% Mizar ND problem: t1_bhsp_4,bhsp_4,89,63 fof(dh_c1_3__bhsp_4,definition, ( ( ( ~ v3_struct_0(c1_3__bhsp_4) & v3_rlvect_1(c1_3__bhsp_4) & v4_rlvect_1(c1_3__bhsp_4) & v5_rlvect_1(c1_3__bhsp_4) & v6_rlvect_1(c1_3__bhsp_4) & v7_rlvect_1(c1_3__bhsp_4) & v2_bhsp_1(c1_3__bhsp_4) & l1_bhsp_1(c1_3__bhsp_4) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,A),k1_bhsp_4(c1_3__bhsp_4,B)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,A,B)) ) ) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & v2_bhsp_1(C) & l1_bhsp_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(C)) & m2_relset_1(D,k5_numbers,u1_struct_0(C)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,u1_struct_0(C)) & m2_relset_1(E,k5_numbers,u1_struct_0(C)) ) => k8_bhsp_1(C,k1_bhsp_4(C,D),k1_bhsp_4(C,E)) = k1_bhsp_4(C,k8_bhsp_1(C,D,E)) ) ) ) ), introduced(definition,[new_symbol(c1_3__bhsp_4),file(bhsp_4,c1_3__bhsp_4)]), [interesting(0.8),axiom,file(bhsp_4,c1_3__bhsp_4)]). fof(dh_c2_3__bhsp_4,definition, ( ( ( v1_funct_1(c2_3__bhsp_4) & v1_funct_2(c2_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(c2_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,A)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,A)) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(C,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,B),k1_bhsp_4(c1_3__bhsp_4,C)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,B,C)) ) ) ), introduced(definition,[new_symbol(c2_3__bhsp_4),file(bhsp_4,c2_3__bhsp_4)]), [interesting(0.8),axiom,file(bhsp_4,c2_3__bhsp_4)]). fof(dh_c3_3__bhsp_4,definition, ( ( ( v1_funct_1(c3_3__bhsp_4) & v1_funct_2(c3_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(c3_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4)) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,A)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,A)) ) ), introduced(definition,[new_symbol(c3_3__bhsp_4),file(bhsp_4,c3_3__bhsp_4)]), [interesting(0.8),axiom,file(bhsp_4,c3_3__bhsp_4)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). fof(redefinition_k1_domain_1,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(redefinition_k8_funct_2,definition,( ! [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), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_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), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). 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), [interesting(0.9),axiom,file(rlvect_1,u1_rlvect_1)]). fof(cc12_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc18_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_xreal_0,theorem,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]). fof(cc20_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc2_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]). fof(cc3_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc3_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]). fof(cc4_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), [interesting(0.9),axiom,file(int_1,cc4_int_1)]). fof(cc4_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]). fof(cc5_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]). fof(cc6_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]). fof(cc7_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]). fof(cc8_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]). fof(fc10_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]). fof(fc11_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]). fof(fc12_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]). fof(fc1_int_1,theorem,( ! [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), [interesting(0.9),axiom,file(int_1,fc1_int_1)]). fof(fc1_seq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_xcmplx_0(k1_funct_1(A,B)) & v1_xreal_0(k1_funct_1(A,B)) ) ) ), file(seq_1,fc1_seq_1), [interesting(0.9),axiom,file(seq_1,fc1_seq_1)]). fof(fc3_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]). fof(fc6_int_1,theorem,( ! [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), [interesting(0.9),axiom,file(int_1,fc6_int_1)]). fof(fc6_membered,theorem, ( 