% Mizar problem: t15_polynom6,polynom6,1732,62 fof(t15_polynom6,conjecture,( ! [A] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v4_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => r2_quofield(k30_polynom1(A,k30_polynom1(B,C)),k30_polynom1(k14_ordinal2(A,B),C)) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_gobrd13,cc1_polynom1,cc1_relset_1,cc1_vectsp_1,cc1_xreal_0,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_gobrd13,cc2_quofield,cc2_vectsp_1,cc2_xreal_0,cc3_arytm_3,cc3_polynom1,cc3_quofield,cc3_vectsp_1,cc3_xreal_0,cc4_polynom1,cc4_quofield,cc4_vectsp_1,cc4_xreal_0,cc5_polynom1,cc5_quofield,cc5_xreal_0,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k23_polynom1,commutativity_k2_xcmplx_0,commutativity_k4_rlvect_1,commutativity_k9_polynom1,connectedness_r1_xreal_0,d10_polynom1,d10_xboole_0,d11_finseq_1,d12_funct_1,d12_rlvect_1,d13_grcat_1,d14_polynom1,d1_funct_2,d21_polynom1,d21_quofield,d22_quofield,d23_quofield,d24_quofield,d26_polynom1,d26_quofield,d27_polynom1,d2_card_3,d2_finseq_1,d2_polynom6,d3_finseq_1,d3_tarski,d4_finseq_1,d4_finseq_4,d5_funct_1,d6_funcop_1,d7_group_6,d8_endalg,d8_funct_1,d8_matrlin,d9_polynom1,d9_vectsp_1,dt_g3_vectsp_1,dt_k10_finseq_1,dt_k12_polynom1,dt_k13_finseq_1,dt_k13_polynom1,dt_k14_ordinal2,dt_k14_polynom1,dt_k15_dtconstr,dt_k15_polynom1,dt_k15_rvsum_1,dt_k16_finseq_1,dt_k16_polynom1,dt_k1_card_1,dt_k1_card_3,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_group_1,dt_k1_matrlin,dt_k1_nat_1,dt_k1_numbers,dt_k1_polynom6,dt_k1_relat_1,dt_k1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_polynom1,dt_k22_polynom1,dt_k23_polynom1,dt_k26_polynom1,dt_k27_polynom1,dt_k28_polynom1,dt_k2_finseq_1,dt_k2_funct_2,dt_k2_group_1,dt_k2_polynom3,dt_k2_polynom6,dt_k2_relat_1,dt_k2_rlvect_1,dt_k2_vectsp_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k30_polynom1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_polynom1,dt_k3_wsierp_1,dt_k4_card_1,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_finseq_4,dt_k4_relset_1,dt_k4_rlvect_1,dt_k5_binarith,dt_k5_finsop_1,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_polynom1,dt_k8_funct_2,dt_k8_matrlin,dt_k9_polynom1,dt_k9_relat_1,dt_k9_rlvect_1,dt_k9_wsierp_1,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_polynom1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_4,dt_m2_finseq_1,dt_m2_finseq_2,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_finseq_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_polynom1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_4,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_finseq_1,fc11_xreal_0,fc12_xreal_0,fc13_finset_1,fc13_polynom1,fc14_finset_1,fc14_polynom1,fc15_finseq_1,fc16_finseq_1,fc17_finseq_1,fc17_polynom1,fc18_polynom1,fc1_finseq_1,fc1_finseq_2,fc1_ordinal2,fc1_polynom1,fc1_polynom6,fc1_struct_0,fc20_polynom1,fc23_polynom1,fc25_polynom1,fc2_finseq_1,fc2_polynom2,fc2_polynom6,fc30_polynom1,fc31_polynom1,fc32_polynom1,fc35_polynom1,fc36_polynom1,fc37_polynom1,fc38_polynom1,fc39_polynom1,fc3_arytm_3,fc3_polynom1,fc3_polynom2,fc3_polynom6,fc3_xreal_0,fc40_polynom1,fc41_polynom1,fc43_polynom1,fc44_polynom1,fc5_finseq_1,fc5_polynom1,fc6_polynom1,fc7_finseq_1,fc7_funcop_1,fc7_xreal_0,fc8_xreal_0,fc9_finseq_1,fc9_polynom1,fc9_xreal_0,free_g3_vectsp_1,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc14_polynom1,rc1_arytm_3,rc1_finseq_1,rc1_finseq_2,rc1_finset_1,rc1_funcop_1,rc1_funct_1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_polynom1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_polynom1,rc3_struct_0,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_polynom1,rc4_struct_0,rc4_xreal_0,rc5_struct_0,rc6_finseq_1,rc6_vectsp_1,rc7_finseq_1,rc7_polynom1,rc7_vectsp_1,rc8_finseq_1,rc8_polynom1,rc9_polynom1,redefinition_k14_polynom1,redefinition_k15_polynom1,redefinition_k1_matrlin,redefinition_k1_nat_1,redefinition_k23_polynom1,redefinition_k2_finseq_1,redefinition_k2_funct_2,redefinition_k2_polynom3,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_polynom1,redefinition_k3_wsierp_1,redefinition_k4_card_1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k4_rlvect_1,redefinition_k5_finsop_1,redefinition_k5_numbers,redefinition_k5_polynom1,redefinition_k8_funct_2,redefinition_k9_wsierp_1,redefinition_m1_polynom1,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r6_pboole,s1_polynom2__e10_21_3_1_1__polynom6,s1_polynom2__e51_21_3_1_1__polynom6,s1_polynom2__e7_21_3_1_1_9__polynom6,s1_polynom2__e8_21_3_1_1_1__polynom6,s3_funct_1__e22_21_3_1_1__polynom6,s3_funct_2__e2_21__polynom6,s3_funct_2__e39_21_3_1_1__polynom6,s3_funct_2__e3_21_7_1__polynom6,s3_funct_2__e4_21_7__polynom6,s3_funct_2__e7_21_7_1__polynom6,s3_funct_2__e8_21_7__polynom6,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r2_quofield,symmetry_r6_pboole,t10_finseq_2,t10_subset_1,t113_funct_2,t12_funct_1,t12_relset_1,t13_finset_1,t14_polynom6,t16_polynom3,t17_finseq_1,t18_nat_1,t19_polynom2,t1_numerals,t1_real,t1_subset,t22_polynom3,t24_finseq_4,t27_finseq_3,t29_nat_1,t2_group_7,t2_real,t2_subset,t31_finseq_3,t31_polynom1,t32_polynom1,t34_polynom1,t38_nat_1,t3_real,t3_subset,t4_real,t4_subset,t5_polynom6,t5_real,t5_subset,t6_boole,t6_polynom6,t6_real,t72_polynom1,t7_boole,t7_polynom6,t7_real,t81_polynom1,t84_polynom1,t8_boole,t8_real,t90_polynom1]), [file(polynom6,t15_polynom6)]). 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_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). 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_gobrd13,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => v1_matrlin(B) ) ), file(gobrd13,cc1_gobrd13), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). 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(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). 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_quofield,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_quofield(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_grcat_1(C,A,B) & v1_endalg(C,A,B) & v1_group_6(C,A,B) ) ) ) ) ), file(quofield,cc2_quofield), []). 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_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). 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_quofield,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_grcat_1(C,A,B) & v1_endalg(C,A,B) & v1_group_6(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_quofield(C,A,B) ) ) ) ) ), file(quofield,cc3_quofield), []). 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_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_quofield,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v4_quofield(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_quofield(C,A,B) & v3_quofield(C,A,B) ) ) ) ) ), file(quofield,cc4_quofield), []). 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_quofield,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_quofield(C,A,B) & v3_quofield(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v4_quofield(C,A,B) ) ) ) ) ), file(quofield,cc5_quofield), []). 