% Mizar problem: t39_weddwitt,weddwitt,2604,55 fof(t39_weddwitt,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => v7_group_1(A) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v11_vectsp_1,abstractness_v1_group_1,abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc10_monoid_0,cc11_monoid_0,cc1_card_1,cc1_eqrel_1,cc1_finseq_1,cc1_finset_1,cc1_fsm_1,cc1_funct_1,cc1_group_2,cc1_nat_1,cc1_polynom1,cc1_real_1,cc1_relset_1,cc1_vectsp_1,cc2_card_1,cc2_eqrel_1,cc2_finset_1,cc2_funct_1,cc2_group_2,cc2_int_1,cc2_nat_1,cc2_polynom1,cc2_vectsp_1,cc3_card_1,cc3_int_1,cc3_nat_1,cc3_polynom1,cc3_vectsp_1,cc4_int_1,cc4_polynom1,cc4_vectsp_1,cc5_monoid_0,cc5_polynom1,cc5_vectsp_1,cc6_monoid_0,cc7_monoid_0,cc8_monoid_0,cc9_monoid_0,commutativity_k11_binop_2,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xboole_0,commutativity_k3_xcmplx_0,commutativity_k9_binop_2,connectedness_r1_xreal_0,d10_xboole_0,d1_absvalue,d1_complfld,d1_nat_1,d1_rlvect_1,d1_tarski,d1_xboole_0,d2_finseq_2,d2_xcmplx_0,d3_finseq_1,d3_realset1,d3_tarski,d3_weddwitt,d3_xboole_0,d4_finseq_1,d4_finseq_4,d4_wellord2,d4_xboole_0,d5_funct_1,d5_group_2,d5_real_1,d7_finseq_1,d7_xboole_0,d8_funct_1,dt_g1_group_1,dt_g3_vectsp_1,dt_g4_vectsp_1,dt_k10_binop_2,dt_k10_group_5,dt_k11_binop_2,dt_k15_rvsum_1,dt_k16_complex1,dt_k18_group_2,dt_k1_card_1,dt_k1_complfld,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_int_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_prepower,dt_k1_real_1,dt_k1_realset1,dt_k1_relat_1,dt_k1_tarski,dt_k1_uniroots,dt_k1_vectsp_9,dt_k1_weddwitt,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k27_binop_2,dt_k29_binop_2,dt_k2_finseq_1,dt_k2_finseq_2,dt_k2_funcop_1,dt_k2_nat_1,dt_k2_newton,dt_k2_numbers,dt_k2_polynom4,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_euler_2,dt_k3_finseq_1,dt_k3_nat_1,dt_k3_real_1,dt_k3_weddwitt,dt_k3_wsierp_1,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k4_card_1,dt_k4_finseq_1,dt_k4_finseq_2,dt_k4_finseq_4,dt_k4_finseqop,dt_k4_nat_1,dt_k4_weddwitt,dt_k4_wsierp_1,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_complex1,dt_k5_finsub_1,dt_k5_int_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_uniroots,dt_k5_weddwitt,dt_k6_complex1,dt_k6_domain_1,dt_k6_int_1,dt_k6_prepower,dt_k6_uniroots,dt_k6_weddwitt,dt_k6_xcmplx_0,dt_k7_finseq_1,dt_k7_group_3,dt_k7_prepower,dt_k7_relat_1,dt_k7_weddwitt,dt_k8_finseq_1,dt_k9_binop_2,dt_k9_group_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_l4_vectsp_1,dt_m1_eqrel_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_group_2,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,dt_u2_vectsp_1,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_l4_vectsp_1,existence_m1_eqrel_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_group_2,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_finset_1,fc11_finseq_1,fc11_finset_1,fc12_finset_1,fc12_polynom1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc1_finseq_1,fc1_finseq_2,fc1_finset_1,fc1_fsm_1,fc1_funcop_1,fc1_int_1,fc1_nat_1,fc1_numbers,fc1_ordinal2,fc1_polynom1,fc1_struct_0,fc1_subset_1,fc1_uniroots,fc1_weddwitt,fc20_polynom1,fc2_card_1,fc2_finseq_1,fc2_funcop_1,fc2_int_1,fc2_nat_1,fc2_numbers,fc2_subset_1,fc2_weddwitt,fc3_funcop_1,fc3_int_1,fc3_nat_1,fc3_polynom1,fc3_weddwitt,fc4_funct_1,fc4_int_1,fc4_nat_1,fc4_ordinal2,fc4_polynom1,fc4_subset_1,fc4_weddwitt,fc5_int_1,fc5_polynom1,fc5_weddwitt,fc6_funct_1,fc6_int_1,fc6_polynom5,fc6_vectsp_1,fc7_funcop_1,fc7_int_1,fc7_polynom1,fc8_int_1,fc8_polynom1,fc9_finset_1,fc9_funcop_1,fc9_int_1,fraenkel_a_1_0_weddwitt,fraenkel_a_1_2_weddwitt,free_g1_group_1,free_g3_vectsp_1,free_g4_vectsp_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,projectivity_k16_complex1,projectivity_k1_int_2,projectivity_k1_prepower,rc10_vectsp_1,rc11_polynom1,rc11_vectsp_1,rc12_polynom1,rc12_vectsp_1,rc13_vectsp_1,rc1_card_1,rc1_finseq_1,rc1_finseq_2,rc1_finset_1,rc1_fsm_1,rc1_funcop_1,rc1_funct_1,rc1_group_2,rc1_int_1,rc1_nat_1,rc1_subset_1,rc1_uniroots,rc1_weddwitt,rc2_card_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_polynom1,rc2_polynom5,rc2_subset_1,rc2_uniroots,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_polynom1,rc3_struct_0,rc4_finseq_1,rc4_finset_1,rc4_fsm_1,rc4_funct_1,rc4_polynom1,rc4_struct_0,rc5_funct_1,rc5_struct_0,rc6_finseq_1,rc6_polynom1,rc6_vectsp_1,rc7_finseq_1,rc7_polynom1,rc7_vectsp_1,rc8_finseq_1,rc8_vectsp_1,rc9_vectsp_1,redefinition_k10_binop_2,redefinition_k11_binop_2,redefinition_k18_group_2,redefinition_k1_int_2,redefinition_k1_nat_1,redefinition_k1_prepower,redefinition_k1_real_1,redefinition_k2_finseq_1,redefinition_k2_nat_1,redefinition_k3_euler_2,redefinition_k3_finseq_1,redefinition_k3_real_1,redefinition_k3_wsierp_1,redefinition_k4_card_1,redefinition_k4_finseq_1,redefinition_k4_finseqop,redefinition_k4_wsierp_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_uniroots,redefinition_k6_domain_1,redefinition_k7_prepower,redefinition_k8_finseq_1,redefinition_k9_binop_2,redefinition_k9_wsierp_1,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r2_wellord2,reflexivity_r1_nat_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r2_int_1,reflexivity_r2_wellord2,s2_finseq_1__e37_53__weddwitt,s2_finseq_1__e55_53__weddwitt,s3_funct_1__e16_53__weddwitt,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,symmetry_r2_wellord2,t101_newton,t105_rvsum_1,t10_xreal_1,t110_rvsum_1,t11_finseq_2,t12_funct_1,t12_prepower,t13_finset_1,t13_weddwitt,t14_weddwitt,t15_funcop_1,t15_weddwitt,t16_int_1,t18_nat_1,t19_nat_1,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t1_xboole_1,t21_card_1,t21_int_2,t21_uniroots,t21_weddwitt,t22_uniroots,t22_weddwitt,t26_pepin,t2_arithm,t2_boole,t2_real,t2_subset,t2_tarski,t31_finseq_3,t31_weddwitt,t32_weddwitt,t33_weddwitt,t34_weddwitt,t35_finseq_1,t35_weddwitt,t37_weddwitt,t37_zfmisc_1,t38_finseq_1,t38_nat_1,t38_weddwitt,t3_arithm,t3_boole,t3_real,t3_subset,t44_finseq_1,t45_prepower,t45_xboole_1,t46_prepower,t4_arithm,t4_boole,t4_real,t4_subset,t54_nat_1,t56_uniroots,t57_nat_1,t5_finseq_1,t5_nat_2,t5_real,t5_subset,t5_weddwitt,t60_card_2,t62_uniroots,t63_uniroots,t64_uniroots,t6_boole,t6_real,t6_zfmisc_1,t73_finseq_4,t77_finseq_4,t79_card_1,t7_boole,t7_real,t8_boole,t8_real,t90_group_1,t93_group_5,t98_finseq_3,t98_group_3,t9_xreal_1]), [file(weddwitt,t39_weddwitt)]). fof(abstractness_v11_vectsp_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l4_vectsp_1(B,A) ) => ( v11_vectsp_1(B,A) => B = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) ) ) ), file(vectsp_1,v11_vectsp_1), []). fof(abstractness_v1_group_1,axiom,( ! [A] : ( l1_group_1(A) => ( v1_group_1(A) => A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ), file(group_1,v1_group_1), []). fof(abstractness_v3_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( v3_vectsp_1(A) => A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) ) ) ), file(vectsp_1,v3_vectsp_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v14_monoid_0(A) & v15_monoid_0(A) ) => ( ~ v3_struct_0(A) & v16_monoid_0(A) ) ) ) ), file(monoid_0,cc10_monoid_0), []). fof(cc11_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v4_group_1(A) & v13_monoid_0(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) & v16_monoid_0(A) ) ) ) ), file(monoid_0,cc11_monoid_0), []). fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(card_1,cc1_card_1), []). fof(cc1_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(eqrel_1,cc1_eqrel_1), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_fsm_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_eqrel_1(B,A) => ( v1_finset_1(B) & v1_setfam_1(B) ) ) ) ), file(fsm_1,cc1_fsm_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => v4_group_1(B) ) ) ), file(group_2,cc1_group_2), []). fof(cc1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). fof(cc1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ( v1_xreal_0(A) & v1_xcmplx_0(A) ) ) ), file(real_1,cc1_real_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) ) ) ), file(vectsp_1,cc1_vectsp_1), []). fof(cc2_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc2_card_1), []). fof(cc2_eqrel_1,axiom,( ! [A,B] : ( m1_eqrel_1(B,A) => v1_setfam_1(B) ) ), file(eqrel_1,cc2_eqrel_1), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ( v4_group_1(B) & v7_group_1(B) ) ) ) ), file(group_2,cc2_group_2), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_polynom1,axiom,( ! [A] : ( l2_vectsp_1(A) => ( ( ~ v3_struct_0(A) & ~ v10_vectsp_1(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) ) ) ) ), file(polynom1,cc2_polynom1), []). fof(cc2_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) ) ) ), file(vectsp_1,cc2_vectsp_1), []). fof(cc3_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ) ), file(polynom1,cc3_polynom1), []). fof(cc3_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v2_group_1(A) ) => ( ~ v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) ) ) ), file(vectsp_1,cc3_vectsp_1), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_polynom1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k5_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v7_seqm_3(B) ) ) ) ), file(polynom1,cc4_polynom1), []). fof(cc4_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(cc5_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) ) => ( ~ v3_struct_0(A) & v13_monoid_0(A) ) ) ) ), file(monoid_0,cc5_monoid_0), []). fof(cc5_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) ) ), file(polynom1,cc5_polynom1), []). fof(cc5_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_group_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v6_vectsp_1(A) ) ) ) ), file(vectsp_1,cc5_vectsp_1), []). fof(cc6_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v4_group_1(A) & v13_monoid_0(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) & v3_group_1(A) ) ) ) ), file(monoid_0,cc6_monoid_0), []). fof(cc7_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v13_monoid_0(A) ) => ( ~ v3_struct_0(A) & v11_monoid_0(A) & v12_monoid_0(A) ) ) ) ), file(monoid_0,cc7_monoid_0), []). fof(cc8_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v11_monoid_0(A) & v12_monoid_0(A) ) => ( ~ v3_struct_0(A) & v13_monoid_0(A) ) ) ) ), file(monoid_0,cc8_monoid_0), []). fof(cc9_monoid_0,axiom,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v16_monoid_0(A) ) => ( ~ v3_struct_0(A) & v14_monoid_0(A) & v15_monoid_0(A) ) ) ) ), file(monoid_0,cc9_monoid_0), []). fof(commutativity_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k11_binop_2(A,B) = k11_binop_2(B,A) ) ), file(binop_2,k11_binop_2), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) ), file(nat_1,k2_nat_1), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k9_binop_2(B,A) ) ), file(binop_2,k9_binop_2), []). 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_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xreal_0(0,A) => k16_complex1(A) = A ) & ( ~ r1_xreal_0(0,A) => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ), file(absvalue,d1_absvalue), []). fof(d1_complfld,axiom,( ! [A] : ( ( v3_vectsp_1(A) & l3_vectsp_1(A) ) => ( A = k1_complfld <=> ( u1_struct_0(A) = k2_numbers & u1_rlvect_1(A) = k27_binop_2 & u1_group_1(A) = k29_binop_2 & u1_vectsp_1(A) = k6_complex1 & u2_struct_0(A) = k5_complex1 ) ) ) ), file(complfld,d1_complfld), []). fof(d1_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( C = k3_nat_1(A,B) <=> ~ ( ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),D) & ~ r1_xreal_0(B,D) ) ) & ~ ( C = 0 & B = 0 ) ) ) ) ) ) ), file(nat_1,d1_nat_1), []). fof(d1_rlvect_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( r1_rlvect_1(A,B) <=> r2_hidden(B,u1_struct_0(A)) ) ) ), file(rlvect_1,d1_rlvect_1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_xboole_0,axiom,( ! [A] : ( A = k1_xboole_0 <=> ! [B] : ~ r2_hidden(B,A) ) ), file(xboole_0,d1_xboole_0), []). fof(d2_finseq_2,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B) ) ), file(finseq_2,d2_finseq_2), []). fof(d2_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) <=> r2_hidden(A,k2_numbers) ) ), file(xcmplx_0,d2_xcmplx_0), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_realset1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B)) ) ), file(realset1,d3_realset1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => k3_weddwitt(A) = a_1_0_weddwitt(A) ) ), file(weddwitt,d3_weddwitt), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). 