% Mizar problem: t36_hahnban1,hahnban1,1914,44 fof(t36_hahnban1,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v4_hahnban1(B,k1_complfld,A) & v7_hahnban1(B,A) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => ! [C] : ( m1_vectsp_4(C,k1_complfld,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k1_complfld)) & v1_hahnban1(D,k1_complfld,C) & v2_hahnban1(D,k1_complfld,C) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(k1_complfld)) ) => ~ ( ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F = E => r1_xreal_0(k3_complfld(k8_funct_2(u1_struct_0(C),u1_struct_0(k1_complfld),D,E)),k8_funct_2(u1_struct_0(A),k1_numbers,B,F)) ) ) ) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_complfld)) & v1_hahnban1(E,k1_complfld,A) & v2_hahnban1(E,k1_complfld,A) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_complfld)) ) => ~ ( k8_relset_1(u1_struct_0(A),u1_struct_0(k1_complfld),E,u1_struct_0(C)) = D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r1_xreal_0(k3_complfld(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),E,F)),k8_funct_2(u1_struct_0(A),k1_numbers,B,F)) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_rlvect_1,abstractness_v2_rlvect_1,abstractness_v3_vectsp_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_complfld,cc1_funct_1,cc1_hahnban,cc1_hahnban1,cc1_membered,cc1_relset_1,cc1_vectsp_1,cc1_xcmplx_0,cc1_xreal_0,cc20_membered,cc2_funct_1,cc2_hahnban,cc2_hahnban1,cc2_membered,cc2_vectsp_1,cc2_xcmplx_0,cc2_xreal_0,cc3_hahnban1,cc3_membered,cc3_vectsp_1,cc3_xreal_0,cc4_membered,cc4_vectsp_1,cc4_xreal_0,cc5_membered,cc5_vectsp_1,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k10_group_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k9_complex1,connectedness_r1_xreal_0,d12_hahnban1,d19_hahnban1,d1_binop_1,d1_complfld,d1_hahnban1,d22_hahnban1,d23_hahnban1,d24_vectsp_1,d25_hahnban1,d27_hahnban1,d28_hahnban1,d2_hahnban1,d2_vectsp_4,d3_realset1,d3_tarski,d5_tarski,d6_complex1,d8_complex1,dt_g1_rlvect_1,dt_g2_rlvect_1,dt_g3_vectsp_1,dt_k10_group_1,dt_k10_hahnban1,dt_k11_hahnban1,dt_k13_complex1,dt_k13_hahnban1,dt_k14_complex1,dt_k15_complex1,dt_k15_hahnban1,dt_k16_complex1,dt_k16_hahnban1,dt_k17_complex1,dt_k18_complex1,dt_k1_binop_1,dt_k1_complex1,dt_k1_complfld,dt_k1_funct_1,dt_k1_group_1,dt_k1_hahnban1,dt_k1_nattra_1,dt_k1_numbers,dt_k1_real_1,dt_k1_realset1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_xcmplx_0,dt_k1_zfmisc_1,dt_k27_binop_2,dt_k29_binop_2,dt_k2_binop_1,dt_k2_complex1,dt_k2_hahnban1,dt_k2_numbers,dt_k2_partfun1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_complex1,dt_k3_complfld,dt_k3_real_1,dt_k3_supinf_1,dt_k3_xcmplx_0,dt_k4_complex1,dt_k4_real_1,dt_k4_tarski,dt_k4_xcmplx_0,dt_k5_arytm_0,dt_k5_complex1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k6_complex1,dt_k6_real_1,dt_k6_supinf_1,dt_k6_vectsp_1,dt_k6_xcmplx_0,dt_k7_complex1,dt_k7_relat_1,dt_k7_xcmplx_0,dt_k8_funct_2,dt_k8_relset_1,dt_k9_complex1,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_rlvect_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_l4_vectsp_1,dt_m1_relset_1,dt_m1_rlsub_1,dt_m1_subset_1,dt_m1_vectsp_4,dt_m2_relset_1,dt_u1_group_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u1_vectsp_1,dt_u2_rlvect_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_rlvect_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_l4_vectsp_1,existence_m1_relset_1,existence_m1_rlsub_1,existence_m1_subset_1,existence_m1_vectsp_4,existence_m2_relset_1,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_membered,fc12_xreal_0,fc13_membered,fc13_xreal_0,fc14_membered,fc14_xreal_0,fc15_membered,fc15_xreal_0,fc16_membered,fc16_xreal_0,fc17_xreal_0,fc18_xreal_0,fc19_hahnban1,fc19_xreal_0,fc1_complfld,fc1_membered,fc1_rlvect_1,fc1_struct_0,fc1_subset_1,fc1_xcmplx_0,fc1_xreal_0,fc20_hahnban1,fc20_xreal_0,fc21_hahnban1,fc21_xreal_0,fc22_hahnban1,fc22_xreal_0,fc23_hahnban1,fc23_xreal_0,fc24_hahnban1,fc24_xreal_0,fc25_hahnban1,fc27_hahnban1,fc27_xreal_0,fc28_xreal_0,fc29_xreal_0,fc2_complfld,fc2_membered,fc2_subset_1,fc2_xcmplx_0,fc30_xreal_0,fc3_complfld,fc3_subset_1,fc3_xcmplx_0,fc3_xreal_0,fc4_funct_1,fc4_subset_1,fc4_xcmplx_0,fc4_xreal_0,fc5_membered,fc5_xcmplx_0,fc5_xreal_0,fc6_membered,fc6_xcmplx_0,fc6_xreal_0,fc7_membered,fc7_xreal_0,fc8_membered,fc8_xcmplx_0,fc8_xreal_0,fc9_membered,fc9_xcmplx_0,fc9_xreal_0,free_g1_rlvect_1,free_g2_rlvect_1,free_g3_vectsp_1,involutiveness_k14_complex1,involutiveness_k15_complex1,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,l51_hahnban1,projectivity_k16_complex1,projectivity_k17_complex1,projectivity_k18_complex1,projectivity_k3_complfld,rc10_vectsp_1,rc1_funct_1,rc1_hahnban