% Mizar problem: t67_uproots,uproots,3329,55 fof(t67_uproots,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & v2_polynom5(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( k2_normsp_1(A,B,k5_binarith(k3_algseq_1(A,B),1)) = k2_group_1(A) => B = k10_uproots(A,k8_uproots(A,B)) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_algstr_1,cc1_card_1,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_nat_1,cc1_polynom7,cc1_relset_1,cc1_vectsp_1,cc1_xreal_0,cc20_membered,cc2_algstr_1,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_gobrd13,cc2_int_1,cc2_membered,cc2_nat_1,cc2_polynom1,cc2_vectsp_1,cc2_xreal_0,cc3_algstr_1,cc3_card_1,cc3_int_1,cc3_membered,cc3_nat_1,cc3_polynom1,cc3_vectsp_1,cc3_xreal_0,cc4_algstr_1,cc4_int_1,cc4_membered,cc4_polynom1,cc4_vectsp_1,cc4_xreal_0,cc5_polynom1,cc5_vectsp_1,cc5_xreal_0,cc6_membered,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k10_group_1,commutativity_k15_polynom3,commutativity_k1_nat_1,commutativity_k23_binop_2,commutativity_k2_xcmplx_0,commutativity_k9_polynom1,connectedness_r1_xreal_0,d21_vectsp_1,d2_uproots,d4_polynom5,d5_vectsp_2,d6_algseq_1,d7_polynom5,d8_polynom5,dt_k10_binop_2,dt_k10_group_1,dt_k10_pboole,dt_k10_uproots,dt_k12_polynom3,dt_k13_polynom1,dt_k14_polynom1,dt_k14_polynom3,dt_k15_polynom3,dt_k16_polynom1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_group_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_polynom1,dt_k1_rlvect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k23_binop_2,dt_k2_funcop_1,dt_k2_funct_7,dt_k2_group_1,dt_k2_normsp_1,dt_k2_uproots,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_algseq_1,dt_k3_uproots,dt_k4_polynom5,dt_k4_uproots,dt_k5_algseq_1,dt_k5_binarith,dt_k5_numbers,dt_k5_ordinal2,dt_k5_rlvect_1,dt_k6_uproots,dt_k6_xcmplx_0,dt_k7_rlvect_2,dt_k8_uproots,dt_k9_polynom1,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_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_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc14_finset_1,fc14_polynom1,fc15_polynom1,fc15_xreal_0,fc16_polynom1,fc16_xreal_0,fc17_polynom1,fc17_xreal_0,fc18_polynom1,fc18_xreal_0,fc19_xreal_0,fc1_finset_1,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_uproots,fc20_polynom1,fc20_xreal_0,fc22_polynom1,fc23_polynom1,fc25_polynom1,fc2_finseq_1,fc2_membered,fc2_subset_1,fc3_nat_1,fc3_polynom1,fc3_polynom5,fc3_uproots,fc3_xreal_0,fc4_chain_1,fc4_int_1,fc4_nat_1,fc4_ordinal2,fc4_polynom5,fc4_subset_1,fc5_membered,fc5_polynom1,fc5_xreal_0,fc6_int_1,fc6_membered,fc6_polynom3,fc7_membered,fc7_xreal_0,fc8_int_1,fc8_membered,fc8_polynom3,fc8_xreal_0,fc9_int_1,fc9_membered,fc9_xreal_0,idempotence_k1_funct_4,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc1_card_1,rc1_chain_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_polynom5,rc1_polynom7,rc1_pre_circ,rc1_subset_1,rc1_uproots,rc1_xreal_0,rc2_card_1,rc2_chain_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_polynom1,rc2_subset_1,rc2_uproots,rc2_xreal_0,rc3_chain_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_struct_0,rc3_xreal_0,rc4_finset_1,rc4_funct_1,rc4_struct_0,rc4_xreal_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,rc8_polynom1,rc8_vectsp_1,rc9_polynom1,rc9_vectsp_1,redefinition_k10_binop_2,redefinition_k10_group_1,redefinition_k10_pboole,redefinition_k14_polynom1,redefinition_k15_polynom3,redefinition_k1_nat_1,redefinition_k1_polynom1,redefinition_k23_binop_2,redefinition_k2_normsp_1,redefinition_k4_uproots,redefinition_k5_numbers,redefinition_k7_rlvect_2,redefinition_m1_polynom1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r6_pboole,s1_int_2__e6_90__uproots,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r6_pboole,t13_polynom4,t14_uproots,t19_uproots,t1_arithm,t1_numerals,t1_real,t1_subset,t20_uproots,t2_real,t2_subset,t36_uproots,t38_nat_1,t3_real,t3_subset,t41_polynom5,t43_uproots,t4_arithm,t4_real,t4_subset,t51_binarith,t52_uproots,t56_uproots,t58_uproots,t59_uproots,t5_real,t5_subset,t62_uproots,t63_uproots,t66_uproots,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]), [file(uproots,t67_uproots)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_algstr_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v6_algstr_1(A) ) => ( ~ v3_struct_0(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) ) ) ) ), file(algstr_1,cc1_algstr_1), []). fof(cc1_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_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_nat_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) ) ) ), file(nat_1,cc1_nat_1), []). 