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), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(fc7_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]). fof(fc8_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]). fof(fc9_xreal_0,theorem,( ! [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), [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]). fof(rc1_int_1,theorem,( ? [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), [interesting(0.9),axiom,file(int_1,rc1_int_1)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc1_seq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(seq_1,rc1_seq_1), [interesting(0.9),axiom,file(seq_1,rc1_seq_1)]). fof(rc1_xreal_0,theorem,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]). fof(rc2_int_1,theorem,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), [interesting(0.9),axiom,file(int_1,rc2_int_1)]). fof(rc2_xreal_0,theorem,( ? [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), [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]). fof(rc3_xreal_0,theorem,( ? [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), [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]). fof(rc4_struct_0,theorem,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), [interesting(0.9),axiom,file(struct_0,rc4_struct_0)]). fof(rc4_xreal_0,theorem,( ? [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), [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [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), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(existence_l2_rlvect_1,axiom,( ? [A] : l2_rlvect_1(A) ), file(rlvect_1,l2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,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), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k3_normsp_1,axiom,( ! [A,B,C] : ( ( ~ 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) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k5_numbers,u1_struct_0(A)) & m2_relset_1(k3_normsp_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(normsp_1,k3_normsp_1), [interesting(0.9),axiom,file(normsp_1,k3_normsp_1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(dt_l2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => l1_rlvect_1(A) ) ), file(rlvect_1,l2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc1_relset_1,theorem,( ! [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), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc1_seq_1,theorem,( ! [A,B] : ( v2_membered(B) => ! [C] : ( m1_relset_1(C,A,B) => ( v1_funct_1(C) => ( v1_funct_1(C) & v1_seq_1(C) ) ) ) ) ), file(seq_1,cc1_seq_1), [interesting(0.9),axiom,file(seq_1,cc1_seq_1)]). fof(cc2_int_1,theorem,( ! [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), [interesting(0.9),axiom,file(int_1,cc2_int_1)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(cc9_membered,theorem,( ! [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), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). fof(fc1_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]). fof(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). fof(rc3_struct_0,theorem,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]). fof(rc5_struct_0,theorem,( ! [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), [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,( k2_xcmplx_0(1,0) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). fof(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(d3_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ), file(rlvect_1,d3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d3_rlvect_1)]). fof(commutativity_k1_nat_1,theorem,( ! [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), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(commutativity_k4_rlvect_1,theorem,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(commutativity_k8_bhsp_1,theorem,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => k8_bhsp_1(A,B,C) = k8_bhsp_1(A,C,B) ) ), file(bhsp_1,k8_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k8_bhsp_1)]). fof(existence_l1_bhsp_1,axiom,( ? [A] : l1_bhsp_1(A) ), file(bhsp_1,l1_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,l1_bhsp_1)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_k1_nat_1,definition,( ! [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), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(redefinition_k2_normsp_1,definition,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => k2_normsp_1(A,B,C) = k1_funct_1(B,C) ) ), file(normsp_1,k2_normsp_1), [interesting(0.9),axiom,file(normsp_1,k2_normsp_1)]). fof(redefinition_k4_rlvect_1,definition,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(redefinition_k8_bhsp_1,definition,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => k8_bhsp_1(A,B,C) = k3_normsp_1(A,B,C) ) ), file(bhsp_1,k8_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k8_bhsp_1)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(redefinition_m2_subset_1,definition,( ! [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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k1_bhsp_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v1_funct_1(k1_bhsp_4(A,B)) & v1_funct_2(k1_bhsp_4(A,B),k5_numbers,u1_struct_0(A)) & m2_relset_1(k1_bhsp_4(A,B),k5_numbers,u1_struct_0(A)) ) ) ), file(bhsp_4,k1_bhsp_4), [interesting(0.9),axiom,file(bhsp_4,k1_bhsp_4)]). 