1,rc1_membered,rc1_rlvect_1,rc1_subset_1,rc1_vectsp_1,rc1_xcmplx_0,rc1_xreal_0,rc2_funct_1,rc2_hahnban1,rc2_rlvect_1,rc2_subset_1,rc2_xcmplx_0,rc2_xreal_0,rc3_funct_1,rc3_hahnban1,rc3_rlvect_1,rc3_struct_0,rc3_xreal_0,rc4_rlvect_1,rc4_struct_0,rc4_xreal_0,rc5_rlvect_1,rc5_struct_0,rc6_rlvect_1,rc6_vectsp_1,rc7_vectsp_1,rc8_vectsp_1,rc9_vectsp_1,redefinition_k10_group_1,redefinition_k13_complex1,redefinition_k15_complex1,redefinition_k17_complex1,redefinition_k18_complex1,redefinition_k1_nattra_1,redefinition_k1_real_1,redefinition_k2_binop_1,redefinition_k2_partfun1,redefinition_k3_complex1,redefinition_k3_complfld,redefinition_k3_real_1,redefinition_k4_complex1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k6_supinf_1,redefinition_k7_complex1,redefinition_k8_funct_2,redefinition_k8_relset_1,redefinition_k9_complex1,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,t113_funct_2,t12_arytm_0,t131_complex1,t139_complex1,t140_complex1,t153_complex1,t1_arithm,t1_numerals,t1_subset,t22_vectsp_4,t27_complex1,t28_complex1,t29_complex1,t2_arithm,t2_subset,t2_xreal_1,t30_hahnban1,t32_hahnban1,t33_hahnban1,t35_hahnban,t35_hahnban1,t3_arithm,t3_subset,t4_arithm,t4_hahnban1,t4_subset,t5_arithm,t5_hahnban1,t5_subset,t60_xcmplx_1,t6_arithm,t6_boole,t6_complfld,t72_funct_1,t7_boole,t8_boole]), [file(hahnban1,t36_hahnban1)]). fof(abstractness_v1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( v1_rlvect_1(A) => A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ) ), file(rlvect_1,v1_rlvect_1), []). fof(abstractness_v2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => ( v2_rlvect_1(A) => A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ), file(rlvect_1,v2_rlvect_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_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => v1_xcmplx_0(A) ) ), file(complfld,cc1_complfld), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_hahnban,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),k6_supinf_1) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v2_hahnban(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v1_hahnban(B,A) ) ) ) ) ), file(hahnban,cc1_hahnban), []). fof(cc1_hahnban1,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_vectsp_1(A) & v8_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) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v2_hahnban1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v3_hahnban1(C,A,B) ) ) ) ) ), file(hahnban1,cc1_hahnban1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) ) ) ), file(vectsp_1,cc1_vectsp_1), []). fof(cc1_xcmplx_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => v1_xcmplx_0(A) ) ), file(xcmplx_0,cc1_xcmplx_0), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_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_hahnban,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),k6_supinf_1) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v3_hahnban(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v4_hahnban(B,A) ) ) ) ) ), file(hahnban,cc2_hahnban), []). fof(cc2_hahnban1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & ~ v3_struct_0(B) & l4_vectsp_1(B,A) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(B),k1_numbers) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v5_hahnban1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v4_hahnban1(C,A,B) ) ) ) ) ), file(hahnban1,cc2_hahnban1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_vectsp_1,axiom,( ! [A] : ( l3_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v7_vectsp_1(A) ) ) ) ), file(vectsp_1,cc2_vectsp_1), []). fof(cc2_xcmplx_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xcmplx_0(A) ) ), file(xcmplx_0,cc2_xcmplx_0), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v6_hahnban1(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v8_hahnban1(B,k1_complfld,A) ) ) ) ) ), file(hahnban1,cc3_hahnban1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v2_group_1(A) ) => ( ~ v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) ) ) ), file(vectsp_1,cc3_vectsp_1), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) ) ) ) ), file(vectsp_1,cc4_vectsp_1), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => v1_membered(A) ) ), file(membered,cc5_membered), []). fof(cc5_vectsp_1,axiom,( ! [A] : ( l1_vectsp_1(A) => ( ( ~ v3_struct_0(A) & v7_group_1(A) & v8_vectsp_1(A) ) => ( ~ v3_struct_0(A) & v6_vectsp_1(A) ) ) ) ), file(vectsp_1,cc5_vectsp_1), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k10_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k10_group_1(A,B,C) = k10_group_1(A,C,B) ) ), file(group_1,k10_group_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(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_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_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), []). fof(commutativity_k9_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k9_complex1(A,B) = k9_complex1(B,A) ) ), file(complex1,k9_complex1), []). 