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(d4_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & k1_relat_1(C) = A & k2_relat_1(C) = B ) ) ), file(wellord2,d4_wellord2), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(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(d5_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) ) => ( m1_group_2(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B)) ) ) ) ) ), file(group_2,d5_group_2), []). fof(d5_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d7_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) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k7_finseq_1(A,B) <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ), file(finseq_1,d7_finseq_1), []). fof(d7_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), []). fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), []). fof(dt_g1_group_1,axiom,( ! [A,B] : ( ( 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_group_1(g1_group_1(A,B)) & l1_group_1(g1_group_1(A,B)) ) ) ), file(group_1,g1_group_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_g4_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) ) => ( v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) ), file(vectsp_1,g4_vectsp_1), []). fof(dt_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k10_binop_2(A,B),k1_numbers) ) ), file(binop_2,k10_binop_2), []). fof(dt_k10_group_5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ( v1_group_1(k10_group_5(A)) & m1_group_2(k10_group_5(A),A) ) ) ), file(group_5,k10_group_5), []). fof(dt_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k11_binop_2(A,B),k1_numbers) ) ), file(binop_2,k11_binop_2), []). 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_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). fof(dt_k18_group_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k18_group_2(A,B),k5_finsub_1(A)) ) ), file(group_2,k18_group_2), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_complfld,axiom, ( v3_vectsp_1(k1_complfld) & l3_vectsp_1(k1_complfld) ), file(complfld,k1_complfld), []). 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_int_2,axiom,( ! [A] : ( v1_int_1(A) => m2_subset_1(k1_int_2(A),k1_numbers,k5_numbers) ) ), file(int_2,k1_int_2), []). 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_prepower,axiom,( ! [A] : ( v1_int_1(A) => m2_subset_1(k1_prepower(A),k1_numbers,k5_numbers) ) ), file(prepower,k1_prepower), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_realset1,axiom,( $true ), file(realset1,k1_realset1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_uniroots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k1_uniroots(A)) & v1_group_1(k1_uniroots(A)) & v3_group_1(k1_uniroots(A)) & v4_group_1(k1_uniroots(A)) & l1_group_1(k1_uniroots(A)) ) ) ), file(uniroots,k1_uniroots), []). fof(dt_k1_vectsp_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) ) => m2_subset_1(k1_vectsp_9(A,B),k1_numbers,k5_numbers) ) ), file(vectsp_9,k1_vectsp_9), []). fof(dt_k1_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_group_1(k1_weddwitt(A,B)) & m1_group_2(k1_weddwitt(A,B),A) ) ) ), file(weddwitt,k1_weddwitt), []). 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_k27_binop_2,axiom, ( v1_funct_1(k27_binop_2) & v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) ), file(binop_2,k27_binop_2), []). fof(dt_k29_binop_2,axiom, ( v1_funct_1(k29_binop_2) & v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) ), file(binop_2,k29_binop_2), []). 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_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => ( v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) ) ) ), file(finseq_2,k2_finseq_2), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k2_nat_1), []). fof(dt_k2_newton,axiom,( $true ), file(newton,k2_newton), []). fof(dt_k2_numbers,axiom,( $true ), file(numbers,k2_numbers), []). fof(dt_k2_polynom4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_group_1(A) & l3_vectsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & v1_algseq_1(B,A) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_polynom4(A,B,C),u1_struct_0(A)) ) ), file(polynom4,k2_polynom4), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_euler_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k3_euler_2(A,B),k1_numbers,k5_numbers) ) ), file(euler_2,k3_euler_2), []). 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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k3_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k3_nat_1), []). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k3_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => m1_eqrel_1(k3_weddwitt(A),u1_struct_0(A)) ) ), file(weddwitt,k3_weddwitt), []). 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_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). 