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), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k2_normsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k2_normsp_1(A,B,C),u1_struct_0(A)) ) ), file(normsp_1,k2_normsp_1), [interesting(0.9),axiom,file(normsp_1,k2_normsp_1)]). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_k8_bhsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m1_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( v1_funct_1(k8_bhsp_1(A,B,C)) & v1_funct_2(k8_bhsp_1(A,B,C),k5_numbers,u1_struct_0(A)) & m2_relset_1(k8_bhsp_1(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(bhsp_1,k8_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k8_bhsp_1)]). fof(dt_l1_bhsp_1,axiom,( ! [A] : ( l1_bhsp_1(A) => l2_rlvect_1(A) ) ), file(bhsp_1,l1_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,l1_bhsp_1)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,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), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(dt_c1_3__bhsp_4,assumption, ( ~ v3_struct_0(c1_3__bhsp_4) & v3_rlvect_1(c1_3__bhsp_4) & v4_rlvect_1(c1_3__bhsp_4) & v5_rlvect_1(c1_3__bhsp_4) & v6_rlvect_1(c1_3__bhsp_4) & v7_rlvect_1(c1_3__bhsp_4) & v2_bhsp_1(c1_3__bhsp_4) & l1_bhsp_1(c1_3__bhsp_4) ), introduced(assumption,[file(bhsp_4,c1_3__bhsp_4)]), [interesting(0.8),axiom,file(bhsp_4,c1_3__bhsp_4)]). fof(dt_c2_3__bhsp_4,assumption, ( v1_funct_1(c2_3__bhsp_4) & v1_funct_2(c2_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(c2_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ), introduced(assumption,[file(bhsp_4,c2_3__bhsp_4)]), [interesting(0.8),axiom,file(bhsp_4,c2_3__bhsp_4)]). fof(dt_c3_3__bhsp_4,assumption, ( v1_funct_1(c3_3__bhsp_4) & v1_funct_2(c3_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(c3_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ), introduced(assumption,[file(bhsp_4,c3_3__bhsp_4)]), [interesting(0.8),axiom,file(bhsp_4,c3_3__bhsp_4)]). fof(fc2_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(dh_c1_3_2__bhsp_4,definition, ( ( m2_subset_1(c1_3_2__bhsp_4,k1_numbers,k5_numbers) => k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(c1_3_2__bhsp_4,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(A,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),A),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(A,1))) ) ), introduced(definition,[new_symbol(c1_3_2__bhsp_4),file(bhsp_4,c1_3_2__bhsp_4)]), [interesting(0.65),axiom,file(bhsp_4,c1_3_2__bhsp_4)]). fof(dt_c1_3_2__bhsp_4,assumption,( m2_subset_1(c1_3_2__bhsp_4,k1_numbers,k5_numbers) ), introduced(assumption,[file(bhsp_4,c1_3_2__bhsp_4)]), [interesting(0.65),axiom,file(bhsp_4,c1_3_2__bhsp_4)]). fof(d5_normsp_1,definition,( ! [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] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) ) => ( D = k3_normsp_1(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k2_normsp_1(A,D,E) = k4_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,C,E)) ) ) ) ) ) ) ), file(normsp_1,d5_normsp_1), [interesting(0.9),axiom,file(normsp_1,d5_normsp_1)]). fof(e1_3_2_1__bhsp_4,plain,( k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(c1_3_2__bhsp_4,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1)),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l2_rlvect_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k8_bhsp_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k3_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_k8_bhsp_1,dt_l2_rlvect_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc1_numerals,spc1_boole,d5_normsp_1]), [interesting(0.5),file(bhsp_4,e1_3_2_1__bhsp_4),[file(bhsp_4,e1_3_2_1__bhsp_4)]]). fof(d1_bhsp_4,definition,( ! [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) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( C = k1_bhsp_4(A,B) <=> ( k2_normsp_1(A,C,0) = k2_normsp_1(A,B,0) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k2_normsp_1(A,C,k1_nat_1(D,1)) = k4_rlvect_1(A,k2_normsp_1(A,C,D),k2_normsp_1(A,B,k1_nat_1(D,1))) ) ) ) ) ) ) ), file(bhsp_4,d1_bhsp_4), [interesting(0.9),axiom,file(bhsp_4,d1_bhsp_4)]). fof(e2_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1)),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) = k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,existence_l1_bhsp_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_l1_bhsp_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d1_bhsp_4]), [interesting(0.5),file(bhsp_4,e2_3_2_1__bhsp_4),[file(bhsp_4,e2_3_2_1__bhsp_4)]]). fof(e3_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) = k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1)),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,existence_l1_bhsp_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_l1_bhsp_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d1_bhsp_4]), [interesting(0.5),file(bhsp_4,e3_3_2_1__bhsp_4),[file(bhsp_4,e3_3_2_1__bhsp_4)]]). fof(d6_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ( v4_rlvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ), file(rlvect_1,d6_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d6_rlvect_1)]). fof(e4_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1)),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4))) = k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[reflexivity_r1_tarski,fc1_seq_1,rc1_seq_1,antisymmetry_r2_hidden,existence_l2_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_k5_ordinal2,dt_l2_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_ordinal2,fc3_xreal_0,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,spc6_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_bhsp_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_domain_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_bhsp_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_rlvect_1,cc15_membered,cc2_int_1,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k2_normsp_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,d3_rlvect_1,spc1_numerals,spc1_boole,d6_rlvect_1]), [interesting(0.5),file(bhsp_4,e4_3_2_1__bhsp_4),[file(bhsp_4,e4_3_2_1__bhsp_4)]]). fof(e5_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)) = k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1)),k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1)))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[reflexivity_r1_tarski,fc1_seq_1,rc1_seq_1,antisymmetry_r2_hidden,existence_l2_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_k5_ordinal2,dt_l2_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_ordinal2,fc3_xreal_0,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,spc6_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_bhsp_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_domain_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_bhsp_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_rlvect_1,cc15_membered,cc2_int_1,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k2_normsp_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,d3_rlvect_1,spc1_numerals,spc1_boole,d6_rlvect_1]), [interesting(0.5),file(bhsp_4,e5_3_2_1__bhsp_4),[file(bhsp_4,e5_3_2_1__bhsp_4)]]). fof(e6_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1)),k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,k1_nat_1(c1_3_2__bhsp_4,1)))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)) = k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l2_rlvect_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k8_bhsp_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k3_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_k8_bhsp_1,dt_l2_rlvect_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc1_numerals,spc1_boole,d5_normsp_1]), [interesting(0.5),file(bhsp_4,e6_3_2_1__bhsp_4),[file(bhsp_4,e6_3_2_1__bhsp_4)]]). fof(e7_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)) = k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[reflexivity_r1_tarski,fc1_seq_1,rc1_seq_1,antisymmetry_r2_hidden,existence_l2_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_k5_ordinal2,dt_l2_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_ordinal2,fc3_xreal_0,fc5_membered,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,spc6_arithm,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_bhsp_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_domain_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_normsp_1,dt_k5_numbers,dt_k8_funct_2,dt_l1_bhsp_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_rlvect_1,cc15_membered,cc2_int_1,fc1_struct_0,fc2_membered,rc3_struct_0,rc4_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k8_bhsp_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k2_normsp_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_k8_bhsp_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,d3_rlvect_1,spc1_numerals,spc1_boole,d6_rlvect_1]), [interesting(0.5),file(bhsp_4,e7_3_2_1__bhsp_4),[file(bhsp_4,e7_3_2_1__bhsp_4)]]). fof(e8_3_2_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),c1_3_2__bhsp_4)),