% Mizar ND problem: t2_bhsp_6,bhsp_6,127,33 fof(dh_c1_3__bhsp_6,definition, ( ( ( ~ v3_struct_0(c1_3__bhsp_6) & v3_rlvect_1(c1_3__bhsp_6) & v4_rlvect_1(c1_3__bhsp_6) & v5_rlvect_1(c1_3__bhsp_6) & v6_rlvect_1(c1_3__bhsp_6) & v7_rlvect_1(c1_3__bhsp_6) & v2_bhsp_1(c1_3__bhsp_6) & l1_bhsp_1(c1_3__bhsp_6) ) => ( ( v1_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v2_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v1_setwiseo(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(A,B) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( C = k4_subset_1(u1_struct_0(c1_3__bhsp_6),A,B) => k1_bhsp_6(c1_3__bhsp_6,C) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,A),k1_bhsp_6(c1_3__bhsp_6,B)) ) ) ) ) ) ) ) => ! [D] : ( ( ~ v3_struct_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v5_rlvect_1(D) & v6_rlvect_1(D) & v7_rlvect_1(D) & v2_bhsp_1(D) & l1_bhsp_1(D) ) => ( ( v1_binop_1(u1_rlvect_1(D),u1_struct_0(D)) & v2_binop_1(u1_rlvect_1(D),u1_struct_0(D)) & v1_setwiseo(u1_rlvect_1(D),u1_struct_0(D)) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) ) => ! [F] : ( ( v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D))) ) => ( r1_xboole_0(E,F) => ! [G] : ( ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D))) ) => ( G = k4_subset_1(u1_struct_0(D),E,F) => k1_bhsp_6(D,G) = k4_rlvect_1(D,k1_bhsp_6(D,E),k1_bhsp_6(D,F)) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_3__bhsp_6),file(bhsp_6,c1_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c1_3__bhsp_6)]). fof(e1_3__bhsp_6,assumption, ( v1_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v2_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v1_setwiseo(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) ), introduced(assumption,[file(bhsp_6,e1_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,e1_3__bhsp_6)]). fof(dh_c2_3__bhsp_6,definition, ( ( ( v1_finset_1(c2_3__bhsp_6) & m1_subset_1(c2_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(c2_3__bhsp_6,A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( B = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,A) => k1_bhsp_6(c1_3__bhsp_6,B) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,A)) ) ) ) ) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(C,D) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( E = k4_subset_1(u1_struct_0(c1_3__bhsp_6),C,D) => k1_bhsp_6(c1_3__bhsp_6,E) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,C),k1_bhsp_6(c1_3__bhsp_6,D)) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_3__bhsp_6),file(bhsp_6,c2_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c2_3__bhsp_6)]). fof(dh_c3_3__bhsp_6,definition, ( ( ( v1_finset_1(c3_3__bhsp_6) & m1_subset_1(c3_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(c2_3__bhsp_6,c3_3__bhsp_6) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( A = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,A) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ) ) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(c2_3__bhsp_6,B) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( C = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,B) => k1_bhsp_6(c1_3__bhsp_6,C) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,B)) ) ) ) ) ), introduced(definition,[new_symbol(c3_3__bhsp_6),file(bhsp_6,c3_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c3_3__bhsp_6)]). fof(e2_3__bhsp_6,assumption,( r1_xboole_0(c2_3__bhsp_6,c3_3__bhsp_6) ), introduced(assumption,[file(bhsp_6,e2_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,e2_3__bhsp_6)]). fof(dh_c4_3__bhsp_6,definition, ( ( ( v1_finset_1(c4_3__bhsp_6) & m1_subset_1(c4_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( c4_3__bhsp_6 = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,c4_3__bhsp_6) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( A = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,A) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ) ), introduced(definition,[new_symbol(c4_3__bhsp_6),file(bhsp_6,c4_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c4_3__bhsp_6)]). fof(e3_3__bhsp_6,assumption,( c4_3__bhsp_6 = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) ), introduced(assumption,[file(bhsp_6,e3_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,e3_3__bhsp_6)]). 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_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(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(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_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(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). 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(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_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). 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(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_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(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_k6_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), [interesting(0.9),axiom,file(relat_1,k6_relat_1)]). 