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_finseqop,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,A) ) => m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)) ) ), file(finseqop,k4_finseqop), []). fof(dt_k4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k4_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k4_nat_1), []). fof(dt_k4_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k4_weddwitt(A)) & v4_group_1(k4_weddwitt(A)) & v7_group_1(k4_weddwitt(A)) & v3_rlvect_1(k4_weddwitt(A)) & v4_rlvect_1(k4_weddwitt(A)) & v5_rlvect_1(k4_weddwitt(A)) & v6_rlvect_1(k4_weddwitt(A)) & v3_vectsp_1(k4_weddwitt(A)) & v7_vectsp_1(k4_weddwitt(A)) & v8_vectsp_1(k4_weddwitt(A)) & v9_vectsp_1(k4_weddwitt(A)) & ~ v10_vectsp_1(k4_weddwitt(A)) & l3_vectsp_1(k4_weddwitt(A)) ) ) ), file(weddwitt,k4_weddwitt), []). fof(dt_k4_wsierp_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_finseq_1(C,B) & m1_finseq_1(D,B) ) => m1_trees_4(k4_wsierp_1(A,B,C,D),A,B) ) ), file(wsierp_1,k4_wsierp_1), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_complex1,axiom,( m1_subset_1(k5_complex1,k2_numbers) ), file(complex1,k5_complex1), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k5_int_1(A,B)) ) ), file(int_1,k5_int_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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_uniroots,axiom,( ! [A,B] : ( ( v1_int_1(A) & m1_subset_1(B,k5_numbers) ) => v1_int_1(k5_uniroots(A,B)) ) ), file(uniroots,k5_uniroots), []). fof(dt_k5_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_weddwitt(A,B)) & v4_group_1(k5_weddwitt(A,B)) & v3_rlvect_1(k5_weddwitt(A,B)) & v4_rlvect_1(k5_weddwitt(A,B)) & v5_rlvect_1(k5_weddwitt(A,B)) & v6_rlvect_1(k5_weddwitt(A,B)) & v3_vectsp_1(k5_weddwitt(A,B)) & v6_vectsp_1(k5_weddwitt(A,B)) & v7_vectsp_1(k5_weddwitt(A,B)) & v8_vectsp_1(k5_weddwitt(A,B)) & v9_vectsp_1(k5_weddwitt(A,B)) & ~ v10_vectsp_1(k5_weddwitt(A,B)) & l3_vectsp_1(k5_weddwitt(A,B)) ) ) ), file(weddwitt,k5_weddwitt), []). fof(dt_k6_complex1,axiom,( m1_subset_1(k6_complex1,k2_numbers) ), file(complex1,k6_complex1), []). fof(dt_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), []). fof(dt_k6_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k6_int_1(A,B)) ) ), file(int_1,k6_int_1), []). fof(dt_k6_prepower,axiom,( $true ), file(prepower,k6_prepower), []). fof(dt_k6_uniroots,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ( v1_funct_1(k6_uniroots(A)) & v1_funct_2(k6_uniroots(A),k5_numbers,u1_struct_0(k1_complfld)) & v1_algseq_1(k6_uniroots(A),k1_complfld) & m2_relset_1(k6_uniroots(A),k5_numbers,u1_struct_0(k1_complfld)) ) ) ), file(uniroots,k6_uniroots), []). fof(dt_k6_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k6_weddwitt(A)) & v3_rlvect_1(k6_weddwitt(A)) & v4_rlvect_1(k6_weddwitt(A)) & v5_rlvect_1(k6_weddwitt(A)) & v6_rlvect_1(k6_weddwitt(A)) & v11_vectsp_1(k6_weddwitt(A),k4_weddwitt(A)) & v12_vectsp_1(k6_weddwitt(A),k4_weddwitt(A)) & l4_vectsp_1(k6_weddwitt(A),k4_weddwitt(A)) ) ) ), file(weddwitt,k6_weddwitt), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k7_group_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k7_group_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_3,k7_group_3), []). fof(dt_k7_prepower,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & v1_int_1(B) ) => m1_subset_1(k7_prepower(A,B),k1_numbers) ) ), file(prepower,k7_prepower), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k7_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k7_weddwitt(A,B)) & v3_rlvect_1(k7_weddwitt(A,B)) & v4_rlvect_1(k7_weddwitt(A,B)) & v5_rlvect_1(k7_weddwitt(A,B)) & v6_rlvect_1(k7_weddwitt(A,B)) & v11_vectsp_1(k7_weddwitt(A,B),k4_weddwitt(A)) & v12_vectsp_1(k7_weddwitt(A,B),k4_weddwitt(A)) & l4_vectsp_1(k7_weddwitt(A,B),k4_weddwitt(A)) ) ) ), file(weddwitt,k7_weddwitt), []). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k9_binop_2(A,B),k1_numbers) ) ), file(binop_2,k9_binop_2), []). fof(dt_k9_group_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => m2_subset_1(k9_group_1(A),k1_numbers,k5_numbers) ) ), file(group_1,k9_group_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_l4_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l4_vectsp_1(B,A) => l1_rlvect_1(B) ) ) ), file(vectsp_1,l4_vectsp_1), []). fof(dt_m1_eqrel_1,axiom,( ! [A,B] : ( m1_eqrel_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,m1_eqrel_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_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ( ~ v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) ) ) ) ), file(group_2,m1_group_2), []). 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(dt_u2_vectsp_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l4_vectsp_1(B,A) ) => ( v1_funct_1(u2_vectsp_1(A,B)) & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) ) ) ), file(vectsp_1,u2_vectsp_1), []). 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_l4_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l4_vectsp_1(B,A) ) ), file(vectsp_1,l4_vectsp_1), []). fof(existence_m1_eqrel_1,axiom,( ! [A] : ? [B] : m1_eqrel_1(B,A) ), file(eqrel_1,m1_eqrel_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_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ? [B] : m1_group_2(B,A) ) ), file(group_2,m1_group_2), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). fof(fc12_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_matrlin(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funcop_1(k7_finseq_1(A,B)) & v1_matrlin(k7_finseq_1(A,B)) ) ) ), file(polynom1,fc12_polynom1), []). fof(fc13_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_polynom1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) ), file(polynom1,fc14_polynom1), []). fof(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(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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_fsm_1,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) ), file(fsm_1,fc1_fsm_1), []). fof(fc1_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_polynom1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( ~ v3_struct_0(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ), file(polynom1,fc1_polynom1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_uniroots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k1_uniroots(A)) & v1_group_1(k1_uniroots(A)) & v2_group_1(k1_uniroots(A)) & v3_group_1(k1_uniroots(A)) & v4_group_1(k1_uniroots(A)) & v6_group_1(k1_uniroots(A)) ) ) ), file(uniroots,fc1_uniroots), []). fof(fc1_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v6_group_1(A) & l1_group_1(A) ) => ( ~ v3_struct_0(k10_group_5(A)) & v1_group_1(k10_group_5(A)) & v2_group_1(k10_group_5(A)) & v3_group_1(k10_group_5(A)) & v4_group_1(k10_group_5(A)) & v6_group_1(k10_group_5(A)) & v11_monoid_0(k10_group_5(A)) & v12_monoid_0(k10_group_5(A)) & v13_monoid_0(k10_group_5(A)) & v14_monoid_0(k10_group_5(A)) & v15_monoid_0(k10_group_5(A)) & v16_monoid_0(k10_group_5(A)) ) ) ), file(weddwitt,fc1_weddwitt), []). 