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(d12_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l4_vectsp_1(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) ) => ( v2_hahnban1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k6_vectsp_1(A,B,E,D)) = k1_group_1(A,E,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D)) ) ) ) ) ) ) ), file(hahnban1,d12_hahnban1), []). fof(d19_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => ( v7_hahnban1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,D,C)) = k4_real_1(k3_complfld(D),k8_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ), file(hahnban1,d19_hahnban1), []). fof(d1_binop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ), file(binop_1,d1_binop_1), []). 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_hahnban1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k1_hahnban1(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) ) ) ), file(hahnban1,d1_hahnban1), []). fof(d22_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v2_rlvect_1(B) & l2_rlvect_1(B) ) => ( B = k10_hahnban1(A) <=> ( g1_rlvect_1(u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B)) = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_binop_1(u2_rlvect_1(B),C,D) = k6_vectsp_1(k1_complfld,A,k1_hahnban1(C,0),D) ) ) ) ) ) ) ), file(hahnban1,d22_hahnban1), []). fof(d23_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & m2_relset_1(C,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ( C = k11_hahnban1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k3_complex1(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,D)) ) ) ) ) ) ), file(hahnban1,d23_hahnban1), []). fof(d24_vectsp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l4_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_vectsp_1(A,B,C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) ) ) ) ) ), file(vectsp_1,d24_vectsp_1), []). fof(d25_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => k13_hahnban1(A,B) = B ) ) ), file(hahnban1,d25_hahnban1), []). fof(d27_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & m2_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( C = k15_hahnban1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),k1_numbers,C,D) = k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,D)) ) ) ) ) ) ), file(hahnban1,d27_hahnban1), []). fof(d28_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) ) => ( C = k16_hahnban1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),C,D) = k1_hahnban1(k8_funct_2(u1_struct_0(A),k1_numbers,k13_hahnban1(A,B),D),k1_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,k15_hahnban1(A,k13_hahnban1(A,B)),D))) ) ) ) ) ) ), file(hahnban1,d28_hahnban1), []). fof(d2_hahnban1,axiom,( k2_hahnban1 = k7_complex1 ), file(hahnban1,d2_hahnban1), []). fof(d2_vectsp_4,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] : ( ( ~ 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) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) ) => ( m1_vectsp_4(C,A,B) <=> ( r1_tarski(u1_struct_0(C),u1_struct_0(B)) & u2_struct_0(C) = u2_struct_0(B) & u1_rlvect_1(C) = k1_realset1(u1_rlvect_1(B),u1_struct_0(C)) & u2_vectsp_1(A,C) = k7_relat_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(C))) ) ) ) ) ) ), file(vectsp_4,d2_vectsp_4), []). 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(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_complex1,axiom,( k5_complex1 = 0 ), file(complex1,d6_complex1), []). fof(d8_complex1,axiom,( k7_complex1 = k5_arytm_0(0,1) ), file(complex1,d8_complex1), []). fof(dt_g1_rlvect_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) ) => ( v1_rlvect_1(g1_rlvect_1(A,B,C)) & l1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ), file(rlvect_1,g1_rlvect_1), []). fof(dt_g2_rlvect_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(B,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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) ) => ( v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & l2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ), file(rlvect_1,g2_rlvect_1), []). fof(dt_g3_vectsp_1,axiom,( ! [A,B,C,D,E] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ), file(vectsp_1,g3_vectsp_1), []). fof(dt_k10_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k10_group_1), []). fof(dt_