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_k23_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => k23_polynom1(A,B,C,D) = k23_polynom1(A,B,D,C) ) ), file(polynom1,k23_polynom1), []). fof(commutativity_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_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_1), []). fof(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(d10_polynom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( l2_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m2_relset_1(C,A,u1_struct_0(B)) ) => ( v2_polynom1(C,A,B) <=> v1_finset_1(k12_polynom1(A,B,C)) ) ) ) ) ), file(polynom1,d10_polynom1), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d11_finseq_1,axiom,( ! [A,B] : ( B = k13_finseq_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m2_finseq_1(C,A) ) ) ), file(finseq_1,d11_finseq_1), []). fof(d12_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k9_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & D = k1_funct_1(A,E) ) ) ) ) ), file(funct_1,d12_funct_1), []). fof(d12_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k9_rlvect_1(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) & C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) & k8_funct_2(k5_numbers,u1_struct_0(A),D,0) = k1_rlvect_1(A) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F = k1_funct_1(B,k1_nat_1(E,1)) => ( r1_xreal_0(k3_finseq_1(B),E) | k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) ) ) ) ) ) ) ) ) ) ), file(rlvect_1,d12_rlvect_1), []). fof(d13_grcat_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_grcat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ), file(grcat_1,d13_grcat_1), []). fof(d14_polynom1,axiom,( ! [A,B] : ( B = k13_polynom1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) ) ) ), file(polynom1,d14_polynom1), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d21_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) ) => ( E = k22_polynom1(A,B,C,D) <=> ! [F] : ( ( v7_seqm_3(F) & v1_polynom1(F) & m1_pboole(F,A) ) => k15_polynom1(A,B,E,F) = k2_rlvect_1(B,k15_polynom1(A,B,C,F),k15_polynom1(A,B,D,F)) ) ) ) ) ) ) ), file(polynom1,d21_polynom1), []). fof(d21_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_quofield(C,A,B) <=> ( v1_grcat_1(C,A,B) & v1_group_6(C,A,B) & v1_endalg(C,A,B) ) ) ) ) ) ), file(quofield,d21_quofield), []). fof(d22_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v2_quofield(C,A,B) <=> ( v1_quofield(C,A,B) & k2_relat_1(C) = u1_struct_0(B) ) ) ) ) ) ), file(quofield,d22_quofield), []). fof(d23_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v3_quofield(C,A,B) <=> ( v1_quofield(C,A,B) & v2_funct_1(C) ) ) ) ) ) ), file(quofield,d23_quofield), []). fof(d24_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v4_quofield(C,A,B) <=> ( v3_quofield(C,A,B) & v2_quofield(C,A,B) ) ) ) ) ) ), file(quofield,d24_quofield), []). fof(d26_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l3_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) ) => ( E = k28_polynom1(A,B,C,D) <=> ! [F] : ( ( v7_seqm_3(F) & v1_polynom1(F) & m1_pboole(F,A) ) => ? [G] : ( m2_finseq_1(G,u1_struct_0(B)) & k15_polynom1(A,B,E,F) = k9_rlvect_1(B,G) & k3_finseq_1(G) = k3_finseq_1(k21_polynom1(A,F)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( r2_hidden(H,k4_finseq_1(G)) & ! [I] : ( ( v7_seqm_3(I) & v1_polynom1(I) & m1_pboole(I,A) ) => ! [J] : ( ( v7_seqm_3(J) & v1_polynom1(J) & m1_pboole(J,A) ) => ~ ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,F),H) = k10_finseq_1(I,J) & k4_finseq_4(k5_numbers,u1_struct_0(B),G,H) = k1_group_1(B,k15_polynom1(A,B,C,I),k15_polynom1(A,B,D,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(polynom1,d26_polynom1), []). fof(d26_quofield,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ( r2_quofield(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v4_quofield(C,A,B) ) ) ) ) ), file(quofield,d26_quofield), []). fof(d27_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_vectsp_1(C) & l3_vectsp_1(C) ) => ( C = k30_polynom1(A,B) <=> ( ! [D] : ( r2_hidden(D,u1_struct_0(C)) <=> ( v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(F,k14_polynom1(A),B) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(B)) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(G,k14_polynom1(A),B) & m2_relset_1(G,k14_polynom1(A),u1_struct_0(B)) ) => ( ( D = F & E = G ) => k2_rlvect_1(C,D,E) = k22_polynom1(A,B,F,G) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(F,k14_polynom1(A),B) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(B)) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(G,k14_polynom1(A),B) & m2_relset_1(G,k14_polynom1(A),u1_struct_0(B)) ) => ( ( D = F & E = G ) => k1_group_1(C,D,E) = k28_polynom1(A,B,F,G) ) ) ) ) ) & k1_rlvect_1(C) = k26_polynom1(A,B) & k2_vectsp_1(C) = k27_polynom1(A,B) ) ) ) ) ) ), file(polynom1,d27_polynom1), []). fof(d2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) ) => ( B = k1_card_3(A) <=> ( k1_relat_1(B) = k1_relat_1(A) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ) ), file(card_3,d2_card_3), []). fof(d2_finseq_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_finseq_1(A) <=> ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ), file(finseq_1,d2_finseq_1), []). fof(d2_polynom6,axiom,( ! [A] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v7_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(k30_polynom1(B,C))) & v2_polynom1(D,k14_polynom1(A),k30_polynom1(B,C)) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) & v2_polynom1(E,k14_polynom1(k14_ordinal2(A,B)),C) & m2_relset_1(E,k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) ) => ( E = k2_polynom6(A,B,C,D) <=> ! [F] : ( m1_polynom1(F,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ? [G] : ( m1_polynom1(G,A,k14_polynom1(A)) & ? [H] : ( m1_polynom1(H,B,k14_polynom1(B)) & ? [I] : ( v1_funct_1(I) & v1_funct_2(I,k14_polynom1(B),u1_struct_0(C)) & v2_polynom1(I,k14_polynom1(B),C) & m2_relset_1(I,k14_polynom1(B),u1_struct_0(C)) & I = k15_polynom1(A,k30_polynom1(B,C),D,G) & r6_pboole(k14_ordinal2(A,B),F,k1_polynom6(A,B,G,H)) & k15_polynom1(k14_ordinal2(A,B),C,E,F) = k15_polynom1(B,C,I,H) ) ) ) ) ) ) ) ) ) ) ), file(polynom6,d2_polynom6), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_1), []). fof(d4_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d6_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_funcop_1(A) <=> ! [B] : ( r2_hidden(B,k1_relat_1(A)) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) ), file(funcop_1,d6_funcop_1), []). fof(d7_group_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_group_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_group_6(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_group_1(A,D,E)) = k1_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ), file(group_6,d7_group_6), []). fof(d8_endalg,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_vectsp_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_vectsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_endalg(C,A,B) <=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_group_1(A)) = k2_group_1(B) ) ) ) ) ), file(endalg,d8_endalg), []). fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), []). fof(d8_matrlin,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( C = k8_matrlin(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(k5_numbers,u1_struct_0(A),C,D) = k9_rlvect_1(A,k1_matrlin(u1_struct_0(A),k5_numbers,k3_finseq_2(u1_struct_0(A)),B,D)) ) ) ) ) ) ) ) ), file(matrlin,d8_matrlin), []). fof(d9_polynom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( l2_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m2_relset_1(C,A,u1_struct_0(B)) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( D = k12_polynom1(A,B,C) <=> ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) <=> k8_funct_2(A,u1_struct_0(B),C,E) != k1_rlvect_1(B) ) ) ) ) ) ) ) ), file(polynom1,d9_polynom1), []). fof(d9_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => k2_vectsp_1(A) = u1_vectsp_1(A) ) ), file(vectsp_1,d9_vectsp_1), []). fof(dt_g3_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ), file(vectsp_1,g3_vectsp_1), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k12_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_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_polynom1,axiom,( $true ), file(polynom1,k13_polynom1), []). fof(dt_k14_ordinal2,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k14_ordinal2(A,B)) ) ), file(ordinal2,k14_ordinal2), []). fof(dt_k14_polynom1,axiom,( ! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ), file(polynom1,k14_polynom1), []). fof(dt_k15_dtconstr,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => m2_finseq_2(k15_dtconstr(A,B),A,k3_finseq_2(A)) ) ), file(dtconstr,k15_dtconstr), []). fof(dt_k15_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => m1_subset_1(k15_polynom1(A,B,C,D),u1_struct_0(B)) ) ), file(polynom1,k15_polynom1), []). fof(dt_k15_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m1_subset_1(k15_rvsum_1(A),k1_numbers) ) ), file(rvsum_1,k15_rvsum_1), []). fof(dt_k16_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & v4_ordinal2(C) ) => m2_finseq_1(k16_finseq_1(A,B,C),A) ) ), file(finseq_1,k16_finseq_1), []). fof(dt_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_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) ) ) ), file(card_3,k1_card_3), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k1_group_1), []). fof(dt_k1_matrlin,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => m2_finseq_2(k1_matrlin(A,B,C,D,E),A,C) ) ), file(matrlin,k1_matrlin), []). 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_polynom6,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & m1_subset_1(C,k14_polynom1(A)) & m1_subset_1(D,k14_polynom1(B)) ) => m1_polynom1(k1_polynom6(A,B,C,D),k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) ) ), file(polynom6,k1_polynom6), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_rlvect_1,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ), file(rlvect_1,k1_rlvect_1), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k21_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => m2_finseq_1(k21_polynom1(A,B),k4_finseq_2(2,k14_polynom1(A))) ) ), file(polynom1,k21_polynom1), []). fof(dt_k22_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_funct_1(k22_polynom1(A,B,C,D)) & v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k22_polynom1), []). fof(dt_k23_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_funct_1(k23_polynom1(A,B,C,D)) & v1_funct_2(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k23_polynom1), []). fof(dt_k26_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => ( v1_funct_1(k26_polynom1(A,B)) & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k26_polynom1), []). fof(dt_k27_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_group_1(B) & l2_vectsp_1(B) ) => ( v1_funct_1(k27_polynom1(A,B)) & v1_funct_2(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k27_polynom1), []). fof(dt_k28_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l3_vectsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_funct_1(k28_polynom1(A,B,C,D)) & v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & m2_relset_1(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ), file(polynom1,k28_polynom1), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ), file(funct_2,k2_funct_2), []). 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_polynom3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_2(k2_polynom3(A,B,C),A,k4_finseq_2(2,A)) ) ), file(polynom3,k2_polynom3), []). fof(dt_k2_polynom6,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & ~ v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & v2_polynom1(D,k14_polynom1(A),k30_polynom1(B,C)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) ) => ( v1_funct_1(k2_polynom6(A,B,C,D)) & v1_funct_2(k2_polynom6(A,B,C,D),k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) & v2_polynom1(k2_polynom6(A,B,C,D),k14_polynom1(k14_ordinal2(A,B)),C) & m2_relset_1(k2_polynom6(A,B,C,D),k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) ) ) ), file(polynom6,k2_polynom6), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), []). fof(dt_k2_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)) ) ), file(vectsp_1,k2_vectsp_1), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k30_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) & l3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,k30_polynom1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => m2_finseq_2(k3_polynom1(A,B,C,D,E),A,C) ) ), file(polynom1,k3_polynom1), []). fof(dt_k3_wsierp_1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k3_wsierp_1(A,B),k1_numbers,k5_numbers) ) ), file(wsierp_1,k3_wsierp_1), []). fof(dt_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), []). fof(dt_k5_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_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k5_finsop_1(A),k5_finsub_1(k5_numbers)) ) ), file(finsop_1,k5_finsop_1), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_polynom1,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => ( v1_card_3(k5_polynom1(A,B)) & m1_trees_4(k5_polynom1(A,B),k1_numbers,k5_numbers) ) ) ), file(polynom1,k5_polynom1), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_matrlin,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => m2_finseq_1(k8_matrlin(A,B),u1_struct_0(A)) ) ), file(matrlin,k8_matrlin), []). 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_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_k9_rlvect_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) ) => m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)) ) ), file(rlvect_1,k9_rlvect_1), []). fof(dt_k9_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => m2_subset_1(k9_wsierp_1(A),k1_numbers,k5_numbers) ) ), file(wsierp_1,k9_wsierp_1), []). fof(dt_l1_group_1,axiom,( ! [A] : ( l1_group_1(A) => l1_struct_0(A) ) ), file(group_1,l1_group_1), []). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => l1_group_1(A) ) ), file(vectsp_1,l1_vectsp_1), []). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), []). fof(dt_l2_vectsp_1,axiom,( ! [A] : ( l2_vectsp_1(A) => ( l1_vectsp_1(A) & l2_struct_0(A) ) ) ), file(vectsp_1,l2_vectsp_1), []). fof(dt_l3_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( l1_rlvect_1(A) & l2_vectsp_1(A) ) ) ), file(vectsp_1,l3_vectsp_1), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ! [C] : ( m1_polynom1(C,A,B) => ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) ) ) ), file(polynom1,m1_polynom1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) => m2_finseq_1(C,A) ) ) ), file(trees_4,m1_trees_4), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_group_1,axiom,( ! [A] : ( l1_group_1(A) => ( v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(group_1,u1_group_1), []). fof(dt_u1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( v1_funct_1(u1_rlvect_1(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u1_rlvect_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u1_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)) ) ), file(vectsp_1,u1_vectsp_1), []). fof(dt_u2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ), file(struct_0,u2_struct_0), []). fof(existence_l1_group_1,axiom,( ? [A] : l1_group_1(A) ), file(group_1,l1_group_1), []). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_vectsp_1,axiom,( ? [A] : l1_vectsp_1(A) ), file(vectsp_1,l1_vectsp_1), []). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), []). fof(existence_l2_vectsp_1,axiom,( ? [A] : l2_vectsp_1(A) ), file(vectsp_1,l2_vectsp_1), []). fof(existence_l3_vectsp_1,axiom,( ? [A] : l3_vectsp_1(A) ), file(vectsp_1,l3_vectsp_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_polynom1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) ) => ? [C] : m1_polynom1(C,A,B) ) ), file(polynom1,m1_polynom1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m1_trees_4(C,A,B) ) ), file(trees_4,m1_trees_4), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_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_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_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(fc13_finset_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => v1_finset_1(k9_relat_1(A,B)) ) ), file(finset_1,fc13_finset_1), []). fof(fc13_polynom1,axiom,( ! [A,B] : ( ( v1_xboole_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => ( v1_relat_1(k15_dtconstr(A,B)) & v1_funct_1(k15_dtconstr(A,B)) & v2_funct_1(k15_dtconstr(A,B)) & v1_xboole_0(k15_dtconstr(A,B)) & v1_finset_1(k15_dtconstr(A,B)) & v1_finseq_1(k15_dtconstr(A,B)) & v1_membered(k15_dtconstr(A,B)) & v2_membered(k15_dtconstr(A,B)) & v3_membered(k15_dtconstr(A,B)) & v4_membered(k15_dtconstr(A,B)) & v5_membered(k15_dtconstr(A,B)) ) ) ), file(polynom1,fc13_polynom1), []). 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_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_xboole_0(k16_finseq_1(A,B,0)) & v1_relat_1(k16_finseq_1(A,B,0)) & v1_funct_1(k16_finseq_1(A,B,0)) & v2_funct_1(k16_finseq_1(A,B,0)) & v1_finset_1(k16_finseq_1(A,B,0)) & v1_finseq_1(k16_finseq_1(A,B,0)) ) ) ), file(finseq_1,fc15_finseq_1), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc17_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(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(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_finseq_2,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ), file(finseq_2,fc1_finseq_2), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( ~ v3_struct_0(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ), file(polynom1,fc1_polynom1), []). fof(fc1_polynom6,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( v3_ordinal1(k14_ordinal2(A,B)) & ~ v1_xboole_0(k14_ordinal2(A,B)) ) ) ), file(polynom6,fc1_polynom6), []). 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(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(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_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_polynom6,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( v3_ordinal1(k14_ordinal2(B,A)) & ~ v1_xboole_0(k14_ordinal2(B,A)) ) ) ), file(polynom6,fc2_polynom6), []). fof(fc30_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v7_seqm_3(B) & v1_polynom1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k21_polynom1(A,B)) & v1_funct_1(k21_polynom1(A,B)) & v2_funct_1(k21_polynom1(A,B)) & ~ v1_xboole_0(k21_polynom1(A,B)) & v1_finset_1(k21_polynom1(A,B)) & v1_finseq_1(k21_polynom1(A,B)) & v1_funcop_1(k21_polynom1(A,B)) & v1_matrlin(k21_polynom1(A,B)) & v1_polynom1(k21_polynom1(A,B)) ) ) ), file(polynom1,fc30_polynom1), []). fof(fc31_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & m1_subset_1(B,k14_polynom1(A)) ) => ( v1_relat_1(k21_polynom1(A,B)) & v1_funct_1(k21_polynom1(A,B)) & v2_funct_1(k21_polynom1(A,B)) & ~ v1_xboole_0(k21_polynom1(A,B)) & v1_finset_1(k21_polynom1(A,B)) & v1_finseq_1(k21_polynom1(A,B)) & v1_funcop_1(k21_polynom1(A,B)) & v1_matrlin(k21_polynom1(A,B)) & v1_polynom1(k21_polynom1(A,B)) ) ) ), file(polynom1,fc31_polynom1), []). fof(fc32_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_relat_1(k22_polynom1(A,B,C,D)) & v1_funct_1(k22_polynom1(A,B,C,D)) & v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k22_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ), file(polynom1,fc32_polynom1), []). fof(fc35_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & l2_struct_0(B) ) => ( v1_relat_1(k26_polynom1(A,B)) & v1_funct_1(k26_polynom1(A,B)) & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B) ) ) ), file(polynom1,fc35_polynom1), []). fof(fc36_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( v1_relat_1(k27_polynom1(A,B)) & v1_funct_1(k27_polynom1(A,B)) & v1_funct_2(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k27_polynom1(A,B),k14_polynom1(A),B) ) ) ), file(polynom1,fc36_polynom1), []). fof(fc37_polynom1,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & l3_vectsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(C,k14_polynom1(A),B) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => ( v1_relat_1(k28_polynom1(A,B,C,D)) & v1_funct_1(k28_polynom1(A,B,C,D)) & v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(k28_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ), file(polynom1,fc37_polynom1), []). fof(fc38_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v3_rlvect_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc38_polynom1), []). fof(fc39_polynom1,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => ( ~ v3_struct_0(k30_polynom1(A,B)) & v4_rlvect_1(k30_polynom1(A,B)) & v3_vectsp_1(k30_polynom1(A,B)) ) ) ), file(polynom1,fc39_polynom1), []). fof(fc3_arytm_3,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) ) => ( v1_ordinal1(k14_ordinal2(A,B)) & v2_ordinal1(k14_ordinal2(A,B)) & v3_ordinal1(k14_ordinal2(A,B)) & v4_ordinal2(k14_ordinal2(A,B)) ) ) ), file(arytm_3,fc3_arytm_3), []). 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_polynom6,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)) & v5_vectsp_1(k30_polynom1(A,B)) & v6_vectsp_1(k30_polynom1(A,B)) & v7_vectsp_1(k30_polynom1(A,B)) & v8_vectsp_1(k30_polynom1(A,B)) & ~ v3_realset2(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(polynom6,fc3_polynom6), []). 