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(fc2_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) ), file(card_1,fc2_card_1), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_1), []). fof(fc2_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(nat_1,fc2_nat_1), []). fof(fc2_numbers,axiom,( ~ v1_xboole_0(k2_numbers) ), file(numbers,fc2_numbers), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v6_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k1_weddwitt(A,B)) & v1_group_1(k1_weddwitt(A,B)) & v2_group_1(k1_weddwitt(A,B)) & v3_group_1(k1_weddwitt(A,B)) & v4_group_1(k1_weddwitt(A,B)) & v6_group_1(k1_weddwitt(A,B)) & v11_monoid_0(k1_weddwitt(A,B)) & v12_monoid_0(k1_weddwitt(A,B)) & v13_monoid_0(k1_weddwitt(A,B)) & v14_monoid_0(k1_weddwitt(A,B)) & v15_monoid_0(k1_weddwitt(A,B)) & v16_monoid_0(k1_weddwitt(A,B)) ) ) ), file(weddwitt,fc2_weddwitt), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_polynom1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_matrlin(k1_xboole_0) ), file(polynom1,fc3_polynom1), []). fof(fc3_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v1_xboole_0(k7_group_3(A,B)) ) ), file(weddwitt,fc3_weddwitt), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). fof(fc4_polynom1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finset_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_funcop_1(k2_finseq_2(A,B)) & v1_matrlin(k2_finseq_2(A,B)) ) ) ), file(polynom1,fc4_polynom1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ( ~ v3_struct_0(k4_weddwitt(A)) & v2_group_1(k4_weddwitt(A)) & v4_group_1(k4_weddwitt(A)) & v6_group_1(k4_weddwitt(A)) & v7_group_1(k4_weddwitt(A)) & v3_rlvect_1(k4_weddwitt(A)) & v4_rlvect_1(k4_weddwitt(A)) & v5_rlvect_1(k4_weddwitt(A)) & v6_rlvect_1(k4_weddwitt(A)) & v3_vectsp_1(k4_weddwitt(A)) & v4_vectsp_1(k4_weddwitt(A)) & v5_vectsp_1(k4_weddwitt(A)) & v6_vectsp_1(k4_weddwitt(A)) & v7_vectsp_1(k4_weddwitt(A)) & v8_vectsp_1(k4_weddwitt(A)) & v9_vectsp_1(k4_weddwitt(A)) & ~ v10_vectsp_1(k4_weddwitt(A)) & ~ v3_realset2(k4_weddwitt(A)) ) ) ), file(weddwitt,fc4_weddwitt), []). fof(fc5_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), []). fof(fc5_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & v1_finset_1(k1_funct_1(A,B)) & v1_finseq_1(k1_funct_1(A,B)) ) ) ), file(polynom1,fc5_polynom1), []). fof(fc5_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_weddwitt(A,B)) & v2_group_1(k5_weddwitt(A,B)) & v4_group_1(k5_weddwitt(A,B)) & v6_group_1(k5_weddwitt(A,B)) & v3_rlvect_1(k5_weddwitt(A,B)) & v4_rlvect_1(k5_weddwitt(A,B)) & v5_rlvect_1(k5_weddwitt(A,B)) & v6_rlvect_1(k5_weddwitt(A,B)) & v3_vectsp_1(k5_weddwitt(A,B)) & v4_vectsp_1(k5_weddwitt(A,B)) & v5_vectsp_1(k5_weddwitt(A,B)) & v6_vectsp_1(k5_weddwitt(A,B)) & v7_vectsp_1(k5_weddwitt(A,B)) & v8_vectsp_1(k5_weddwitt(A,B)) & v9_vectsp_1(k5_weddwitt(A,B)) & ~ v10_vectsp_1(k5_weddwitt(A,B)) & ~ v3_realset2(k5_weddwitt(A,B)) ) ) ), file(weddwitt,fc5_weddwitt), []). fof(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc6_polynom5,axiom, ( ~ v3_struct_0(k1_complfld) & v2_group_1(k1_complfld) & v4_group_1(k1_complfld) & v7_group_1(k1_complfld) & v3_rlvect_1(k1_complfld) & v4_rlvect_1(k1_complfld) & v5_rlvect_1(k1_complfld) & v6_rlvect_1(k1_complfld) & v3_vectsp_1(k1_complfld) & v4_vectsp_1(k1_complfld) & v5_vectsp_1(k1_complfld) & v6_vectsp_1(k1_complfld) & v7_vectsp_1(k1_complfld) & v8_vectsp_1(k1_complfld) & v9_vectsp_1(k1_complfld) & ~ v10_vectsp_1(k1_complfld) & v2_vectsp_2(k1_complfld) & v1_algstr_1(k1_complfld) & v2_algstr_1(k1_complfld) & v3_algstr_1(k1_complfld) & v4_algstr_1(k1_complfld) & v5_algstr_1(k1_complfld) & v6_algstr_1(k1_complfld) & ~ v3_realset2(k1_complfld) & v2_polynom5(k1_complfld) ), file(polynom5,fc6_polynom5), []). fof(fc6_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( l1_struct_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) ) => ( ~ v3_struct_0(g4_vectsp_1(A,B,C,D,E)) & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) ), file(vectsp_1,fc6_vectsp_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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). fof(fc7_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_card_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_card_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_card_3(k7_finseq_1(A,B)) ) ) ), file(polynom1,fc7_polynom1), []). fof(fc8_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), []). fof(fc8_polynom1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)) ) ) ), file(polynom1,fc8_polynom1), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_1), []). fof(fc9_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), []). fof(fraenkel_a_1_0_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) ) => ( r2_hidden(A,a_1_0_weddwitt(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & C = k7_group_3(B,D) ) ) ) ) ), file(weddwitt,a_1_0_weddwitt), []). fof(fraenkel_a_1_2_weddwitt,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v4_group_1(B) & v6_group_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & v9_vectsp_1(B) & ~ v10_vectsp_1(B) & l3_vectsp_1(B) ) => ( r2_hidden(A,a_1_2_weddwitt(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_uniroots(B)))) & A = C & r2_hidden(C,k3_weddwitt(k1_uniroots(B))) & k4_card_1(C) = 1 ) ) ) ), file(weddwitt,a_1_2_weddwitt), []). fof(free_g1_group_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) ) => ! [C,D] : ( g1_group_1(A,B) = g1_group_1(C,D) => ( A = C & B = D ) ) ) ), file(group_1,g1_group_1), []). 