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(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(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(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(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_funct_2,theorem,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). 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(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(fc2_funct_1,theorem,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) ) ), file(funct_1,fc2_funct_1), [interesting(0.9),axiom,file(funct_1,fc2_funct_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(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(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). 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(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(redefinition_k6_partfun1,definition,( ! [A] : k6_partfun1(A) = k6_relat_1(A) ), file(partfun1,k6_partfun1), [interesting(0.9),axiom,file(partfun1,k6_partfun1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]). 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_k6_partfun1,axiom,( ! [A] : ( v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A) ) ), file(partfun1,k6_partfun1), [interesting(0.9),axiom,file(partfun1,k6_partfun1)]). 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(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(cc1_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(cc1_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). 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(cc2_funct_1,theorem,( ! [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), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(cc5_funct_2,theorem,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]). fof(cc6_funct_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]). fof(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). 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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). fof(rc1_funct_2,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). 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(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). 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(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(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(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(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_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(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_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_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(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(redefinition_k4_relset_1,definition,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_relset_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_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(dt_k1_bhsp_6,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_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k1_bhsp_6(A,B),u1_struct_0(A)) ) ), file(bhsp_6,k1_bhsp_6), [interesting(0.9),axiom,file(bhsp_6,k1_bhsp_6)]). 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_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_k5_bhsp_5,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & 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_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) ) => m1_subset_1(k5_bhsp_5(A,B,C,D,E),A) ) ), file(bhsp_5,k5_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,k5_bhsp_5)]). 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_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_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), [interesting(0.9),axiom,file(rlvect_1,u1_rlvect_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_6,assumption, ( ~ v3_struct_0(c1_3__bhsp_6) & v3_rlvect_1(c1_3__bhsp_6) & v4_rlvect_1(c1_3__bhsp_6) & v5_rlvect_1(c1_3__bhsp_6) & v6_rlvect_1(c1_3__bhsp_6) & v7_rlvect_1(c1_3__bhsp_6) & v2_bhsp_1(c1_3__bhsp_6) & l1_bhsp_1(c1_3__bhsp_6) ), introduced(assumption,[file(bhsp_6,c1_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c1_3__bhsp_6)]). fof(dt_c2_3__bhsp_6,assumption, ( v1_finset_1(c2_3__bhsp_6) & m1_subset_1(c2_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ), introduced(assumption,[file(bhsp_6,c2_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c2_3__bhsp_6)]). fof(dt_c3_3__bhsp_6,assumption, ( v1_finset_1(c3_3__bhsp_6) & m1_subset_1(c3_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ), introduced(assumption,[file(bhsp_6,c3_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c3_3__bhsp_6)]). fof(dt_c4_3__bhsp_6,assumption, ( v1_finset_1(c4_3__bhsp_6) & m1_subset_1(c4_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ), introduced(assumption,[file(bhsp_6,c4_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c4_3__bhsp_6)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). 