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(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(fc5_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc5_finseq_1), []). fof(fc5_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(fc6_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v1_finset_1(k1_card_3(A)) & v1_finseq_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) ) ) ), file(polynom1,fc6_polynom1), []). fof(fc7_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc7_finseq_1), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(k1_card_3(A)) & v1_funct_1(k1_card_3(A)) & v2_funct_1(k1_card_3(A)) & v1_xboole_0(k1_card_3(A)) & v1_finset_1(k1_card_3(A)) & v1_membered(k1_card_3(A)) & v2_membered(k1_card_3(A)) & v3_membered(k1_card_3(A)) & v4_membered(k1_card_3(A)) & v5_membered(k1_card_3(A)) & v1_card_3(k1_card_3(A)) ) ) ), file(polynom1,fc9_polynom1), []). 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_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finseq_2,axiom,( ! [A] : ? [B] : ( m1_finseq_2(B,A) & ~ v1_xboole_0(B) ) ), file(finseq_2,rc1_finseq_2), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_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_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_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_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_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc3_polynom1), []). fof(rc3_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_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_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_polynom1,axiom,( ? [A] : ( m1_finseq_1(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc4_polynom1), []). fof(rc4_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc6_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc6_vectsp_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v7_seqm_3(A) ) ), file(polynom1,rc7_polynom1), []). fof(rc7_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc7_vectsp_1), []). fof(rc8_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(rc9_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc9_polynom1), []). fof(redefinition_k14_polynom1,axiom,( ! [A] : k14_polynom1(A) = k13_polynom1(A) ), file(polynom1,k14_polynom1), []). fof(redefinition_k15_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => k15_polynom1(A,B,C,D) = k1_funct_1(C,D) ) ), file(polynom1,k15_polynom1), []). fof(redefinition_k1_matrlin,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => k1_matrlin(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) ), file(matrlin,k1_matrlin), []). 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_k23_polynom1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) ) => k23_polynom1(A,B,C,D) = k22_polynom1(A,B,C,D) ) ), file(polynom1,k23_polynom1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ), file(funct_2,k2_funct_2), []). fof(redefinition_k2_polynom3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k2_polynom3(A,B,C) = k10_finseq_1(B,C) ) ), file(polynom3,k2_polynom3), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k3_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(C) & m1_finseq_2(C,A) & v1_funct_1(D) & m1_relset_1(D,B,C) ) => k3_polynom1(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) ), file(polynom1,k3_polynom1), []). fof(redefinition_k3_wsierp_1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k3_wsierp_1(A,B) = k1_funct_1(A,B) ) ), file(wsierp_1,k3_wsierp_1), []). fof(redefinition_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), []). fof(redefinition_k5_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k5_finsop_1(A) = k1_relat_1(A) ) ), file(finsop_1,k5_finsop_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_polynom1,axiom,( ! [A,B] : ( m1_finseq_1(B,k3_finseq_2(A)) => k5_polynom1(A,B) = k1_card_3(B) ) ), file(polynom1,k5_polynom1), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k9_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => k9_wsierp_1(A) = k15_rvsum_1(A) ) ), file(wsierp_1,k9_wsierp_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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) <=> m1_finseq_1(C,B) ) ) ), file(trees_4,m1_trees_4), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_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_polynom2__e10_21_3_1_1__polynom6,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v4_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & v2_polynom1(D,k14_polynom1(A),k30_polynom1(B,C)) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & v2_polynom1(E,k14_polynom1(A),k30_polynom1(B,C)) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & m1_polynom1(F,B,k14_polynom1(B)) & v7_seqm_3(G) & v1_polynom1(G) & m1_pboole(G,A) & m2_finseq_1(H,u1_struct_0(k30_polynom1(B,C))) ) => ( ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ~ ( r2_hidden(I,k2_finseq_1(k3_finseq_1(H))) & ! [J] : ( m1_subset_1(J,k3_finseq_2(u1_struct_0(C))) => ~ ? [K] : ( v7_seqm_3(K) & v1_polynom1(K) & m1_pboole(K,A) & ? [L] : ( v7_seqm_3(L) & v1_polynom1(L) & m1_pboole(L,A) & ? [M] : ( m2_finseq_1(M,u1_struct_0(C)) & ? [N] : ( v1_funct_1(N) & v1_funct_2(N,k14_polynom1(B),u1_struct_0(C)) & v2_polynom1(N,k14_polynom1(B),C) & m2_relset_1(N,k14_polynom1(B),u1_struct_0(C)) & ? [O] : ( v1_funct_1(O) & v1_funct_2(O,k14_polynom1(B),u1_struct_0(C)) & v2_polynom1(O,k14_polynom1(B),C) & m2_relset_1(O,k14_polynom1(B),u1_struct_0(C)) & N = k15_polynom1(A,k30_polynom1(B,C),D,K) & O = k15_polynom1(A,k30_polynom1(B,C),E,L) & M = J & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,G),I) = k10_finseq_1(K,L) & k3_finseq_1(M) = k3_finseq_1(k21_polynom1(B,F)) & ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ~ ( r2_hidden(P,k4_finseq_1(M)) & ! [Q] : ( ( v7_seqm_3(Q) & v1_polynom1(Q) & m1_pboole(Q,B) ) => ! [R] : ( ( v7_seqm_3(R) & v1_polynom1(R) & m1_pboole(R,B) ) => ~ ( k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,F),P) = k10_finseq_1(Q,R) & k4_finseq_4(k5_numbers,u1_struct_0(C),M,P) = k1_group_1(C,k15_polynom1(B,C,N,Q),k15_polynom1(B,C,O,R)) ) ) ) ) ) ) ) ) ) ) ) ) ) => ? [I] : ( m2_finseq_1(I,k3_finseq_2(u1_struct_0(C))) & k4_finseq_1(I) = k2_finseq_1(k3_finseq_1(H)) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( r2_hidden(J,k2_finseq_1(k3_finseq_1(H))) => ? [S] : ( v7_seqm_3(S) & v1_polynom1(S) & m1_pboole(S,A) & ? [T] : ( v7_seqm_3(T) & v1_polynom1(T) & m1_pboole(T,A) & ? [U] : ( m2_finseq_1(U,u1_struct_0(C)) & ? [V] : ( v1_funct_1(V) & v1_funct_2(V,k14_polynom1(B),u1_struct_0(C)) & v2_polynom1(V,k14_polynom1(B),C) & m2_relset_1(V,k14_polynom1(B),u1_struct_0(C)) & ? [W] : ( v1_funct_1(W) & v1_funct_2(W,k14_polynom1(B),u1_struct_0(C)) & v2_polynom1(W,k14_polynom1(B),C) & m2_relset_1(W,k14_polynom1(B),u1_struct_0(C)) & V = k15_polynom1(A,k30_polynom1(B,C),D,S) & W = k15_polynom1(A,k30_polynom1(B,C),E,T) & U = k4_finseq_4(k5_numbers,k3_finseq_2(u1_struct_0(C)),I,J) & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,G),J) = k10_finseq_1(S,T) & k3_finseq_1(U) = k3_finseq_1(k21_polynom1(B,F)) & ! [X] : ( m2_subset_1(X,k1_numbers,k5_numbers) => ~ ( r2_hidden(X,k4_finseq_1(U)) & ! [Y] : ( ( v7_seqm_3(Y) & v1_polynom1(Y) & m1_pboole(Y,B) ) => ! [Z] : ( ( v7_seqm_3(Z) & v1_polynom1(Z) & m1_pboole(Z,B) ) => ~ ( k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,F),X) = k10_finseq_1(Y,Z) & k4_finseq_4(k5_numbers,u1_struct_0(C),U,X) = k1_group_1(C,k15_polynom1(B,C,V,Y),k15_polynom1(B,C,W,Z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(polynom6,s1_polynom2__e10_21_3_1_1__polynom6), []). fof(s1_polynom2__e51_21_3_1_1__polynom6,axiom,( ! [A,B,C,D,E,F] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v4_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & m1_polynom1(D,B,k14_polynom1(B)) & v7_seqm_3(E) & v1_polynom1(E) & m1_pboole(E,A) & m2_finseq_1(F,u1_struct_0(k30_polynom1(B,C))) ) => ( ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r2_hidden(G,k2_finseq_1(k3_finseq_1(F))) & ! [H] : ( m1_subset_1(H,k3_finseq_2(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))))) => ~ ? [I] : ( m1_polynom1(I,A,k14_polynom1(A)) & ? [J] : ( m1_polynom1(J,A,k14_polynom1(A)) & ? [K] : ( m2_finseq_1(K,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))) & K = H & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,E),G) = k2_polynom3(k14_polynom1(A),I,J) & k3_finseq_1(K) = k3_finseq_1(k21_polynom1(B,D)) & ! [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) => ~ ( r2_hidden(L,k4_finseq_1(K)) & ! [M] : ( m1_polynom1(M,B,k14_polynom1(B)) => ! [N] : ( m1_polynom1(N,B,k14_polynom1(B)) => ~ ( k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,D),L) = k2_polynom3(k14_polynom1(B),M,N) & k1_matrlin(k14_polynom1(k14_ordinal2(A,B)),k5_numbers,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))),K,L) = k2_polynom3(k14_polynom1(k14_ordinal2(A,B)),k1_polynom6(A,B,I,M),k1_polynom6(A,B,J,N)) ) ) ) ) ) ) ) ) ) ) ) => ? [G] : ( m2_finseq_1(G,k3_finseq_2(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))))) & k4_finseq_1(G) = k2_finseq_1(k3_finseq_1(F)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k2_finseq_1(k3_finseq_1(F))) => ? [O] : ( m1_polynom1(O,A,k14_polynom1(A)) & ? [P] : ( m1_polynom1(P,A,k14_polynom1(A)) & ? [Q] : ( m2_finseq_1(Q,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))) & Q = k4_finseq_4(k5_numbers,k3_finseq_2(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))),G,H) & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,E),H) = k2_polynom3(k14_polynom1(A),O,P) & k3_finseq_1(Q) = k3_finseq_1(k21_polynom1(B,D)) & ! [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) => ~ ( r2_hidden(R,k4_finseq_1(Q)) & ! [S] : ( m1_polynom1(S,B,k14_polynom1(B)) => ! [T] : ( m1_polynom1(T,B,k14_polynom1(B)) => ~ ( k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,D),R) = k2_polynom3(k14_polynom1(B),S,T) & k1_matrlin(k14_polynom1(k14_ordinal2(A,B)),k5_numbers,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))),Q,R) = k2_polynom3(k14_polynom1(k14_ordinal2(A,B)),k1_polynom6(A,B,O,S),k1_polynom6(A,B,P,T)) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(polynom6,s1_polynom2__e51_21_3_1_1__polynom6), []). fof(s1_polynom2__e7_21_3_1_1_9__polynom6,axiom,( ! [A,B,C,D,E] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & m1_polynom1(C,B,k14_polynom1(B)) & m1_polynom1(D,A,k14_polynom1(A)) & m1_polynom1(E,A,k14_polynom1(A)) ) => ( ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k2_finseq_1(k3_finseq_1(k21_polynom1(B,C)))) & ! [G] : ( m1_subset_1(G,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))) => ~ ? [H] : ( m1_polynom1(H,B,k14_polynom1(B)) & ? [I] : ( m1_polynom1(I,B,k14_polynom1(B)) & k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,C),F) = k2_polynom3(k14_polynom1(B),H,I) & G = k2_polynom3(k14_polynom1(k14_ordinal2(A,B)),k1_polynom6(A,B,D,H),k1_polynom6(A,B,E,I)) ) ) ) ) ) => ? [F] : ( m2_finseq_1(F,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))) & k4_finseq_1(F) = k2_finseq_1(k3_finseq_1(k21_polynom1(B,C))) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r2_hidden(G,k2_finseq_1(k3_finseq_1(k21_polynom1(B,C)))) => ? [J] : ( m1_polynom1(J,B,k14_polynom1(B)) & ? [K] : ( m1_polynom1(K,B,k14_polynom1(B)) & k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,C),G) = k2_polynom3(k14_polynom1(B),J,K) & k4_finseq_4(k5_numbers,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))),F,G) = k2_polynom3(k14_polynom1(k14_ordinal2(A,B)),k1_polynom6(A,B,D,J),k1_polynom6(A,B,E,K)) ) ) ) ) ) ) ) ), file(polynom6,s1_polynom2__e7_21_3_1_1_9__polynom6), []). fof(s1_polynom2__e8_21_3_1_1_1__polynom6,axiom,( ! [A,B,C,D,E] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(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) & m1_polynom1(C,A,k14_polynom1(A)) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(D,k14_polynom1(A),B) & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(E,k14_polynom1(A),B) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) ) => ( ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k2_finseq_1(k3_finseq_1(k21_polynom1(A,C)))) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ? [H] : ( v7_seqm_3(H) & v1_polynom1(H) & m1_pboole(H,A) & ? [I] : ( v7_seqm_3(I) & v1_polynom1(I) & m1_pboole(I,A) & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,C),F) = k10_finseq_1(H,I) & G = k1_group_1(B,k15_polynom1(A,B,D,H),k15_polynom1(A,B,E,I)) ) ) ) ) ) => ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & k4_finseq_1(F) = k2_finseq_1(k3_finseq_1(k21_polynom1(A,C))) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r2_hidden(G,k2_finseq_1(k3_finseq_1(k21_polynom1(A,C)))) => ? [J] : ( v7_seqm_3(J) & v1_polynom1(J) & m1_pboole(J,A) & ? [K] : ( v7_seqm_3(K) & v1_polynom1(K) & m1_pboole(K,A) & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,C),G) = k10_finseq_1(J,K) & k4_finseq_4(k5_numbers,u1_struct_0(B),F,G) = k1_group_1(B,k15_polynom1(A,B,D,J),k15_polynom1(A,B,E,K)) ) ) ) ) ) ) ) ), file(polynom6,s1_polynom2__e8_21_3_1_1_1__polynom6), []). fof(s3_funct_1__e22_21_3_1_1__polynom6,axiom,( ! [A,B,C,D,E] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(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) & m1_polynom1(C,A,k14_polynom1(A)) & m2_finseq_1(D,u1_struct_0(k30_polynom1(A,B))) & v1_relat_1(E) & v1_funct_1(E) & v1_funcop_1(E) ) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & k1_relat_1(F) = k4_finseq_1(D) & ! [G] : ( r2_hidden(G,k4_finseq_1(D)) => k1_funct_1(F,G) = k1_funct_1(k1_funct_1(E,G),C) ) ) ) ), file(polynom6,s3_funct_1__e22_21_3_1_1__polynom6), []). fof(s3_funct_2__e2_21__polynom6,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v4_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(k30_polynom1(A,k30_polynom1(B,C)))) => ? [E] : ( m1_subset_1(E,u1_struct_0(k30_polynom1(k14_ordinal2(A,B),C))) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & v2_polynom1(F,k14_polynom1(A),k30_polynom1(B,C)) & m2_relset_1(F,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) ) => ( D = F => E = k2_polynom6(A,B,C,F) ) ) ) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k30_polynom1(A,k30_polynom1(B,C))),u1_struct_0(k30_polynom1(k14_ordinal2(A,B),C))) & m2_relset_1(D,u1_struct_0(k30_polynom1(A,k30_polynom1(B,C))),u1_struct_0(k30_polynom1(k14_ordinal2(A,B),C))) & ! [E] : ( m1_subset_1(E,u1_struct_0(k30_polynom1(A,k30_polynom1(B,C)))) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & v2_polynom1(G,k14_polynom1(A),k30_polynom1(B,C)) & m2_relset_1(G,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) ) => ( E = G => k8_funct_2(u1_struct_0(k30_polynom1(A,k30_polynom1(B,C))),u1_struct_0(k30_polynom1(k14_ordinal2(A,B),C)),D,E) = k2_polynom6(A,B,C,G) ) ) ) ) ) ) ), file(polynom6,s3_funct_2__e2_21__polynom6), []). fof(s3_funct_2__e39_21_3_1_1__polynom6,axiom,( ! [A,B,C,D,E] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(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) & m1_polynom1(C,A,k14_polynom1(A)) & m2_finseq_1(D,u1_struct_0(k30_polynom1(A,B))) & v1_funct_1(E) & v1_funct_2(E,k5_numbers,u1_struct_0(k30_polynom1(A,B))) & m2_relset_1(E,k5_numbers,u1_struct_0(k30_polynom1(A,B))) ) => ( ! [F] : ( m1_subset_1(F,k5_numbers) => ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(H,k14_polynom1(A),B) & m2_relset_1(H,k14_polynom1(A),u1_struct_0(B)) ) => ( ( r1_xreal_0(F,k3_finseq_1(D)) & H = k8_funct_2(k5_numbers,u1_struct_0(k30_polynom1(A,B)),E,F) ) => G = k15_polynom1(A,B,H,C) ) ) ) ) => ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k5_numbers,u1_struct_0(B)) & m2_relset_1(F,k5_numbers,u1_struct_0(B)) & ! [G] : ( m1_subset_1(G,k5_numbers) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k14_polynom1(A),u1_struct_0(B)) & v2_polynom1(I,k14_polynom1(A),B) & m2_relset_1(I,k14_polynom1(A),u1_struct_0(B)) ) => ( ( r1_xreal_0(G,k3_finseq_1(D)) & I = k8_funct_2(k5_numbers,u1_struct_0(k30_polynom1(A,B)),E,G) ) => k8_funct_2(k5_numbers,u1_struct_0(B),F,G) = k15_polynom1(A,B,I,C) ) ) ) ) ) ) ), file(polynom6,s3_funct_2__e39_21_3_1_1__polynom6), []). fof(s3_funct_2__e3_21_7_1__polynom6,axiom,( ! [A,B,C,D,E] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v4_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(k14_ordinal2(A,B)),C) & m2_relset_1(D,k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) & m1_polynom1(E,A,k14_polynom1(A)) ) => ( ! [F] : ( m1_subset_1(F,k14_polynom1(B)) => ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & ! [H] : ( m1_polynom1(H,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ( r6_pboole(k14_ordinal2(A,B),H,k1_polynom6(A,B,E,F)) => G = k15_polynom1(k14_ordinal2(A,B),C,D,H) ) ) ) ) => ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k14_polynom1(B),u1_struct_0(C)) & m2_relset_1(F,k14_polynom1(B),u1_struct_0(C)) & ! [G] : ( m1_subset_1(G,k14_polynom1(B)) => ! [I] : ( m1_polynom1(I,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ( r6_pboole(k14_ordinal2(A,B),I,k1_polynom6(A,B,E,G)) => k8_funct_2(k14_polynom1(B),u1_struct_0(C),F,G) = k15_polynom1(k14_ordinal2(A,B),C,D,I) ) ) ) ) ) ) ), file(polynom6,s3_funct_2__e3_21_7_1__polynom6), []). fof(s3_funct_2__e4_21_7__polynom6,axiom,( ! [A,B,C,D] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) & ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v2_group_1(C) & v4_group_1(C) & v7_vectsp_1(C) & ~ v3_realset2(C) & l3_vectsp_1(C) & v1_funct_1(D) & v1_funct_2(D,k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) & v2_polynom1(D,k14_polynom1(k14_ordinal2(A,B)),C) & m2_relset_1(D,k14_polynom1(k14_ordinal2(A,B)),u1_struct_0(C)) ) => ( ! [E] : ( m1_subset_1(E,k14_polynom1(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(k30_polynom1(B,C))) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & G = F & ! [H] : ( m1_polynom1(H,B,k14_polynom1(B)) => ! [I] : ( m1_polynom1(I,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ( r6_pboole(k14_ordinal2(A,B),I,k1_polynom6(A,B,E,H)) => k1_funct_1(G,H) = k15_polynom1(k14_ordinal2(A,B),C,D,I) ) ) ) ) ) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & m2_relset_1(E,k14_polynom1(A),u1_struct_0(k30_polynom1(B,C))) & ! [F] : ( m1_subset_1(F,k14_polynom1(A)) => ? [J] : ( v1_relat_1(J) & v1_funct_1(J) & J = k8_funct_2(k14_polynom1(A),u1_struct_0(k30_polynom1(B,C)),E,F) & ! [K] : ( m1_polynom1(K,B,k14_polynom1(B)) => ! [L] : ( m1_polynom1(L,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ( r6_pboole(k14_ordinal2(A,B),L,k1_polynom6(A,B,F,K)) => k1_funct_1(J,K) = k15_polynom1(k14_ordinal2(A,B),C,D,L) ) ) ) ) ) ) ) ) ), file(polynom6,s3_funct_2__e4_21_7__polynom6), []). fof(s3_funct_2__e7_21_7_1__polynom6,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( ! [C] : ( m1_subset_1(C,k14_polynom1(k14_ordinal2(A,B))) => ? [D] : ( m1_subset_1(D,k14_polynom1(B)) & ? [E] : ( m1_polynom1(E,A,k14_polynom1(A)) & ? [F] : ( m1_polynom1(F,B,k14_polynom1(B)) & C = k1_polynom6(A,B,E,F) & D = F ) ) ) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(k14_ordinal2(A,B)),k14_polynom1(B)) & m2_relset_1(C,k14_polynom1(k14_ordinal2(A,B)),k14_polynom1(B)) & ! [D] : ( m1_subset_1(D,k14_polynom1(k14_ordinal2(A,B))) => ? [G] : ( m1_polynom1(G,A,k14_polynom1(A)) & ? [H] : ( m1_polynom1(H,B,k14_polynom1(B)) & D = k1_polynom6(A,B,G,H) & k8_funct_2(k14_polynom1(k14_ordinal2(A,B)),k14_polynom1(B),C,D) = H ) ) ) ) ) ) ), file(polynom6,s3_funct_2__e7_21_7_1__polynom6), []). fof(s3_funct_2__e8_21_7__polynom6,axiom,( ! [A,B] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( ! [C] : ( m1_subset_1(C,k14_polynom1(k14_ordinal2(A,B))) => ? [D] : ( m1_subset_1(D,k14_polynom1(A)) & ? [E] : ( m1_polynom1(E,A,k14_polynom1(A)) & ? [F] : ( m1_polynom1(F,B,k14_polynom1(B)) & C = k1_polynom6(A,B,E,F) & D = E ) ) ) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(k14_ordinal2(A,B)),k14_polynom1(A)) & m2_relset_1(C,k14_polynom1(k14_ordinal2(A,B)),k14_polynom1(A)) & ! [D] : ( m1_subset_1(D,k14_polynom1(k14_ordinal2(A,B))) => ? [G] : ( m1_polynom1(G,A,k14_polynom1(A)) & ? [H] : ( m1_polynom1(H,B,k14_polynom1(B)) & D = k1_polynom6(A,B,G,H) & k8_funct_2(k14_polynom1(k14_ordinal2(A,B)),k14_polynom1(A),C,D) = G ) ) ) ) ) ) ), file(polynom6,s3_funct_2__e8_21_7__polynom6), []). 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_r2_quofield,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & l3_vectsp_1(B) ) => ( r2_quofield(A,B) => r2_quofield(B,A) ) ) ), file(quofield,r2_quofield), []). 