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(free_g4_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) ) => ! [F,G,H,I,J] : ( g4_vectsp_1(A,B,C,D,E) = g4_vectsp_1(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) ), file(vectsp_1,g4_vectsp_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k1_int_2,axiom,( ! [A] : ( v1_int_1(A) => k1_int_2(k1_int_2(A)) = k1_int_2(A) ) ), file(int_2,k1_int_2), []). fof(projectivity_k1_prepower,axiom,( ! [A] : ( v1_int_1(A) => k1_prepower(k1_prepower(A)) = k1_prepower(A) ) ), file(prepower,k1_prepower), []). fof(rc10_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) ) ), file(vectsp_1,rc10_vectsp_1), []). 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(rc11_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l4_vectsp_1(B,A) & v11_vectsp_1(B,A) ) ) ), file(vectsp_1,rc11_vectsp_1), []). 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(rc12_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l4_vectsp_1(B,A) & ~ v3_struct_0(B) & v11_vectsp_1(B,A) ) ) ), file(vectsp_1,rc12_vectsp_1), []). fof(rc13_vectsp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) ) => ? [B] : ( l4_vectsp_1(B,A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) ) ) ), file(vectsp_1,rc13_vectsp_1), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_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_fsm_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_eqrel_1(B,A) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_setfam_1(B) ) ) ), file(fsm_1,rc1_fsm_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_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ? [B] : ( m1_group_2(B,A) & ~ v3_struct_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) & v4_group_1(B) ) ) ), file(group_2,rc1_group_2), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_uniroots,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v6_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & ~ v3_realset2(A) ) ), file(uniroots,rc1_uniroots), []). fof(rc1_weddwitt,axiom,( ? [A] : ( l1_group_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v4_group_1(A) & v6_group_1(A) & v11_monoid_0(A) & v12_monoid_0(A) & v13_monoid_0(A) & v14_monoid_0(A) & v15_monoid_0(A) & v16_monoid_0(A) ) ), file(weddwitt,rc1_weddwitt), []). fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) ), file(card_1,rc2_card_1), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_matrlin(A) ) ), file(polynom1,rc2_polynom1), []). fof(rc2_polynom5,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & v2_vectsp_2(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) & v6_algstr_1(A) & ~ v3_realset2(A) & v2_polynom5(A) ) ), file(polynom5,rc2_polynom5), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_uniroots,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v6_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & ~ v3_realset2(A) ) ), file(uniroots,rc2_uniroots), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_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(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_fsm_1,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) & v6_group_1(A) ) ), file(fsm_1,rc4_fsm_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(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_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_polynom1,axiom,( ? [A] : ( l3_vectsp_1(A) & ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v3_realset2(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v5_algstr_1(A) & v6_algstr_1(A) ) ), file(polynom1,rc6_polynom1), []). fof(rc6_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc6_vectsp_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_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_vectsp_1,axiom,( ? [A] : ( l1_group_1(A) & ~ v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) ) ), file(vectsp_1,rc8_vectsp_1), []). fof(rc9_vectsp_1,axiom,( ? [A] : ( l1_vectsp_1(A) & ~ v3_struct_0(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) ), file(vectsp_1,rc9_vectsp_1), []). fof(redefinition_k10_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) ), file(binop_2,k10_binop_2), []). fof(redefinition_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k11_binop_2(A,B) = k3_xcmplx_0(A,B) ) ), file(binop_2,k11_binop_2), []). fof(redefinition_k18_group_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k18_group_2(A,B) = k1_tarski(B) ) ), file(group_2,k18_group_2), []). fof(redefinition_k1_int_2,axiom,( ! [A] : ( v1_int_1(A) => k1_int_2(A) = k16_complex1(A) ) ), file(int_2,k1_int_2), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_prepower,axiom,( ! [A] : ( v1_int_1(A) => k1_prepower(A) = k16_complex1(A) ) ), file(prepower,k1_prepower), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ), file(nat_1,k2_nat_1), []). fof(redefinition_k3_euler_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k3_euler_2(A,B) = k2_newton(A,B) ) ), file(euler_2,k3_euler_2), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). 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_finseqop,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,A) ) => k4_finseqop(A,B,C) = k2_finseq_2(B,C) ) ), file(finseqop,k4_finseqop), []). fof(redefinition_k4_wsierp_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_finseq_1(C,B) & m1_finseq_1(D,B) ) => k4_wsierp_1(A,B,C,D) = k7_finseq_1(C,D) ) ), file(wsierp_1,k4_wsierp_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k5_uniroots,axiom,( ! [A,B] : ( ( v1_int_1(A) & m1_subset_1(B,k5_numbers) ) => k5_uniroots(A,B) = k2_newton(A,B) ) ), file(uniroots,k5_uniroots), []). fof(redefinition_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), []). fof(redefinition_k7_prepower,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & v1_int_1(B) ) => k7_prepower(A,B) = k6_prepower(A,B) ) ), file(prepower,k7_prepower), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k9_binop_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_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_r2_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