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l2_rlvect_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k8_bhsp_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k3_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_k8_bhsp_1,dt_l2_rlvect_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc1_numerals,spc1_boole,d5_normsp_1]), [interesting(0.5),file(bhsp_4,e8_3_2_1__bhsp_4),[file(bhsp_4,e8_3_2_1__bhsp_4)]]). fof(e1_3_2__bhsp_4,plain,( k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(c1_3_2__bhsp_4,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[e1_3_2_1__bhsp_4,e2_3_2_1__bhsp_4,e3_3_2_1__bhsp_4,e4_3_2_1__bhsp_4,e5_3_2_1__bhsp_4,e6_3_2_1__bhsp_4,e7_3_2_1__bhsp_4,e8_3_2_1__bhsp_4]), [interesting(0.65),file(bhsp_4,e1_3_2__bhsp_4),[file(bhsp_4,e1_3_2__bhsp_4)]]). fof(i2_3_2__bhsp_4,theorem,( $true ), introduced(tautology,[file(bhsp_4,i2_3_2__bhsp_4)]), [interesting(0.65),trivial,file(bhsp_4,i2_3_2__bhsp_4)]). fof(i1_3_2__bhsp_4,plain,( k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(c1_3_2__bhsp_4,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(conclusion,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c1_3_2__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[e1_3_2__bhsp_4,i2_3_2__bhsp_4]), [interesting(0.65),file(bhsp_4,i1_3_2__bhsp_4),[file(bhsp_4,i1_3_2__bhsp_4)]]). fof(i1_3_2_tmp__bhsp_4,plain, ( m2_subset_1(c1_3_2__bhsp_4,k1_numbers,k5_numbers) => k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(c1_3_2__bhsp_4,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),c1_3_2__bhsp_4),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(c1_3_2__bhsp_4,1))) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4]),discharge_asm(discharge,[dt_c1_3_2__bhsp_4])],[dt_c1_3_2__bhsp_4,i1_3_2__bhsp_4]), [interesting(0.8),e2_3__bhsp_4]). fof(e2_3__bhsp_4,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),k1_nat_1(A,1)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),A),k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),k1_nat_1(A,1))) ) ), inference(let,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[i1_3_2_tmp__bhsp_4,dh_c1_3_2__bhsp_4]), [interesting(0.8),file(bhsp_4,e2_3__bhsp_4),[file(bhsp_4,e2_3__bhsp_4)]]). fof(e1_3_1__bhsp_4,plain,( k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),0) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),0),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_seq_1,fc6_membered,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l2_rlvect_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k8_bhsp_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_numbers,dt_k2_normsp_1,dt_k3_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_k8_bhsp_1,dt_l2_rlvect_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc0_boole,d5_normsp_1]), [interesting(0.65),file(bhsp_4,e1_3_1__bhsp_4),[file(bhsp_4,e1_3_1__bhsp_4)]]). fof(e2_3_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),0),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),0)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,0),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,existence_l1_bhsp_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_l1_bhsp_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d1_bhsp_4]), [interesting(0.65),file(bhsp_4,e2_3_1__bhsp_4),[file(bhsp_4,e2_3_1__bhsp_4)]]). fof(e3_3_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,0),k2_normsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4),0)) = k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,0),k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,existence_l1_bhsp_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_l1_bhsp_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,d1_bhsp_4]), [interesting(0.65),file(bhsp_4,e3_3_1__bhsp_4),[file(bhsp_4,e3_3_1__bhsp_4)]]). fof(e4_3_1__bhsp_4,plain,( k4_rlvect_1(c1_3__bhsp_4,k2_normsp_1(c1_3__bhsp_4,c2_3__bhsp_4,0),k2_normsp_1(c1_3__bhsp_4,c3_3__bhsp_4,0)) = k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),0) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_seq_1,fc6_membered,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l2_rlvect_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k8_bhsp_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_normsp_1,dt_k3_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_k8_bhsp_1,dt_l2_rlvect_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc0_boole,d5_normsp_1]), [interesting(0.65),file(bhsp_4,e4_3_1__bhsp_4),[file(bhsp_4,e4_3_1__bhsp_4)]]). fof(e1_3__bhsp_4,plain,( k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)),0) = k2_normsp_1(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4),0) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[e1_3_1__bhsp_4,e2_3_1__bhsp_4,e3_3_1__bhsp_4,e4_3_1__bhsp_4]), [interesting(0.8),file(bhsp_4,e1_3__bhsp_4),[file(bhsp_4,e1_3__bhsp_4)]]). fof(e3_3__bhsp_4,plain,( k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[dt_k4_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_xreal_0,cc20_membered,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_int_1,fc1_seq_1,fc3_xreal_0,fc6_int_1,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,rc1_int_1,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_int_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,spc6_arithm,t1_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_normsp_1,dt_k5_ordinal2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc1_seq_1,cc2_int_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc5_membered,rc3_struct_0,rc5_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r0_r1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_rlvect_1,commutativity_k1_nat_1,commutativity_k4_rlvect_1,commutativity_k8_bhsp_1,existence_l1_bhsp_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_normsp_1,redefinition_k4_rlvect_1,redefinition_k5_numbers,redefinition_k8_bhsp_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_bhsp_4,dt_k1_nat_1,dt_k1_numbers,dt_k2_normsp_1,dt_k4_rlvect_1,dt_k5_numbers,dt_k8_bhsp_1,dt_l1_bhsp_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4,fc2_membered,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_3__bhsp_4,e1_3__bhsp_4,d1_bhsp_4]), [interesting(0.8),file(bhsp_4,e3_3__bhsp_4),[file(bhsp_4,e3_3__bhsp_4)]]). fof(i4_3__bhsp_4,theorem,( $true ), introduced(tautology,[file(bhsp_4,i4_3__bhsp_4)]), [interesting(0.8),trivial,file(bhsp_4,i4_3__bhsp_4)]). fof(i3_3__bhsp_4,plain,( k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4)) ), inference(conclusion,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4,dt_c3_3__bhsp_4])],[e3_3__bhsp_4,i4_3__bhsp_4]), [interesting(0.8),file(bhsp_4,i3_3__bhsp_4),[file(bhsp_4,i3_3__bhsp_4)]]). fof(i3_3_tmp__bhsp_4,plain, ( ( v1_funct_1(c3_3__bhsp_4) & v1_funct_2(c3_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(c3_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,c3_3__bhsp_4)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,c3_3__bhsp_4)) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4]),discharge_asm(discharge,[dt_c3_3__bhsp_4])],[dt_c3_3__bhsp_4,i3_3__bhsp_4]), [interesting(0.8),i2_3__bhsp_4]). fof(i2_3__bhsp_4,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,A)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,A)) ) ), inference(let,[status(thm),assumptions([dt_c1_3__bhsp_4,dt_c2_3__bhsp_4])],[i3_3_tmp__bhsp_4,dh_c3_3__bhsp_4]), [interesting(0.8),file(bhsp_4,i2_3__bhsp_4),[file(bhsp_4,i2_3__bhsp_4)]]). fof(i2_3_tmp__bhsp_4,plain, ( ( v1_funct_1(c2_3__bhsp_4) & v1_funct_2(c2_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(c2_3__bhsp_4,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,c2_3__bhsp_4),k1_bhsp_4(c1_3__bhsp_4,A)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,c2_3__bhsp_4,A)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bhsp_4]),discharge_asm(discharge,[dt_c2_3__bhsp_4])],[dt_c2_3__bhsp_4,i2_3__bhsp_4]), [interesting(0.8),i1_3__bhsp_4]). fof(i1_3__bhsp_4,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,A),k1_bhsp_4(c1_3__bhsp_4,B)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,A,B)) ) ) ), inference(let,[status(thm),assumptions([dt_c1_3__bhsp_4])],[i2_3_tmp__bhsp_4,dh_c2_3__bhsp_4]), [interesting(0.8),file(bhsp_4,i1_3__bhsp_4),[file(bhsp_4,i1_3__bhsp_4)]]). fof(i1_3_tmp__bhsp_4,plain, ( ( ~ v3_struct_0(c1_3__bhsp_4) & v3_rlvect_1(c1_3__bhsp_4) & v4_rlvect_1(c1_3__bhsp_4) & v5_rlvect_1(c1_3__bhsp_4) & v6_rlvect_1(c1_3__bhsp_4) & v7_rlvect_1(c1_3__bhsp_4) & v2_bhsp_1(c1_3__bhsp_4) & l1_bhsp_1(c1_3__bhsp_4) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(A,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) & m2_relset_1(B,k5_numbers,u1_struct_0(c1_3__bhsp_4)) ) => k8_bhsp_1(c1_3__bhsp_4,k1_bhsp_4(c1_3__bhsp_4,A),k1_bhsp_4(c1_3__bhsp_4,B)) = k1_bhsp_4(c1_3__bhsp_4,k8_bhsp_1(c1_3__bhsp_4,A,B)) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__bhsp_4])],[dt_c1_3__bhsp_4,i1_3__bhsp_4]), [interesting(1),t1_bhsp_4]). fof(t1_bhsp_4,theorem,( ! [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) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => k8_bhsp_1(A,k1_bhsp_4(A,B),k1_bhsp_4(A,C)) = k1_bhsp_4(A,k8_bhsp_1(A,B,C)) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_3_tmp__bhsp_4,dh_c1_3__bhsp_4]), [interesting(1),file(bhsp_4,t1_bhsp_4),[file(bhsp_4,t1_bhsp_4)]]).