k10_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ( v2_rlvect_1(k10_hahnban1(A)) & l2_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,k10_hahnban1), []). fof(dt_k11_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld)) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) ) => ( v1_funct_1(k11_hahnban1(A,B)) & v1_funct_2(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & m2_relset_1(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ), file(hahnban1,k11_hahnban1), []). fof(dt_k13_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => m1_subset_1(k13_complex1(A,B),k2_numbers) ) ), file(complex1,k13_complex1), []). fof(dt_k13_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ( v1_funct_1(k13_hahnban1(A,B)) & v1_funct_2(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers) & m2_relset_1(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers) ) ) ), file(hahnban1,k13_hahnban1), []). fof(dt_k14_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k14_complex1(A)) ) ), file(complex1,k14_complex1), []). fof(dt_k15_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k15_complex1(A),k2_numbers) ) ), file(complex1,k15_complex1), []). fof(dt_k15_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k15_hahnban1(A,B)) & v1_funct_2(k15_hahnban1(A,B),u1_struct_0(A),k1_numbers) & m2_relset_1(k15_hahnban1(A,B),u1_struct_0(A),k1_numbers) ) ) ), file(hahnban1,k15_hahnban1), []). fof(dt_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). fof(dt_k16_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ( v1_funct_1(k16_hahnban1(A,B)) & v1_funct_2(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) & m2_relset_1(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) ) ) ), file(hahnban1,k16_hahnban1), []). fof(dt_k17_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k17_complex1(A),k1_numbers) ) ), file(complex1,k17_complex1), []). fof(dt_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k18_complex1(A),k1_numbers) ) ), file(complex1,k18_complex1), []). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), []). fof(dt_k1_complex1,axiom,( $true ), file(complex1,k1_complex1), []). fof(dt_k1_complfld,axiom, ( v3_vectsp_1(k1_complfld) & l3_vectsp_1(k1_complfld) ), file(complfld,k1_complfld), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k1_group_1), []). fof(dt_k1_hahnban1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k1_hahnban1(A,B),u1_struct_0(k1_complfld)) ) ), file(hahnban1,k1_hahnban1), []). fof(dt_k1_nattra_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( v1_funct_1(k1_nattra_1(A,B,C,D)) & v1_funct_2(k1_nattra_1(A,B,C,D),D,B) & m2_relset_1(k1_nattra_1(A,B,C,D),D,B) ) ) ), file(nattra_1,k1_nattra_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). 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_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_xcmplx_0,axiom,( $true ), file(xcmplx_0,k1_xcmplx_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_binop_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) ) => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ), file(binop_1,k2_binop_1), []). fof(dt_k2_complex1,axiom,( $true ), file(complex1,k2_complex1), []). fof(dt_k2_hahnban1,axiom,( m1_subset_1(k2_hahnban1,u1_struct_0(k1_complfld)) ), file(hahnban1,k2_hahnban1), []). fof(dt_k2_numbers,axiom,( $true ), file(numbers,k2_numbers), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k3_complex1(A),k1_numbers) ) ), file(complex1,k3_complex1), []). fof(dt_k3_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => m1_subset_1(k3_complfld(A),k1_numbers) ) ), file(complfld,k3_complfld), []). 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_supinf_1,axiom,( $true ), file(supinf_1,k3_supinf_1), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k4_complex1(A),k1_numbers) ) ), file(complex1,k4_complex1), []). fof(dt_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). 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_arytm_0,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_arytm_0(A,B),k2_numbers) ) ), file(arytm_0,k5_arytm_0), []). fof(dt_k5_complex1,axiom,( m1_subset_1(k5_complex1,k2_numbers) ), file(complex1,k5_complex1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k6_complex1,axiom,( m1_subset_1(k6_complex1,k2_numbers) ), file(complex1,k6_complex1), []). fof(dt_k6_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ), file(real_1,k6_real_1), []). fof(dt_k6_supinf_1,axiom, ( ~ v1_xboole_0(k6_supinf_1) & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ), file(supinf_1,k6_supinf_1), []). fof(dt_k6_vectsp_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l4_vectsp_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)) ) ), file(vectsp_1,k6_vectsp_1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_complex1,axiom,( m1_subset_1(k7_complex1,k2_numbers) ), file(complex1,k7_complex1), []). 