) <=> r2_tarski(A,B) ) ), file(wellord2,r2_wellord2), []). fof(reflexivity_r1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => r1_nat_1(A,A) ) ), file(nat_1,r1_nat_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(reflexivity_r2_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => r2_int_1(A,A) ) ), file(int_1,r2_int_1), []). fof(reflexivity_r2_wellord2,axiom,( ! [A,B] : r2_wellord2(A,A) ), file(wellord2,r2_wellord2), []). fof(s2_finseq_1__e37_53__weddwitt,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(B) = k3_finseq_1(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(A))) => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ), file(weddwitt,s2_finseq_1__e37_53__weddwitt), []). fof(s2_finseq_1__e55_53__weddwitt,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(B) = k3_finseq_1(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(A))) => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ), file(weddwitt,s2_finseq_1__e55_53__weddwitt), []). fof(s3_funct_1__e16_53__weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k1_relat_1(B) = u1_struct_0(k10_group_5(k1_uniroots(A))) & ! [C] : ( r2_hidden(C,u1_struct_0(k10_group_5(k1_uniroots(A)))) => k1_funct_1(B,C) = k1_tarski(C) ) ) ) ), file(weddwitt,s3_funct_1__e16_53__weddwitt), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(symmetry_r2_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) => r2_wellord2(B,A) ) ), file(wellord2,r2_wellord2), []). fof(t101_newton,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( k5_int_1(A,B) = k3_nat_1(A,B) & k6_int_1(A,B) = k4_nat_1(A,B) ) ) ) ), file(newton,t101_newton), []). fof(t105_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k15_rvsum_1(k8_finseq_1(k1_numbers,A,B)) = k9_binop_2(k15_rvsum_1(A),k15_rvsum_1(B)) ) ) ), file(rvsum_1,t105_rvsum_1), []). fof(t10_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ), file(xreal_1,t10_xreal_1), []). fof(t110_rvsum_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k15_rvsum_1(k4_finseqop(k1_numbers,A,B)) = k11_binop_2(A,B) ) ) ), file(rvsum_1,t110_rvsum_1), []). fof(t11_finseq_2,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k2_relat_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A ) ) ) ) ), file(finseq_2,t11_finseq_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_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v4_ordinal2(B) => ~ ( 0 != A & 0 = k2_newton(A,B) ) ) ) ), file(prepower,t12_prepower), []). fof(t13_finset_1,axiom,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), []). fof(t13_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v6_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_group_1(A) = k2_nat_1(k4_card_1(k7_group_3(A,B)),k9_group_1(k1_weddwitt(A,B))) ) ) ), file(weddwitt,t13_weddwitt), []). fof(t14_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( r2_hidden(B,k3_weddwitt(A)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k7_group_3(A,C) = B ) ) ) ), file(weddwitt,t14_weddwitt), []). fof(t15_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( k2_relat_1(A) = k1_tarski(B) => A = k2_funcop_1(k1_relat_1(A),B) ) ) ), file(funcop_1,t15_funcop_1), []). fof(t15_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v6_group_1(A) & l1_group_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_weddwitt(A)) => ( ( v2_funct_1(B) & k2_relat_1(B) = k3_weddwitt(A) ) => ! [C] : ( m2_finseq_1(C,k5_numbers) => ( ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(C)) => k3_wsierp_1(C,D) = k1_card_1(k1_funct_1(B,D)) ) ) ) => k9_group_1(A) = k9_wsierp_1(C) ) ) ) ) ) ), file(weddwitt,t15_weddwitt), []). fof(t16_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( r1_xreal_0(0,A) => r2_hidden(A,k5_numbers) ) ) ), file(int_1,t16_int_1), []). fof(t18_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => r1_xreal_0(0,A) ) ), file(nat_1,t18_nat_1), []). fof(t19_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ~ ( 0 != A & r1_xreal_0(A,0) ) ) ), file(nat_1,t19_nat_1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t21_card_1,axiom,( ! [A,B] : ( r2_wellord2(A,B) <=> k1_card_1(A) = k1_card_1(B) ) ), file(card_1,t21_card_1), []). fof(t21_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r2_int_1(A,B) <=> r1_nat_1(k1_int_2(A),k1_int_2(B)) ) ) ) ), file(int_2,t21_int_2), []). fof(t21_uniroots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => k9_group_1(k1_uniroots(A)) = k10_binop_2(k4_card_1(u1_struct_0(A)),1) ) ), file(uniroots,t21_uniroots), []). fof(t21_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ~ r1_xreal_0(k4_card_1(u1_struct_0(k4_weddwitt(A))),1) ) ), file(weddwitt,t21_weddwitt), []). fof(t22_uniroots,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( r2_hidden(B,u1_struct_0(k1_uniroots(A))) => r2_hidden(B,u1_struct_0(A)) ) ) ), file(uniroots,t22_uniroots), []). fof(t22_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ( k4_card_1(u1_struct_0(k4_weddwitt(A))) = k4_card_1(u1_struct_0(A)) <=> v7_group_1(A) ) ) ), file(weddwitt,t22_weddwitt), []). fof(t26_pepin,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( ~ r1_xreal_0(A,1) & ~ r1_xreal_0(B,0) & r1_xreal_0(k3_euler_2(A,B),1) ) ) ) ), file(pepin,t26_pepin), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). 