & v7_vectsp_1(C) & v8_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & v1_polynom7(D,A,C) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) ) => ( ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(E,k14_polynom1(A),C) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) ) => ( k4_card_1(k12_polynom1(k14_polynom1(A),C,E)) = 0 => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,D)),k29_polynom1(A,C,E,D),k26_polynom1(A,C)) ) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ! [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)) ) => ( k4_card_1(k12_polynom1(k14_polynom1(A),C,G)) = F => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,D)),k29_polynom1(A,C,G,D),k26_polynom1(A,C)) ) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(H,k14_polynom1(A),C) & m2_relset_1(H,k14_polynom1(A),u1_struct_0(C)) ) => ( k4_card_1(k12_polynom1(k14_polynom1(A),C,H)) = k1_nat_1(F,1) => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,D)),k29_polynom1(A,C,H,D),k26_polynom1(A,C)) ) ) ) ) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(I,k14_polynom1(A),C) & m2_relset_1(I,k14_polynom1(A),u1_struct_0(C)) ) => ( k4_card_1(k12_polynom1(k14_polynom1(A),C,I)) = F => r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,D)),k29_polynom1(A,C,I,D),k26_polynom1(A,C)) ) ) ) ) ) ), file(groeb_3,s1_nat_1__e4_63__groeb_3), []). 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(symmetry_r2_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) => r2_wellord2(B,A) ) ), file(wellord2,r2_wellord2), []). fof(symmetry_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(t13_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : r1_rewrite1(A,B,B) ) ), file(rewrite1,t13_rewrite1), []). fof(t16_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_hidden(k4_tarski(B,C),A) => r1_rewrite1(A,B,C) ) ) ), file(rewrite1,t16_rewrite1), []). fof(t17_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C,D] : ( ( r1_rewrite1(A,B,C) & r1_rewrite1(A,C,D) ) => r1_rewrite1(A,B,D) ) ) ), file(rewrite1,t17_rewrite1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_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)) ) => ( C = k26_polynom1(A,B) <=> k12_polynom1(k14_polynom1(A),B,C) = k1_xboole_0 ) ) ) ), file(polynom7,t1_polynom7), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_card_2,axiom,( 1 = k4_ordinal2 ), file(card_2,t20_card_2), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t36_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A)) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & ~ v3_realset2(C) & l1_rlvect_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) ) => k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)) = k4_xboole_0(k12_polynom1(k14_polynom1(A),C,D),k1_tarski(k3_termord(A,B,C,D))) ) ) ) ) ), file(termord,t36_termord), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t46_card_1,axiom,( ! [A] : ( r2_wellord2(A,k1_xboole_0) <=> A = k1_xboole_0 ) ), file(card_1,t46_card_1), []). fof(t47_groeb_3,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)) & v2_bagorder(B,A) & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) ) => ! [C] : ( ( v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v4_group_1(C) & v7_group_1(C) & v6_vectsp_1(C) & v7_vectsp_1(C) & v8_vectsp_1(C) & v9_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(A),C) & v1_polynom7(D,A,C) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(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)) ) => r5_polyred(A,B,C,k29_polynom1(A,C,D,E),k29_polynom1(A,C,k6_termord(A,B,C,D),E),k1_groeb_1(A,C,E)) ) ) ) ) ) ), file(groeb_3,t47_groeb_3), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t50_card_1,axiom,( ! [A] : k1_card_1(k1_tarski(A)) = k4_ordinal2 ), file(card_1,t50_card_1), []). fof(t5_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_1(B) & v2_algstr_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)) ) => k28_polynom1(A,B,k26_polynom1(A,B),C) = k26_polynom1(A,B) ) ) ) ), file(polyred,t5_polyred), []). 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(t63_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,A) => k4_card_1(k4_xboole_0(A,B)) = k5_real_1(k4_card_1(A),k4_card_1(B)) ) ) ) ), file(card_2,t63_card_2), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).