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_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) ) ) ), file(vectsp_1,cc1_vectsp_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_algstr_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( ( ~ v3_struct_0(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) ) => ( ~ v3_struct_0(A) & v6_algstr_1(A) ) ) ) ), file(algstr_1,cc2_algstr_1), []). fof(cc2_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_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_gobrd13,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_matrlin(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) ), file(gobrd13,cc2_gobrd13), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_nat_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) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_polynom1,axiom,( ! [A] : ( l2_vectsp_1(A) => ( ( ~ v3_struct_0(A) & ~ v10_vectsp_1(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) ) ) ) ), file(polynom1,cc2_polynom1), []). 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_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_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_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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_polynom1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k5_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v7_seqm_3(B) ) ) ) ), file(polynom1,cc4_polynom1), []). fof(cc4_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) ) ) ) ), file(vectsp_1,cc4_vectsp_1), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_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_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_polynom1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_pboole(B,A) => v1_polynom1(B) ) ) ), file(polynom1,cc6_polynom1), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k10_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k10_group_1(A,B,C) = k10_group_1(A,C,B) ) ), file(group_1,k10_group_1), []). fof(commutativity_k15_polynom3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => k15_polynom3(A,B,C) = k15_polynom3(A,C,B) ) ), file(polynom3,k15_polynom3), []). 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_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k23_binop_2(B,A) ) ), file(binop_2,k23_binop_2), []). 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_k9_polynom1,axiom,( ! [A,B,C] : ( ( v1_seq_1(B) & m1_pboole(B,A) & v1_seq_1(C) & m1_pboole(C,A) ) => k9_polynom1(A,B,C) = k9_polynom1(A,C,B) ) ), file(polynom1,k9_polynom1), []). 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(d21_vectsp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_vectsp_1(A) ) => ( v10_vectsp_1(A) <=> k1_rlvect_1(A) = k2_group_1(A) ) ) ), file(vectsp_1,d21_vectsp_1), []). fof(d2_uproots,axiom,( ! [A,B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k2_uproots(A,B,C) = k1_funct_4(k16_polynom1(A),k10_pboole(B,C)) ) ) ), file(uproots,d2_uproots), []). fof(d4_polynom5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_polynom5(A,B,C) = k1_polynom1(k5_numbers,u1_struct_0(A),k1_polynom1(k5_numbers,u1_struct_0(A),k12_polynom3(A),0,B),1,C) ) ) ) ), file(polynom5,d4_polynom5), []). fof(d5_vectsp_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_vectsp_1(A) ) => ( v2_vectsp_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k1_group_1(A,B,C) = k1_rlvect_1(A) & B != k1_rlvect_1(A) & C != k1_rlvect_1(A) ) ) ) ) ) ), file(vectsp_2,d5_vectsp_2), []). fof(d6_algseq_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( C = k5_algseq_1(A,B) <=> ( r1_xreal_0(k3_algseq_1(A,C),1) & k2_normsp_1(A,C,0) = B ) ) ) ) ) ), file(algseq_1,d6_algseq_1), []). fof(d7_polynom5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v1_polynom5(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_polynom5(A,B,C) ) ) ) ) ), file(polynom5,d7_polynom5), []). fof(d8_polynom5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & l3_vectsp_1(A) ) => ( v2_polynom5(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( ~ r1_xreal_0(k3_algseq_1(A,B),1) => v1_polynom5(B,A) ) ) ) ) ), file(polynom5,d8_polynom5), []). fof(dt_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k10_binop_2(A,B),k1_numbers) ) ), file(binop_2,k10_binop_2), []). fof(dt_k10_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k10_group_1), []). fof(dt_k10_pboole,axiom,( ! [A,B] : ( v1_funct_1(k10_pboole(A,B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) ) ), file(pboole,k10_pboole), []). fof(dt_k10_uproots,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_funct_1(k10_uproots(A,B)) & v1_funct_2(k10_uproots(A,B),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k10_uproots(A,B),A) & m2_relset_1(k10_uproots(A,B),k5_numbers,u1_struct_0(A)) ) ) ), file(uproots,k10_uproots), []). fof(dt_k12_polynom3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ( v1_funct_1(k12_polynom3(A)) & v1_funct_2(k12_polynom3(A),k5_numbers,u1_struct_0(A)) & m2_relset_1(k12_polynom3(A),k5_numbers,u1_struct_0(A)) ) ) ), file(polynom3,k12_polynom3), []). 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_k14_polynom3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( v1_funct_1(k14_polynom3(A,B,C)) & v1_funct_2(k14_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) & m2_relset_1(k14_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(polynom3,k14_polynom3), []). fof(dt_k15_polynom3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( v1_funct_1(k15_polynom3(A,B,C)) & v1_funct_2(k15_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) & m2_relset_1(k15_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(polynom3,k15_polynom3), []). fof(dt_k16_polynom1,axiom,( ! [A] : m1_polynom1(k16_polynom1(A),A,k14_polynom1(A)) ), file(polynom1,k16_polynom1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k1_group_1), []). fof(dt_k1_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_polynom1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(E,B) ) => ( v1_funct_1(k1_polynom1(A,B,C,D,E)) & v1_funct_2(k1_polynom1(A,B,C,D,E),A,B) & m2_relset_1(k1_polynom1(A,B,C,D,E),A,B) ) ) ), file(polynom1,k1_polynom1), []). fof(dt_k1_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_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) ), file(binop_2,k23_binop_2), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_funct_7,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) ) ) ), file(funct_7,k2_funct_7), []). fof(dt_k2_group_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ), file(group_1,k2_group_1), []). fof(dt_k2_normsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k2_normsp_1(A,B,C),u1_struct_0(A)) ) ), file(normsp_1,k2_normsp_1), []). fof(dt_k2_uproots,axiom,( ! [A,B,C] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k5_numbers) ) => m1_polynom1(k2_uproots(A,B,C),A,k14_polynom1(A)) ) ), file(uproots,k2_uproots), []). 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_k3_algseq_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) ) => m2_subset_1(k3_algseq_1(A,B),k1_numbers,k5_numbers) ) ), file(algseq_1,k3_algseq_1), []). fof(dt_k3_uproots,axiom,( ! [A,B] : ( ( v1_seq_1(B) & v1_polynom1(B) & m1_pboole(B,A) ) => v1_xreal_0(k3_uproots(A,B)) ) ), file(uproots,k3_uproots), []). fof(dt_k4_polynom5,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( v1_funct_1(k4_polynom5(A,B,C)) & v1_funct_2(k4_polynom5(A,B,C),k5_numbers,u1_struct_0(A)) & m2_relset_1(k4_polynom5(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(polynom5,k4_polynom5), []). fof(dt_k4_uproots,axiom,( ! [A,B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => m2_subset_1(k4_uproots(A,B),k1_numbers,k5_numbers) ) ), file(uproots,k4_uproots), []). fof(dt_k5_algseq_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_funct_1(k5_algseq_1(A,B)) & v1_funct_2(k5_algseq_1(A,B),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