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(t10_finseq_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k3_finseq_1(B) = A & k3_finseq_1(C) = A & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k2_finseq_1(A)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) => B = C ) ) ) ) ), file(finseq_2,t10_finseq_2), []). fof(t10_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ r2_hidden(C,B) ) ) ) ), file(subset_1,t10_subset_1), []). fof(t113_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( ! [E] : ( m1_subset_1(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => C = D ) ) ) ), file(funct_2,t113_funct_2), []). fof(t12_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k1_relat_1(B)) => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ), file(funct_1,t12_funct_1), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t13_finset_1,axiom,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), []). fof(t14_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,B,k14_polynom1(B)) => ! [E] : ( m2_finseq_1(E,k3_finseq_2(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))))) => ( ( k4_finseq_1(E) = k4_finseq_1(k21_polynom1(A,C)) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k4_finseq_1(k21_polynom1(A,C))) & ! [G] : ( m1_polynom1(G,A,k14_polynom1(A)) => ! [H] : ( m1_polynom1(H,A,k14_polynom1(A)) => ! [I] : ( m2_finseq_1(I,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))) => ~ ( I = k1_matrlin(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))),k5_numbers,k3_finseq_2(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B)))),E,F) & k1_matrlin(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,C),F) = k2_polynom3(k14_polynom1(A),G,H) & k3_finseq_1(I) = k3_finseq_1(k21_polynom1(B,D)) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ~ ( r2_hidden(J,k4_finseq_1(I)) & ! [K] : ( m1_polynom1(K,B,k14_polynom1(B)) => ! [L] : ( m1_polynom1(L,B,k14_polynom1(B)) => ~ ( k1_matrlin(k14_polynom1(B),k5_numbers,k4_finseq_2(2,k14_polynom1(B)),k21_polynom1(B,D),J) = k2_polynom3(k14_polynom1(B),K,L) & k1_matrlin(k14_polynom1(k14_ordinal2(A,B)),k5_numbers,k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))),I,J) = k2_polynom3(k14_polynom1(k14_ordinal2(A,B)),k1_polynom6(A,B,G,K),k1_polynom6(A,B,H,L)) ) ) ) ) ) ) ) ) ) ) ) ) => k21_polynom1(k14_ordinal2(A,B),k1_polynom6(A,B,C,D)) = k15_dtconstr(k4_finseq_2(2,k14_polynom1(k14_ordinal2(A,B))),E) ) ) ) ) ) ) ), file(polynom6,t14_polynom6), []). fof(t16_polynom3,axiom,( ! [A,B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,C)) = k16_finseq_1(k5_numbers,k5_polynom1(A,B),C) ) ) ), file(polynom3,t16_polynom3), []). fof(t17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k4_finseq_1(A) = k4_finseq_1(B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) ), file(finseq_1,t17_finseq_1), []). fof(t18_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => r1_xreal_0(0,A) ) ), file(nat_1,t18_nat_1), []). fof(t19_polynom2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v7_vectsp_1(A) & ~ v3_realset2(A) & l3_vectsp_1(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k14_polynom1(B),u1_struct_0(A)) & v2_polynom1(C,k14_polynom1(B),A) & m2_relset_1(C,k14_polynom1(B),u1_struct_0(A)) ) => ( k12_polynom1(k14_polynom1(B),A,C) = k1_xboole_0 => C = k26_polynom1(B,A) ) ) ) ) ), file(polynom2,t19_polynom2), []). 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(t22_polynom3,axiom,( ! [A,B,C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ! [D] : ( m2_finseq_1(D,k3_finseq_2(B)) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ( r2_hidden(E,k5_finsop_1(C)) & r2_hidden(F,k5_finsop_1(D)) & r2_hidden(G,k5_finsop_1(k1_funct_1(C,E))) & r2_hidden(H,k5_finsop_1(k1_funct_1(D,F))) & k5_polynom1(A,C) = k5_polynom1(B,D) & k1_nat_1(k9_wsierp_1(k16_finseq_1(k5_numbers,k5_polynom1(A,C),k5_binarith(E,1))),G) = k1_nat_1(k9_wsierp_1(k16_finseq_1(k5_numbers,k5_polynom1(B,D),k5_binarith(F,1))),H) ) => ( E = F & G = H ) ) ) ) ) ) ) ) ), file(polynom3,t22_polynom3), []). fof(t24_finseq_4,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(B)) ) => k4_finseq_4(k5_numbers,A,B,C) = k1_funct_1(B,C) ) ) ) ), file(finseq_4,t24_finseq_4), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_group_7,axiom,( ! [A,B,C,D] : ( k10_finseq_1(A,B) = k10_finseq_1(C,D) => ( A = C & B = D ) ) ), file(group_7,t2_group_7), []). 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(t31_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ), file(finseq_3,t31_finseq_3), []). fof(t31_polynom1,axiom,( ! [A,B,C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ! [D] : ( m2_finseq_1(D,k3_finseq_2(B)) => ( k5_polynom1(A,C) = k5_polynom1(B,D) => k3_finseq_1(k15_dtconstr(A,C)) = k3_finseq_1(k15_dtconstr(B,D)) ) ) ) ), file(polynom1,t31_polynom1), []). fof(t32_polynom1,axiom,( ! [A,B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ~ ( r2_hidden(C,k4_finseq_1(k15_dtconstr(A,B))) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(E,k4_finseq_1(k1_funct_1(B,D))) & C = k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(D,1)))),E) & k1_funct_1(k1_funct_1(B,D),E) = k1_funct_1(k15_dtconstr(A,B),C) ) ) ) ) ) ), file(polynom1,t32_polynom1), []). fof(t34_polynom1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) => k9_rlvect_1(A,k15_dtconstr(u1_struct_0(A),B)) = k9_rlvect_1(A,k8_matrlin(A,B)) ) ) ), file(polynom1,t34_polynom1), []). 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(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(t5_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,B,k14_polynom1(B)) => ( r6_pboole(k14_ordinal2(A,B),k1_polynom6(A,B,C,D),k16_polynom1(k14_ordinal2(A,B))) <=> ( r6_pboole(A,C,k16_polynom1(A)) & r6_pboole(B,D,k16_polynom1(B)) ) ) ) ) ) ) ), file(polynom6,t5_polynom6), []). 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(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,k14_ordinal2(A,B),k14_polynom1(k14_ordinal2(A,B))) => ? [D] : ( m1_polynom1(D,A,k14_polynom1(A)) & ? [E] : ( m1_polynom1(E,B,k14_polynom1(B)) & r6_pboole(k14_ordinal2(A,B),C,k1_polynom6(A,B,D,E)) ) ) ) ) ) ), file(polynom6,t6_polynom6), []). 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(t72_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ~ ( r2_hidden(B,k4_finseq_1(k21_polynom1(A,C))) & ! [D] : ( ( v7_seqm_3(D) & v1_polynom1(D) & m1_pboole(D,A) ) => ! [E] : ( ( v7_seqm_3(E) & v1_polynom1(E) & m1_pboole(E,A) ) => ~ ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(2,k14_polynom1(A)),k21_polynom1(A,C),B) = k10_finseq_1(D,E) & r6_pboole(A,C,k9_polynom1(A,D,E)) ) ) ) ) ) ) ) ), file(polynom1,t72_polynom1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_polynom1(C,A,k14_polynom1(A)) => ! [D] : ( m1_polynom1(D,A,k14_polynom1(A)) => ! [E] : ( m1_polynom1(E,B,k14_polynom1(B)) => ! [F] : ( m1_polynom1(F,B,k14_polynom1(B)) => ( r6_pboole(k14_ordinal2(A,B),k1_polynom6(A,B,C,E),k1_polynom6(A,B,D,F)) => ( r6_pboole(A,C,D) & r6_pboole(B,E,F) ) ) ) ) ) ) ) ) ), file(polynom6,t7_polynom6), []). 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(t81_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => k15_polynom1(A,B,k26_polynom1(A,B),C) = k1_rlvect_1(B) ) ) ), file(polynom1,t81_polynom1), []). fof(t84_polynom1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_group_1(B) & l2_vectsp_1(B) ) => ( k15_polynom1(A,B,k27_polynom1(A,B),k16_polynom1(A)) = k2_group_1(B) & ! [C] : ( ( v7_seqm_3(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ( C != k16_polynom1(A) => k15_polynom1(A,B,k27_polynom1(A,B),C) = k1_rlvect_1(B) ) ) ) ) ), file(polynom1,t84_polynom1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t90_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v2_group_1(B) & v4_group_1(B) & v7_vectsp_1(B) & ~ v3_realset2(B) & l3_vectsp_1(B) ) => k2_group_1(k30_polynom1(A,B)) = k27_polynom1(A,B) ) ) ), file(polynom1,t90_polynom1), []).