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(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(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). 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(de_c5_3__bhsp_6,definition,( c5_3__bhsp_6 = k6_partfun1(u1_struct_0(c1_3__bhsp_6)) ), introduced(definition,[new_symbol(c5_3__bhsp_6),file(bhsp_6,c5_3__bhsp_6)]), [interesting(0.8),axiom,file(bhsp_6,c5_3__bhsp_6)]). fof(e4_3__bhsp_6,plain, ( v1_funct_1(k6_partfun1(u1_struct_0(c1_3__bhsp_6))) & v1_funct_2(k6_partfun1(u1_struct_0(c1_3__bhsp_6)),u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & m2_relset_1(k6_partfun1(u1_struct_0(c1_3__bhsp_6)),u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_l2_struct_0,dt_l2_struct_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,dt_k1_xboole_0,dt_l1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc3_funct_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l2_rlvect_1,dt_l2_rlvect_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k6_relat_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,fc2_funct_1,rc3_struct_0,t3_subset,existence_m2_relset_1,redefinition_k6_partfun1,redefinition_m2_relset_1,dt_k6_partfun1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__bhsp_6]), [interesting(0.8),file(bhsp_6,e4_3__bhsp_6),[file(bhsp_6,e4_3__bhsp_6)]]). fof(dt_c5_3__bhsp_6,plain, ( v1_funct_1(c5_3__bhsp_6) & v1_funct_2(c5_3__bhsp_6,u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & m2_relset_1(c5_3__bhsp_6,u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_l2_struct_0,dt_l2_struct_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,dt_k1_xboole_0,dt_l1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc3_funct_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l2_rlvect_1,dt_l2_rlvect_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k6_relat_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,fc2_funct_1,rc3_struct_0,t3_subset,existence_m2_relset_1,redefinition_k6_partfun1,redefinition_m2_relset_1,dt_k6_partfun1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__bhsp_6,de_c5_3__bhsp_6,e4_3__bhsp_6]), [interesting(0.8),file(bhsp_6,c5_3__bhsp_6),[file(bhsp_6,c5_3__bhsp_6)]]). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), [interesting(0.9),axiom,file(binop_1,k1_binop_1)]). fof(fc22_membered,theorem,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), [interesting(0.9),axiom,file(membered,fc22_membered)]). fof(fc23_membered,theorem,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), [interesting(0.9),axiom,file(membered,fc23_membered)]). fof(fc24_membered,theorem,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), [interesting(0.9),axiom,file(membered,fc24_membered)]). fof(fc25_membered,theorem,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), [interesting(0.9),axiom,file(membered,fc25_membered)]). fof(fc26_membered,theorem,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), [interesting(0.9),axiom,file(membered,fc26_membered)]). fof(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). fof(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(commutativity_k4_subset_1,theorem,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(idempotence_k4_subset_1,theorem,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(symmetry_r1_xboole_0,theorem,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]). fof(redefinition_k2_binop_1,definition,( ! [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), [interesting(0.9),axiom,file(binop_1,k2_binop_1)]). fof(redefinition_k4_subset_1,definition,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). 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), [interesting(0.9),axiom,file(binop_1,k2_binop_1)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), [interesting(0.9),axiom,file(subset_1,k4_subset_1)]). fof(fc9_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]). fof(d1_funct_2,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), [interesting(0.9),axiom,file(funct_2,d1_funct_2)]). fof(e6_3__bhsp_6,plain,( k4_relset_1(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),c5_3__bhsp_6) = u1_struct_0(c1_3__bhsp_6) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_6])],[existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,existence_l1_rlvect_1,dt_l1_rlvect_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_rlvect_1,dt_k6_relat_1,dt_l2_rlvect_1,cc1_funct_2,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc14_finset_1,fc2_funct_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_nat_1,rc1_xreal_0,rc2_funct_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,redefinition_k6_partfun1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k6_partfun1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,fc6_membered,t6_boole,d1_funct_2]), [interesting(0.8),file(bhsp_6,e6_3__bhsp_6),[file(bhsp_6,e6_3__bhsp_6)]]). fof(t14_bhsp_5,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) ) => ( ( v1_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(C,A) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r1_xboole_0(D,E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,A) & m2_relset_1(F,B,A) ) => ( ( r1_tarski(D,k1_relat_1(F)) & r1_tarski(E,k1_relat_1(F)) ) => ! [G] : ( ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(B)) ) => ( G = k2_xboole_0(D,E) => k5_bhsp_5(A,B,C,G,F) = k2_binop_1(A,A,A,C,k5_bhsp_5(A,B,C,D,F),k5_bhsp_5(A,B,C,E,F)) ) ) ) ) ) ) ) ) ) ) ) ), file(bhsp_5,t14_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,t14_bhsp_5)]). fof(e1_3_1__bhsp_6,plain,( k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c4_3__bhsp_6,c5_3__bhsp_6) = k2_binop_1(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c2_3__bhsp_6,c5_3__bhsp_6),k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c3_3__bhsp_6,c5_3__bhsp_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,dt_c4_3__bhsp_6,e1_3__bhsp_6,e2_3__bhsp_6,e3_3__bhsp_6,dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k6_relat_1,dt_l2_rlvect_1,dt_l2_struct_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,fc2_funct_1,rc1_nat_1,rc1_xreal_0,rc3_funct_1,rc4_struct_0,antisymmetry_r2_hidden,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_relset_1,redefinition_k6_partfun1,dt_k1_binop_1,dt_k1_xboole_0,dt_k6_partfun1,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc3_struct_0,rc5_struct_0,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k4_subset_1,idempotence_k4_subset_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_k2_binop_1,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k4_subset_1,dt_k5_bhsp_5,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,dt_c4_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,fc9_finset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,e1_3__bhsp_6,e2_3__bhsp_6,e3_3__bhsp_6,e6_3__bhsp_6,t14_bhsp_5]), [interesting(0.65),file(bhsp_6,e1_3_1__bhsp_6),[file(bhsp_6,e1_3_1__bhsp_6)]]). fof(t5_rlvect_1,theorem,( ! [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) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) ), file(rlvect_1,t5_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,t5_rlvect_1)]). fof(e2_3_1__bhsp_6,plain,( k2_binop_1(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c2_3__bhsp_6,c5_3__bhsp_6),k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c3_3__bhsp_6,c5_3__bhsp_6)) = k4_rlvect_1(c1_3__bhsp_6,k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c2_3__bhsp_6,c5_3__bhsp_6),k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c3_3__bhsp_6,c5_3__bhsp_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,rc3_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_rlvect_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k4_tarski,dt_k6_relat_1,dt_l2_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc2_funct_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,existence_l1_bhsp_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_k1_domain_1,redefinition_k6_partfun1,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_domain_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k6_partfun1,dt_k8_funct_2,dt_l1_bhsp_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc4_struct_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k2_binop_1,redefinition_k4_rlvect_1,dt_k2_binop_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_k5_bhsp_5,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,d3_rlvect_1,t5_rlvect_1]), [interesting(0.65),file(bhsp_6,e2_3_1__bhsp_6),[file(bhsp_6,e2_3_1__bhsp_6)]]). fof(e9_3__bhsp_6,plain,( k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c4_3__bhsp_6,c5_3__bhsp_6) = k4_rlvect_1(c1_3__bhsp_6,k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c2_3__bhsp_6,c5_3__bhsp_6),k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c3_3__bhsp_6,c5_3__bhsp_6)) ), inference(iterative_eq,[status(thm),assumptions([dt_c4_3__bhsp_6,e1_3__bhsp_6,e2_3__bhsp_6,e3_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,dt_c1_3__bhsp_6])],[e1_3_1__bhsp_6,e2_3_1__bhsp_6]), [interesting(0.8),file(bhsp_6,e9_3__bhsp_6),[file(bhsp_6,e9_3__bhsp_6)]]). fof(t35_funct_1,theorem,( ! [A,B] : ( r2_hidden(B,A) => k1_funct_1(k6_relat_1(A),B) = B ) ), file(funct_1,t35_funct_1), [interesting(0.9),axiom,file(funct_1,t35_funct_1)]). fof(e5_3__bhsp_6,plain,( ! [A] : ( r2_hidden(A,u1_struct_0(c1_3__bhsp_6)) => k1_funct_1(c5_3__bhsp_6,A) = A ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_3__bhsp_6])],[existence_l2_struct_0,dt_l2_struct_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,reflexivity_r1_tarski,existence_l1_rlvect_1,dt_l1_rlvect_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,existence_l2_rlvect_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l2_rlvect_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_subset_1,fc4_subset_1,fc6_membered,rc1_finset_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_k6_partfun1,redefinition_m2_relset_1,dt_k6_partfun1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc1_struct_0,rc1_funct_1,rc2_funct_1,rc3_struct_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k6_relat_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,fc2_funct_1,t1_subset,t7_boole,t35_funct_1]), [interesting(0.8),file(bhsp_6,e5_3__bhsp_6),[file(bhsp_6,e5_3__bhsp_6)]]). fof(t1_bhsp_6,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) ) => ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A)) & v2_binop_1(u1_rlvect_1(A),u1_struct_0(A)) & v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) => ( ( r1_tarski(B,k4_relset_1(u1_struct_0(A),u1_struct_0(A),C)) & ! [D] : ( r2_hidden(D,k4_relset_1(u1_struct_0(A),u1_struct_0(A),C)) => k1_funct_1(C,D) = D ) ) => k1_bhsp_6(A,B) = k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) ) ) ), file(bhsp_6,t1_bhsp_6), [interesting(0.9),axiom,file(bhsp_6,t1_bhsp_6)]). fof(e7_3__bhsp_6,plain,( k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6) = k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c2_3__bhsp_6,c5_3__bhsp_6) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k6_relat_1,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc2_funct_1,fc6_membered,rc1_membered,rc3_funct_1,rc4_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,redefinition_k6_partfun1,dt_k1_relat_1,dt_k2_zfmisc_1,dt_k6_partfun1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_struct_0,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_bhsp_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_bhsp_6,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_relset_1,dt_k5_bhsp_5,dt_l1_bhsp_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c2_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,cc2_finset_1,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e6_3__bhsp_6,e1_3__bhsp_6,e5_3__bhsp_6,t1_bhsp_6]), [interesting(0.8),file(bhsp_6,e7_3__bhsp_6),[file(bhsp_6,e7_3__bhsp_6)]]). fof(e8_3__bhsp_6,plain,( k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6) = k5_bhsp_5(u1_struct_0(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6),u1_rlvect_1(c1_3__bhsp_6),c3_3__bhsp_6,c5_3__bhsp_6) ), inference(mizar_by,[status(thm),assumptions([dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k6_relat_1,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc2_funct_1,fc6_membered,rc1_membered,rc3_funct_1,rc4_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,redefinition_k6_partfun1,dt_k1_relat_1,dt_k2_zfmisc_1,dt_k6_partfun1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_struct_0,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_bhsp_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_bhsp_6,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_relset_1,dt_k5_bhsp_5,dt_l1_bhsp_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c3_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,cc2_finset_1,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e1_3__bhsp_6,e5_3__bhsp_6,e6_3__bhsp_6,t1_bhsp_6]), [interesting(0.8),file(bhsp_6,e8_3__bhsp_6),[file(bhsp_6,e8_3__bhsp_6)]]). fof(e10_3__bhsp_6,plain,( k1_bhsp_6(c1_3__bhsp_6,c4_3__bhsp_6) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c4_3__bhsp_6,e2_3__bhsp_6,e3_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k4_tarski,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k6_relat_1,dt_k8_funct_2,dt_l2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc2_funct_1,fc6_membered,rc1_membered,rc3_funct_1,rc4_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,redefinition_k6_partfun1,dt_k1_relat_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k6_partfun1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_struct_0,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_bhsp_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_k4_rlvect_1,redefinition_m2_relset_1,dt_k1_bhsp_6,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_relset_1,dt_k4_rlvect_1,dt_k5_bhsp_5,dt_l1_bhsp_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,dt_c4_3__bhsp_6,dt_c5_3__bhsp_6,de_c5_3__bhsp_6,cc2_finset_1,fc1_subset_1,t1_subset,t3_subset,t4_subset,t7_boole,e9_3__bhsp_6,e1_3__bhsp_6,e5_3__bhsp_6,e6_3__bhsp_6,e7_3__bhsp_6,e8_3__bhsp_6,t1_bhsp_6]), [interesting(0.8),file(bhsp_6,e10_3__bhsp_6),[file(bhsp_6,e10_3__bhsp_6)]]). fof(i7_3__bhsp_6,theorem,( $true ), introduced(tautology,[file(bhsp_6,i7_3__bhsp_6)]), [interesting(0.8),trivial,file(bhsp_6,i7_3__bhsp_6)]). fof(i6_3__bhsp_6,plain,( k1_bhsp_6(c1_3__bhsp_6,c4_3__bhsp_6) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ), inference(conclusion,[status(thm),assumptions([dt_c4_3__bhsp_6,e2_3__bhsp_6,e3_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6])],[e10_3__bhsp_6,i7_3__bhsp_6]), [interesting(0.8),file(bhsp_6,i6_3__bhsp_6),[file(bhsp_6,i6_3__bhsp_6)]]). fof(i5_3__bhsp_6,plain, ( c4_3__bhsp_6 = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,c4_3__bhsp_6) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_3__bhsp_6,e2_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6]),discharge_asm(discharge,[e3_3__bhsp_6])],[e3_3__bhsp_6,i6_3__bhsp_6]), [interesting(0.8),file(bhsp_6,i5_3__bhsp_6),[file(bhsp_6,i5_3__bhsp_6)]]). fof(i5_3_tmp__bhsp_6,plain, ( ( v1_finset_1(c4_3__bhsp_6) & m1_subset_1(c4_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( c4_3__bhsp_6 = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,c4_3__bhsp_6) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ), inference(discharge_asm,[status(thm),assumptions([e2_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6]),discharge_asm(discharge,[dt_c4_3__bhsp_6])],[dt_c4_3__bhsp_6,i5_3__bhsp_6]), [interesting(0.8),i4_3__bhsp_6]). fof(i4_3__bhsp_6,plain,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( A = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,A) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ) ), inference(let,[status(thm),assumptions([e2_3__bhsp_6,dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6])],[i5_3_tmp__bhsp_6,dh_c4_3__bhsp_6]), [interesting(0.8),file(bhsp_6,i4_3__bhsp_6),[file(bhsp_6,i4_3__bhsp_6)]]). fof(i3_3__bhsp_6,plain, ( r1_xboole_0(c2_3__bhsp_6,c3_3__bhsp_6) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( A = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,A) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,e1_3__bhsp_6,dt_c1_3__bhsp_6]),discharge_asm(discharge,[e2_3__bhsp_6])],[e2_3__bhsp_6,i4_3__bhsp_6]), [interesting(0.8),file(bhsp_6,i3_3__bhsp_6),[file(bhsp_6,i3_3__bhsp_6)]]). fof(i3_3_tmp__bhsp_6,plain, ( ( v1_finset_1(c2_3__bhsp_6) & m1_subset_1(c2_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) & v1_finset_1(c3_3__bhsp_6) & m1_subset_1(c3_3__bhsp_6,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(c2_3__bhsp_6,c3_3__bhsp_6) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( A = k4_subset_1(u1_struct_0(c1_3__bhsp_6),c2_3__bhsp_6,c3_3__bhsp_6) => k1_bhsp_6(c1_3__bhsp_6,A) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,c2_3__bhsp_6),k1_bhsp_6(c1_3__bhsp_6,c3_3__bhsp_6)) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_3__bhsp_6,dt_c1_3__bhsp_6]),discharge_asm(discharge,[dt_c2_3__bhsp_6,dt_c3_3__bhsp_6])],[dt_c2_3__bhsp_6,dt_c3_3__bhsp_6,i3_3__bhsp_6]), [interesting(0.8),i2_3__bhsp_6]). fof(i2_3__bhsp_6,plain,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(A,B) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( C = k4_subset_1(u1_struct_0(c1_3__bhsp_6),A,B) => k1_bhsp_6(c1_3__bhsp_6,C) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,A),k1_bhsp_6(c1_3__bhsp_6,B)) ) ) ) ) ) ), inference(let,[status(thm),assumptions([e1_3__bhsp_6,dt_c1_3__bhsp_6])],[i3_3_tmp__bhsp_6,dh_c2_3__bhsp_6,dh_c3_3__bhsp_6]), [interesting(0.8),file(bhsp_6,i2_3__bhsp_6),[file(bhsp_6,i2_3__bhsp_6)]]). fof(i1_3__bhsp_6,plain, ( ( v1_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v2_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v1_setwiseo(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(A,B) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( C = k4_subset_1(u1_struct_0(c1_3__bhsp_6),A,B) => k1_bhsp_6(c1_3__bhsp_6,C) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,A),k1_bhsp_6(c1_3__bhsp_6,B)) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bhsp_6]),discharge_asm(discharge,[e1_3__bhsp_6])],[e1_3__bhsp_6,i2_3__bhsp_6]), [interesting(0.8),file(bhsp_6,i1_3__bhsp_6),[file(bhsp_6,i1_3__bhsp_6)]]). fof(i1_3_tmp__bhsp_6,plain, ( ( ~ v3_struct_0(c1_3__bhsp_6) & v3_rlvect_1(c1_3__bhsp_6) & v4_rlvect_1(c1_3__bhsp_6) & v5_rlvect_1(c1_3__bhsp_6) & v6_rlvect_1(c1_3__bhsp_6) & v7_rlvect_1(c1_3__bhsp_6) & v2_bhsp_1(c1_3__bhsp_6) & l1_bhsp_1(c1_3__bhsp_6) ) => ( ( v1_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v2_binop_1(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) & v1_setwiseo(u1_rlvect_1(c1_3__bhsp_6),u1_struct_0(c1_3__bhsp_6)) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( r1_xboole_0(A,B) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_3__bhsp_6))) ) => ( C = k4_subset_1(u1_struct_0(c1_3__bhsp_6),A,B) => k1_bhsp_6(c1_3__bhsp_6,C) = k4_rlvect_1(c1_3__bhsp_6,k1_bhsp_6(c1_3__bhsp_6,A),k1_bhsp_6(c1_3__bhsp_6,B)) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__bhsp_6])],[dt_c1_3__bhsp_6,i1_3__bhsp_6]), [interesting(1),t2_bhsp_6]). fof(t2_bhsp_6,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) ) => ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A)) & v2_binop_1(u1_rlvect_1(A),u1_struct_0(A)) & v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(B,C) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( D = k4_subset_1(u1_struct_0(A),B,C) => k1_bhsp_6(A,D) = k4_rlvect_1(A,k1_bhsp_6(A,B),k1_bhsp_6(A,C)) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_3_tmp__bhsp_6,dh_c1_3__bhsp_6]), [interesting(1),file(bhsp_6,t2_bhsp_6),[file(bhsp_6,t2_bhsp_6)]]).