k5_algseq_1(A,B),A) & m2_relset_1(k5_algseq_1(A,B),k5_numbers,u1_struct_0(A)) ) ) ), file(algseq_1,k5_algseq_1), []). fof(dt_k5_binarith,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k5_binarith(A,B),k1_numbers,k5_numbers) ) ), file(binarith,k5_binarith), []). fof(dt_k5_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_rlvect_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ), file(rlvect_1,k5_rlvect_1), []). fof(dt_k6_uproots,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( v1_funct_1(k6_uproots(A,B,C)) & v1_funct_2(k6_uproots(A,B,C),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k6_uproots(A,B,C),A) & m2_relset_1(k6_uproots(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(uproots,k6_uproots), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_finset_1(k7_rlvect_2(A,B)) & m1_subset_1(k7_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(rlvect_2,k7_rlvect_2), []). fof(dt_k8_uproots,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v7_seqm_3(k8_uproots(A,B)) & v1_polynom1(k8_uproots(A,B)) & m1_pboole(k8_uproots(A,B),u1_struct_0(A)) ) ) ), file(uproots,k8_uproots), []). fof(dt_k9_polynom1,axiom,( ! [A,B,C] : ( ( v1_seq_1(B) & m1_pboole(B,A) & v1_seq_1(C) & m1_pboole(C,A) ) => m1_pboole(k9_polynom1(A,B,C),A) ) ), file(polynom1,k9_polynom1), []). 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_struct_0,axiom,( $true ), file(struct_0,u1_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_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(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_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_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_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_polynom1,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & m1_subset_1(C,k5_numbers) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_seq_1(k2_funct_7(A,B,C)) & v7_seqm_3(k2_funct_7(A,B,C)) ) ) ), file(polynom1,fc15_polynom1), []). fof(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_polynom1,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & m1_subset_1(C,k5_numbers) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_seq_1(k2_funct_7(A,B,C)) ) ) ), file(polynom1,fc16_polynom1), []). fof(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_polynom1,axiom,( ! [A,B,C] : ( ( v1_seq_1(B) & m1_pboole(B,A) & v1_seq_1(C) & m1_pboole(C,A) ) => ( v1_relat_1(k9_polynom1(A,B,C)) & v1_funct_1(k9_polynom1(A,B,C)) & v1_seq_1(k9_polynom1(A,B,C)) ) ) ), file(polynom1,fc17_polynom1), []). 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_polynom1,axiom,( ! [A,B,C] : ( ( v7_seqm_3(B) & m1_pboole(B,A) & v7_seqm_3(C) & m1_pboole(C,A) ) => ( v1_relat_1(k9_polynom1(A,B,C)) & v1_funct_1(k9_polynom1(A,B,C)) & v1_seq_1(k9_polynom1(A,B,C)) & v7_seqm_3(k9_polynom1(A,B,C)) ) ) ), file(polynom1,fc18_polynom1), []). 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_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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_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_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_uproots,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v10_vectsp_1(A) & l2_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k4_polynom5(A,B,k2_group_1(A))) & v1_relat_1(k4_polynom5(A,B,k2_group_1(A))) & v1_funct_1(k4_polynom5(A,B,k2_group_1(A))) & v1_funct_2(k4_polynom5(A,B,k2_group_1(A)),k5_numbers,u1_struct_0(A)) & v1_partfun1(k4_polynom5(A,B,k2_group_1(A)),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k4_polynom5(A,B,k2_group_1(A)),A) & v1_uproots(k4_polynom5(A,B,k2_group_1(A)),A) ) ) ), file(uproots,fc1_uproots), []). 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(fc22_polynom1,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) & v1_polynom1(k2_funct_7(A,B,C)) ) ) ), file(polynom1,fc22_polynom1), []). fof(fc23_polynom1,axiom,( ! [A,B,C] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) & v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ( v1_relat_1(k9_polynom1(A,B,C)) & v1_funct_1(k9_polynom1(A,B,C)) & v1_seq_1(k9_polynom1(A,B,C)) & v7_seqm_3(k9_polynom1(A,B,C)) & v1_polynom1(k9_polynom1(A,B,C)) ) ) ), file(polynom1,fc23_polynom1), []). fof(fc25_polynom1,axiom,( ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ), file(polynom1,fc25_polynom1), []). 