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_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_uniroots(A))) => ( C = B => k9_group_1(k1_weddwitt(k1_uniroots(A),C)) = k5_real_1(k4_card_1(u1_struct_0(k5_weddwitt(A,B))),1) ) ) ) ) ), file(weddwitt,t31_weddwitt), []). fof(t32_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => k4_card_1(u1_struct_0(A)) = k3_euler_2(k4_card_1(u1_struct_0(k4_weddwitt(A))),k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A))) ) ), file(weddwitt,t32_weddwitt), []). fof(t33_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ~ r1_xreal_0(k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A)),0) ) ), file(weddwitt,t33_weddwitt), []). fof(t34_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_card_1(u1_struct_0(k5_weddwitt(A,B))) = k3_euler_2(k4_card_1(u1_struct_0(k4_weddwitt(A))),k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B))) ) ) ), file(weddwitt,t34_weddwitt), []). fof(t35_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) ) => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ), file(finseq_1,t35_finseq_1), []). fof(t35_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r1_xreal_0(k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B)),0) ) ) ), file(weddwitt,t35_weddwitt), []). fof(t37_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( m1_subset_1(B,u1_struct_0(k1_uniroots(A))) => r1_nat_1(k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B)),k1_vectsp_9(k4_weddwitt(A),k6_weddwitt(A))) ) ) ) ), file(weddwitt,t37_weddwitt), []). fof(t37_zfmisc_1,axiom,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_1), []). fof(t38_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) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & ~ r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ~ ( r2_hidden(D,k4_finseq_1(B)) & C = k1_nat_1(k3_finseq_1(A),D) ) ) ) ) ) ) ), file(finseq_1,t38_finseq_1), []). 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(t38_weddwitt,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_group_1(A) & v6_group_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & ~ v10_vectsp_1(A) & l3_vectsp_1(A) ) => k4_card_1(u1_struct_0(k10_group_5(k1_uniroots(A)))) = k5_real_1(k4_card_1(u1_struct_0(k4_weddwitt(A))),1) ) ), file(weddwitt,t38_weddwitt), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). 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(t44_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) ) => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ), file(finseq_1,t44_finseq_1), []). fof(t45_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => k6_prepower(A,1) = A ) ), file(prepower,t45_prepower), []). fof(t45_xboole_1,axiom,( ! [A,B] : ( r1_tarski(A,B) => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) ), file(xboole_1,t45_xboole_1), []). fof(t46_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v4_ordinal2(B) => k6_prepower(A,B) = k2_newton(A,B) ) ) ), file(prepower,t46_prepower), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_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(t54_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_nat_1(B,A) => ( r1_xreal_0(A,0) | r1_xreal_0(B,A) ) ) ) ) ), file(nat_1,t54_nat_1), []). fof(t56_uniroots,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( v1_int_1(B) => v1_int_1(k2_polynom4(k1_complfld,k6_uniroots(A),B)) ) ) ) ), file(uniroots,t56_uniroots), []). fof(t57_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( ( r1_nat_1(A,B) & r1_nat_1(A,k2_xcmplx_0(B,C)) ) => r1_nat_1(A,C) ) ) ) ) ), file(nat_1,t57_nat_1), []). fof(t5_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( A = 0 | r2_hidden(A,k2_finseq_1(A)) ) ) ), file(finseq_1,t5_finseq_1), []). fof(t5_nat_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => k3_nat_1(A,A) = 1 ) ), file(nat_2,t5_nat_2), []). 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(t5_weddwitt,axiom,( ! [A] : ( m2_finseq_1(A,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(C,k4_finseq_1(A)) => r1_nat_1(B,k4_finseq_4(k5_numbers,k5_numbers,A,C)) ) ) => r1_nat_1(B,k9_wsierp_1(A)) ) ) ) ), file(weddwitt,t5_weddwitt), []). fof(t60_card_2,axiom,( ! [A] : ( k1_card_1(A) = 1 <=> ? [B] : A = k1_tarski(B) ) ), file(card_2,t60_card_2), []). fof(t62_uniroots,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ( C = B => ! [D] : ( v1_int_1(D) => ( D = k2_polynom4(k1_complfld,k6_uniroots(A),C) => r2_int_1(D,k6_xcmplx_0(k5_uniroots(B,A),1)) ) ) ) ) ) ) ), file(uniroots,t62_uniroots), []). fof(t63_uniroots,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( r1_nat_1(B,A) => ( r1_xreal_0(A,B) | ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ( D = C => ! [E] : ( v1_int_1(E) => ( E = k2_polynom4(k1_complfld,k6_uniroots(A),D) => r2_int_1(E,k5_int_1(k6_xcmplx_0(k5_uniroots(C,A),1),k6_xcmplx_0(k5_uniroots(C,B),1))) ) ) ) ) ) ) ) ) ) ), file(uniroots,t63_uniroots), []). fof(t64_uniroots,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => ( ~ r1_xreal_0(A,1) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(B,1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ( C = B => ! [D] : ( v1_int_1(D) => ~ ( D = k2_polynom4(k1_complfld,k6_uniroots(A),C) & r1_xreal_0(k1_prepower(D),k10_binop_2(B,1)) ) ) ) ) ) ) ) ) ), file(uniroots,t64_uniroots), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t6_zfmisc_1,axiom,( ! [A,B] : ( r1_tarski(k1_tarski(A),k1_tarski(B)) => A = B ) ), file(zfmisc_1,t6_zfmisc_1), []). fof(t73_finseq_4,axiom,( ! [A] : ~ ( v1_finset_1(A) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k2_relat_1(B) = A & v2_funct_1(B) ) ) ) ), file(finseq_4,t73_finseq_4), []). fof(t77_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_funct_1(A) <=> k4_card_1(k2_relat_1(A)) = k3_finseq_1(A) ) ) ), file(finseq_4,t77_finseq_4), []). fof(t79_card_1,axiom,( ! [A] : k4_card_1(k1_tarski(A)) = 1 ), file(card_1,t79_card_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t90_group_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ( v6_group_1(A) => r1_xreal_0(1,k9_group_1(A)) ) ) ), file(group_1,t90_group_1), []). fof(t93_group_5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_rlvect_1(k10_group_5(A),B) <=> k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),B) ) ) ) ), file(group_5,t93_group_5), []). fof(t98_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) ) => ( ( r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(A) & v2_funct_1(B) ) <=> v2_funct_1(k7_finseq_1(A,B)) ) ) ) ), file(finseq_3,t98_finseq_3), []). fof(t98_group_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k7_group_3(A,B)) ) ) ), file(group_3,t98_group_3), []). fof(t9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ), file(xreal_1,t9_xreal_1), []).