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_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ), file(relset_1,k8_relset_1), []). fof(dt_k9_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => m1_subset_1(k9_complex1(A,B),k2_numbers) ) ), file(complex1,k9_complex1), []). 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_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => l1_rlvect_1(A) ) ), file(rlvect_1,l2_rlvect_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_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rlsub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) ) ) ), file(rlsub_1,m1_rlsub_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_vectsp_4,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_vectsp_1(A) & v8_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) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) ) ) ) ), file(vectsp_4,m1_vectsp_4), []). 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_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_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => ( v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u2_rlvect_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_rlvect_1,axiom,( ? [A] : l2_rlvect_1(A) ), file(rlvect_1,l2_rlvect_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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rlsub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ? [B] : m1_rlsub_1(B,A) ) ), file(rlsub_1,m1_rlsub_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_vectsp_4,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_vectsp_1(A) & v8_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) ) => ? [C] : m1_vectsp_4(C,A,B) ) ), file(vectsp_4,m1_vectsp_4), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ( ~ v3_struct_0(k10_hahnban1(A)) & v2_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,fc19_hahnban1), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_complfld,axiom, ( ~ v3_struct_0(k1_complfld) & v3_vectsp_1(k1_complfld) ), file(complfld,fc1_complfld), []). fof(fc1_membered,axiom, ( ~ v1_xboole_0(k2_numbers) & v1_membered(k2_numbers) ), file(membered,fc1_membered), []). fof(fc1_rlvect_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) ) => ( ~ v3_struct_0(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ), file(rlvect_1,fc1_rlvect_1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_xcmplx_0,axiom,( v1_xcmplx_0(k1_xcmplx_0) ), file(xcmplx_0,fc1_xcmplx_0), []). fof(fc1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). fof(fc20_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l4_vectsp_1(A,k1_complfld) ) => ( ~ v3_struct_0(k10_hahnban1(A)) & v2_rlvect_1(k10_hahnban1(A)) & v3_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,fc20_hahnban1), []). fof(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(fc21_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & l4_vectsp_1(A,k1_complfld) ) => ( ~ v3_struct_0(k10_hahnban1(A)) & v2_rlvect_1(k10_hahnban1(A)) & v4_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,fc21_hahnban1), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v5_rlvect_1(A) & l4_vectsp_1(A,k1_complfld) ) => ( ~ v3_struct_0(k10_hahnban1(A)) & v2_rlvect_1(k10_hahnban1(A)) & v5_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,fc22_hahnban1), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v6_rlvect_1(A) & l4_vectsp_1(A,k1_complfld) ) => ( ~ v3_struct_0(k10_hahnban1(A)) & v2_rlvect_1(k10_hahnban1(A)) & v6_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,fc23_hahnban1), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ( ~ v3_struct_0(k10_hahnban1(A)) & v2_rlvect_1(k10_hahnban1(A)) & v7_rlvect_1(k10_hahnban1(A)) ) ) ), file(hahnban1,fc24_hahnban1), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(fc25_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & v2_hahnban(B,k10_hahnban1(A)) & m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ( v1_relat_1(k13_hahnban1(A,B)) & v1_funct_1(k13_hahnban1(A,B)) & v1_funct_2(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers) & v4_hahnban1(k13_hahnban1(A,B),k1_complfld,A) & v5_hahnban1(k13_hahnban1(A,B),k1_complfld,A) ) ) ), file(hahnban1,fc25_hahnban1), []). fof(fc27_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & v3_hahnban(B,k10_hahnban1(A)) & m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ( v1_relat_1(k13_hahnban1(A,B)) & v1_funct_1(k13_hahnban1(A,B)) & v1_funct_2(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers) & v6_hahnban1(k13_hahnban1(A,B),A) & v8_hahnban1(k13_hahnban1(A,B),k1_complfld,A) ) ) ), file(hahnban1,fc27_hahnban1), []). fof(fc27_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), []). fof(fc28_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), []). fof(fc29_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), []). fof(fc2_complfld,axiom, ( ~ v3_struct_0(k1_complfld) & v2_group_1(k1_complfld) & v3_vectsp_1(k1_complfld) & v6_vectsp_1(k1_complfld) & v8_vectsp_1(k1_complfld) ), file(complfld,fc2_complfld), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k2_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc2_xcmplx_0), []). fof(fc30_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), []). fof(fc3_complfld,axiom, ( ~ v3_struct_0(k1_complfld) & v3_rlvect_1(k1_complfld) & v4_rlvect_1(k1_complfld) & v5_rlvect_1(k1_complfld) & v6_rlvect_1(k1_complfld) & v2_group_1(k1_complfld) & v4_group_1(k1_complfld) & v7_group_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) ), file(complfld,fc3_complfld), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc3_xcmplx_0), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_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_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_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k6_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc4_xcmplx_0), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ), file(xcmplx_0,fc5_xcmplx_0), []). fof(fc5_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_xcmplx_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) ) => ( ~ v1_xboole_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) ) ) ), file(xcmplx_0,fc6_xcmplx_0), []). fof(fc6_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_xcmplx_0,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & ~ v1_xboole_0(B) & v1_xcmplx_0(B) ) => ( ~ v1_xboole_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ), file(xcmplx_0,fc8_xcmplx_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_xcmplx_0,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & ~ v1_xboole_0(B) & v1_xcmplx_0(B) ) => ( ~ v1_xboole_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ) ), file(xcmplx_0,fc9_xcmplx_0), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(free_g1_rlvect_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) ) => ! [D,E,F] : ( g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(rlvect_1,g1_rlvect_1), []). fof(free_g2_rlvect_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(B,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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) ) => ! [E,F,G,H] : ( g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(rlvect_1,g2_rlvect_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(involutiveness_k14_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k14_complex1(k14_complex1(A)) = A ) ), file(complex1,k14_complex1), []). fof(involutiveness_k15_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_complex1(k15_complex1(A)) = A ) ), file(complex1,k15_complex1), []). 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(l51_hahnban1,axiom,( k5_complex1 = k5_arytm_0(0,0) ), file(hahnban1,l51_hahnban1), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k17_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k17_complex1(k17_complex1(A)) = k17_complex1(A) ) ), file(complex1,k17_complex1), []). fof(projectivity_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ), file(complex1,k18_complex1), []). fof(projectivity_k3_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k3_complfld(k3_complfld(A)) = k3_complfld(A) ) ), file(complfld,k3_complfld), []). 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(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_hahnban1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) & ~ v3_struct_0(B) & l4_vectsp_1(B,A) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_hahnban1(C,A,B) & v2_hahnban1(C,A,B) & v3_hahnban1(C,A,B) ) ) ), file(hahnban1,rc1_hahnban1), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_rlvect_1,axiom,( ? [A] : ( l1_rlvect_1(A) & v1_rlvect_1(A) ) ), file(rlvect_1,rc1_rlvect_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_vectsp_1,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) ), file(vectsp_1,rc1_vectsp_1), []). fof(rc1_xcmplx_0,axiom,( ? [A] : v1_xcmplx_0(A) ), file(xcmplx_0,rc1_xcmplx_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). 