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_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_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_polynom5,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k4_polynom5(A,B,C)) & v1_relat_1(k4_polynom5(A,B,C)) & v1_funct_1(k4_polynom5(A,B,C)) & v1_funct_2(k4_polynom5(A,B,C),k5_numbers,u1_struct_0(A)) & v1_partfun1(k4_polynom5(A,B,C),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k4_polynom5(A,B,C),A) ) ) ), file(polynom5,fc3_polynom5), []). fof(fc3_uproots,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & v1_uproots(C,A) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k14_polynom3(A,B,C)) & v1_relat_1(k14_polynom3(A,B,C)) & v1_funct_1(k14_polynom3(A,B,C)) & v1_funct_2(k14_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) & v1_partfun1(k14_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k14_polynom3(A,B,C),A) & v1_uproots(k14_polynom3(A,B,C),A) ) ) ), file(uproots,fc3_uproots), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_chain_1,axiom, ( ~ v1_xboole_0(k1_numbers) & ~ v1_realset1(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(chain_1,fc4_chain_1), []). fof(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). fof(fc4_polynom5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & l3_vectsp_1(A) ) => ( ~ v1_xboole_0(k12_polynom3(A)) & v1_relat_1(k12_polynom3(A)) & v1_funct_1(k12_polynom3(A)) & v1_funct_2(k12_polynom3(A),k5_numbers,u1_struct_0(A)) & v1_partfun1(k12_polynom3(A),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k12_polynom3(A),A) & v1_polynom5(k12_polynom3(A),A) ) ) ), file(polynom5,fc4_polynom5), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & v1_finset_1(k1_funct_1(A,B)) & v1_finseq_1(k1_funct_1(A,B)) ) ) ), file(polynom1,fc5_polynom1), []). fof(fc5_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_polynom3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ( ~ v1_xboole_0(k12_polynom3(A)) & v1_relat_1(k12_polynom3(A)) & v1_funct_1(k12_polynom3(A)) & v1_funct_2(k12_polynom3(A),k5_numbers,u1_struct_0(A)) & v1_partfun1(k12_polynom3(A),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k12_polynom3(A),A) ) ) ), file(polynom3,fc6_polynom3), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_polynom3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k14_polynom3(A,B,C)) & v1_relat_1(k14_polynom3(A,B,C)) & v1_funct_1(k14_polynom3(A,B,C)) & v1_funct_2(k14_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) & v1_partfun1(k14_polynom3(A,B,C),k5_numbers,u1_struct_0(A)) & v1_algseq_1(k14_polynom3(A,B,C),A) ) ) ), file(polynom3,fc8_polynom3), []). 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_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(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(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(rc10_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc10_polynom1), []). fof(rc11_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_seq_1(A) & v7_seqm_3(A) & v1_polynom1(A) ) ), file(polynom1,rc11_polynom1), []). fof(rc12_polynom1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc12_polynom1), []). fof(rc13_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc13_polynom1), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_chain_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & 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_int_1(A) & v1_rat_1(A) ) ), file(chain_1,rc1_chain_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_polynom5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & l3_vectsp_1(A) ) => ? [B] : ( m1_relset_1(B,k5_numbers,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_partfun1(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_polynom5(B,A) ) ) ), file(polynom5,rc1_polynom5), []). fof(rc1_polynom7,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) ) ), file(polynom7,rc1_polynom7), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l2_struct_0(A) ) => ? [B] : ( m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) ) ) ), file(uproots,rc1_uproots), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). 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_chain_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & ~ v1_realset1(A) ) ), file(chain_1,rc2_chain_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_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_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_uproots,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) & v6_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & v2_polynom5(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(uproots,rc2_uproots), []). 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_chain_1,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) & ~ v1_realset1(B) ) ) ), file(chain_1,rc3_chain_1), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_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_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(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_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v7_seqm_3(A) ) ), file(polynom1,rc7_polynom1), []). 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_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_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_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) ), file(binop_2,k10_binop_2), []). fof(redefinition_k10_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k10_group_1(A,B,C) = k1_group_1(A,B,C) ) ), file(group_1,k10_group_1), []). fof(redefinition_k10_pboole,axiom,( ! [A,B] : k10_pboole(A,B) = k2_funcop_1(A,B) ), file(pboole,k10_pboole), []). fof(redefinition_k14_polynom1,axiom,( ! [A] : k14_polynom1(A) = k13_polynom1(A) ), file(polynom1,k14_polynom1), []). fof(redefinition_k15_polynom3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => k15_polynom3(A,B,C) = k14_polynom3(A,B,C) ) ), file(polynom3,k15_polynom3), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_polynom1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(E,B) ) => k1_polynom1(A,B,C,D,E) = k2_funct_7(C,D,E) ) ), file(polynom1,k1_polynom1), []). fof(redefinition_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k23_binop_2), []). fof(redefinition_k2_normsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => k2_normsp_1(A,B,C) = k1_funct_1(B,C) ) ), file(normsp_1,k2_normsp_1), []). fof(redefinition_k4_uproots,axiom,( ! [A,B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => k4_uproots(A,B) = k3_uproots(A,B) ) ), file(uproots,k4_uproots), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k7_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k7_rlvect_2(A,B) = k1_tarski(B) ) ), file(rlvect_2,k7_rlvect_2), []). 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_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_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(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_int_2__e6_90__uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & v2_polynom5(A) & l3_vectsp_1(A) ) => ( ( ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( ( k3_algseq_1(A,B) = 1 & r1_xreal_0(1,1) & k2_normsp_1(A,B,k5_binarith(k3_algseq_1(A,B),1)) = k2_group_1(A) ) => B = k10_uproots(A,k8_uproots(A,B)) ) ) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & v1_algseq_1(D,A) & v1_uproots(D,A) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) ) => ( ( k3_algseq_1(A,D) = C & r1_xreal_0(1,C) & k2_normsp_1(A,D,k5_binarith(k3_algseq_1(A,D),1)) = k2_group_1(A) ) => D = k10_uproots(A,k8_uproots(A,D)) ) ) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,u1_struct_0(A)) & v1_algseq_1(E,A) & v1_uproots(E,A) & m2_relset_1(E,k5_numbers,u1_struct_0(A)) ) => ( ( k3_algseq_1(A,E) = k1_nat_1(C,1) & r1_xreal_0(1,k1_nat_1(C,1)) & k2_normsp_1(A,E,k5_binarith(k3_algseq_1(A,E),1)) = k2_group_1(A) ) => E = k10_uproots(A,k8_uproots(A,E)) ) ) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(1,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k5_numbers,u1_struct_0(A)) & v1_algseq_1(F,A) & v1_uproots(F,A) & m2_relset_1(F,k5_numbers,u1_struct_0(A)) ) => ( ( k3_algseq_1(A,F) = C & r1_xreal_0(1,C) & k2_normsp_1(A,F,k5_binarith(k3_algseq_1(A,F),1)) = k2_group_1(A) ) => F = k10_uproots(A,k8_uproots(A,F)) ) ) ) ) ) ) ), file(uproots,s1_int_2__e6_90__uproots), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(symmetry_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_polynom4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( k10_group_1(A,k2_normsp_1(A,B,k5_binarith(k3_algseq_1(A,B),1)),k2_normsp_1(A,C,k5_binarith(k3_algseq_1(A,C),1))) != k1_rlvect_1(A) => k3_algseq_1(A,k14_polynom3(A,B,C)) = k6_xcmplx_0(k1_nat_1(k3_algseq_1(A,B),k3_algseq_1(A,C)),1) ) ) ) ) ), file(polynom4,t13_polynom4), []). fof(t14_uproots,axiom,( ! [A,B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ( k3_uproots(A,B) = 0 => r6_pboole(A,B,k16_polynom1(A)) ) ) ), file(uproots,t14_uproots), []). fof(t19_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v1_uproots(B,A) <=> ~ r1_xreal_0(k3_algseq_1(A,B),0) ) ) ) ), file(uproots,t19_uproots), []). 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_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(t20_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ~ ( ~ r1_xreal_0(k3_algseq_1(A,B),0) & k2_normsp_1(A,B,k5_binarith(k3_algseq_1(A,B),1)) = k1_rlvect_1(A) ) ) ) ), file(uproots,t20_uproots), []). 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(t36_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( v1_uproots(k14_polynom3(A,B,C),A) => ( v1_uproots(B,A) & v1_uproots(C,A) ) ) ) ) ) ), file(uproots,t36_uproots), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(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(t41_polynom5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k1_rlvect_1(A) => k3_algseq_1(A,k4_polynom5(A,B,C)) = 2 ) ) ) ) ), file(polynom5,t41_polynom5), []). fof(t43_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & v1_algseq_1(D,A) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) ) => ( ( C = k14_polynom3(A,k4_polynom5(A,B,k2_group_1(A)),D) & k2_normsp_1(A,C,k5_binarith(k3_algseq_1(A,C),1)) = k2_group_1(A) ) => k2_normsp_1(A,D,k5_binarith(k3_algseq_1(A,D),1)) = k2_group_1(A) ) ) ) ) ) ), file(uproots,t43_uproots), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => k5_binarith(A,A) = 0 ) ), file(binarith,t51_binarith), []). fof(t52_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( r1_polynom5(A,C,B) => C = k15_polynom3(A,k4_polynom5(A,k5_rlvect_1(A,B),k2_group_1(A)),k6_uproots(A,B,C)) ) ) ) ) ), file(uproots,t52_uproots), []). fof(t56_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r6_pboole(u1_struct_0(A),k8_uproots(A,k4_polynom5(A,k5_rlvect_1(A,B),k2_group_1(A))),k2_uproots(u1_struct_0(A),k7_rlvect_2(A,B),1)) ) ) ), file(uproots,t56_uproots), []). fof(t58_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & v1_algseq_1(C,A) & v1_uproots(C,A) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => r6_pboole(u1_struct_0(A),k8_uproots(A,k15_polynom3(A,B,C)),k9_polynom1(u1_struct_0(A),k8_uproots(A,B),k8_uproots(A,C))) ) ) ) ), file(uproots,t58_uproots), []). fof(t59_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & v1_uproots(B,A) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( k3_algseq_1(A,B) = 1 => k4_uproots(u1_struct_0(A),k8_uproots(A,B)) = 0 ) ) ) ), file(uproots,t59_uproots), []). 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(t62_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) ) => k10_uproots(A,k16_polynom1(u1_struct_0(A))) = k5_algseq_1(A,k2_group_1(A)) ) ), file(uproots,t62_uproots), []). fof(t63_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_uproots(A,k2_uproots(u1_struct_0(A),k7_rlvect_2(A,B),1)) = k4_polynom5(A,k5_rlvect_1(A,B),k2_group_1(A)) ) ) ), file(uproots,t63_uproots), []). fof(t66_uproots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( ( v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,u1_struct_0(A)) ) => k10_uproots(A,k9_polynom1(u1_struct_0(A),B,C)) = k15_polynom3(A,k10_uproots(A,B),k10_uproots(A,C)) ) ) ) ), file(uproots,t66_uproots), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_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), []).