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_hahnban1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & ~ v3_struct_0(B) & l4_vectsp_1(B,A) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(B),k1_numbers) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v4_hahnban1(C,A,B) & v5_hahnban1(C,A,B) & v8_hahnban1(C,A,B) ) ) ), file(hahnban1,rc2_hahnban1), []). fof(rc2_rlvect_1,axiom,( ? [A] : ( l2_rlvect_1(A) & v2_rlvect_1(A) ) ), file(rlvect_1,rc2_rlvect_1), []). 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_xcmplx_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) ) ), file(xcmplx_0,rc2_xcmplx_0), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l4_vectsp_1(A,k1_complfld) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v4_hahnban1(B,k1_complfld,A) & v5_hahnban1(B,k1_complfld,A) & v6_hahnban1(B,A) & v7_hahnban1(B,A) ) ) ), file(hahnban1,rc3_hahnban1), []). fof(rc3_rlvect_1,axiom,( ? [A] : ( l2_rlvect_1(A) & ~ v3_struct_0(A) ) ), file(rlvect_1,rc3_rlvect_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_rlvect_1,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v1_rlvect_1(A) ) ), file(rlvect_1,rc4_rlvect_1), []). fof(rc4_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_rlvect_1,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) ), file(rlvect_1,rc5_rlvect_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_rlvect_1,axiom,( ? [A] : ( l2_rlvect_1(A) & ~ v3_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) ) ), file(rlvect_1,rc6_rlvect_1), []). fof(rc6_vectsp_1,axiom,( ? [A] : ( l3_vectsp_1(A) & v3_vectsp_1(A) ) ), file(vectsp_1,rc6_vectsp_1), []). 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_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_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k10_group_1(A,B,C) = k1_group_1(A,B,C) ) ), file(group_1,k10_group_1), []). fof(redefinition_k13_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k13_complex1(A,B) = k7_xcmplx_0(A,B) ) ), file(complex1,k13_complex1), []). fof(redefinition_k15_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_complex1(A) = k14_complex1(A) ) ), file(complex1,k15_complex1), []). fof(redefinition_k17_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k17_complex1(A) = k16_complex1(A) ) ), file(complex1,k17_complex1), []). fof(redefinition_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(A) = k16_complex1(A) ) ), file(complex1,k18_complex1), []). fof(redefinition_k1_nattra_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,k1_zfmisc_1(A)) ) => k1_nattra_1(A,B,C,D) = k7_relat_1(C,D) ) ), file(nattra_1,k1_nattra_1), []). 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_binop_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) ) => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ), file(binop_1,k2_binop_1), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). fof(redefinition_k3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_complex1(A) = k1_complex1(A) ) ), file(complex1,k3_complex1), []). fof(redefinition_k3_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k3_complfld(A) = k16_complex1(A) ) ), file(complfld,k3_complfld), []). 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_k4_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_complex1(A) = k2_complex1(A) ) ), file(complex1,k4_complex1), []). fof(redefinition_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_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_k6_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) ), file(real_1,k6_real_1), []). fof(redefinition_k6_supinf_1,axiom,( k6_supinf_1 = k1_numbers ), file(supinf_1,k6_supinf_1), []). fof(redefinition_k7_complex1,axiom,( k7_complex1 = k1_xcmplx_0 ), file(complex1,k7_complex1), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ), file(relset_1,k8_relset_1), []). fof(redefinition_k9_complex1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) ) => k9_complex1(A,B) = k3_xcmplx_0(A,B) ) ), file(complex1,k9_complex1), []). 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(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(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(t113_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( ! [E] : ( m1_subset_1(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => C = D ) ) ) ), file(funct_2,t113_funct_2), []). fof(t12_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( k5_arytm_0(A,B) = k5_arytm_0(C,D) => ( A = C & B = D ) ) ) ) ) ) ), file(arytm_0,t12_arytm_0), []). fof(t131_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k17_complex1(A) = 0 => A = 0 ) ) ), file(complex1,t131_complex1), []). fof(t139_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k17_complex1(k15_complex1(A)) = k17_complex1(A) ) ), file(complex1,t139_complex1), []). fof(t140_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xreal_0(k3_complex1(A),k17_complex1(A)) ) ), file(complex1,t140_complex1), []). fof(t153_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_real_1(k17_complex1(A),k17_complex1(B)) = k17_complex1(k7_xcmplx_0(A,B)) ) ) ), file(complex1,t153_complex1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t22_vectsp_4,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] : ( ( ~ 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) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ( F = D => k6_vectsp_1(A,E,C,F) = k6_vectsp_1(A,B,C,D) ) ) ) ) ) ) ) ), file(vectsp_4,t22_vectsp_4), []). fof(t27_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k5_arytm_0(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) ) ) ), file(complex1,t27_complex1), []). fof(t28_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( k3_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = A & k4_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = B ) ) ) ), file(complex1,t28_complex1), []). fof(t29_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) = A ) ), file(complex1,t29_complex1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t30_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( m1_vectsp_4(B,k1_complfld,A) => m1_rlsub_1(k10_hahnban1(B),k10_hahnban1(A)) ) ) ), file(hahnban1,t30_hahnban1), []). fof(t32_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v4_hahnban1(B,k1_complfld,A) & v7_hahnban1(B,A) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & v1_hahnban(B,k10_hahnban1(A)) & v4_hahnban(B,k10_hahnban1(A)) & m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ) ), file(hahnban1,t32_hahnban1), []). fof(t33_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld)) & v1_hahnban1(B,k1_complfld,A) & v2_hahnban1(B,k1_complfld,A) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) ) => ( v1_funct_1(k11_hahnban1(A,B)) & v1_funct_2(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & v2_hahnban(k11_hahnban1(A,B),k10_hahnban1(A)) & v3_hahnban(k11_hahnban1(A,B),k10_hahnban1(A)) & m2_relset_1(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ) ), file(hahnban1,t33_hahnban1), []). fof(t35_hahnban,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k6_supinf_1) & v1_hahnban(C,A) & v4_hahnban(C,A) & m2_relset_1(C,u1_struct_0(A),k6_supinf_1) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),k6_supinf_1) & v2_hahnban(D,B) & v3_hahnban(D,B) & m2_relset_1(D,u1_struct_0(B),k6_supinf_1) ) => ~ ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( E = F => r1_xreal_0(k8_funct_2(u1_struct_0(B),k6_supinf_1,D,E),k8_funct_2(u1_struct_0(A),k6_supinf_1,C,F)) ) ) ) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),k6_supinf_1) & v2_hahnban(E,A) & v3_hahnban(E,A) & m2_relset_1(E,u1_struct_0(A),k6_supinf_1) ) => ~ ( k2_partfun1(u1_struct_0(A),k6_supinf_1,E,u1_struct_0(B)) = D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r1_xreal_0(k8_funct_2(u1_struct_0(A),k6_supinf_1,E,F),k8_funct_2(u1_struct_0(A),k6_supinf_1,C,F)) ) ) ) ) ) ) ) ) ), file(hahnban,t35_hahnban), []). fof(t35_hahnban1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v12_vectsp_1(A,k1_complfld) & l4_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) & v2_hahnban(B,k10_hahnban1(A)) & v3_hahnban(B,k10_hahnban1(A)) & m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) => ( v1_funct_1(k16_hahnban1(A,B)) & v1_funct_2(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) & v1_hahnban1(k16_hahnban1(A,B),k1_complfld,A) & v2_hahnban1(k16_hahnban1(A,B),k1_complfld,A) & m2_relset_1(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) ) ) ) ), file(hahnban1,t35_hahnban1), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_hahnban1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k17_complex1(k5_arytm_0(A,0)) = k18_complex1(A) ) ), file(hahnban1,t4_hahnban1), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). fof(t5_hahnban1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => k2_xcmplx_0(k17_complex1(A),k3_xcmplx_0(0,k7_complex1)) = k3_xcmplx_0(k7_xcmplx_0(k15_complex1(A),k2_xcmplx_0(k17_complex1(A),k3_xcmplx_0(0,k7_complex1))),A) ) ), file(hahnban1,t5_hahnban1), []). 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(t60_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != 0 => k7_xcmplx_0(A,A) = 1 ) ) ), file(xcmplx_1,t60_xcmplx_1), []). fof(t6_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( A = C & B = D ) => k10_group_1(k1_complfld,A,B) = k3_xcmplx_0(C,D) ) ) ) ) ) ), file(complfld,t6_complfld), []). fof(t72_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t72_funct_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).