% Mizar ND problem: t2_bhsp_7,bhsp_7,681,51 fof(dh_c1_5__bhsp_7,definition, ( ( ( ~ v3_struct_0(c1_5__bhsp_7) & v3_rlvect_1(c1_5__bhsp_7) & v4_rlvect_1(c1_5__bhsp_7) & v5_rlvect_1(c1_5__bhsp_7) & v6_rlvect_1(c1_5__bhsp_7) & v7_rlvect_1(c1_5__bhsp_7) & v2_bhsp_1(c1_5__bhsp_7) & l1_bhsp_1(c1_5__bhsp_7) ) => ( ( v1_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v2_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v1_setwiseo(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ! [A] : ( ( v1_finset_1(A) & m1_bhsp_5(A,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(A,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),B,C) = C ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(A,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(D,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,C,D) = k2_bhsp_1(c1_5__bhsp_7,D,D) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,A,C) ) ) ) ) ) ) ) ) => ! [E] : ( ( ~ v3_struct_0(E) & v3_rlvect_1(E) & v4_rlvect_1(E) & v5_rlvect_1(E) & v6_rlvect_1(E) & v7_rlvect_1(E) & v2_bhsp_1(E) & l1_bhsp_1(E) ) => ( ( v1_binop_1(u1_rlvect_1(E),u1_struct_0(E)) & v2_binop_1(u1_rlvect_1(E),u1_struct_0(E)) & v1_setwiseo(u1_rlvect_1(E),u1_struct_0(E)) ) => ! [F] : ( ( v1_finset_1(F) & m1_bhsp_5(F,E) ) => ( ~ v1_xboole_0(F) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(E),u1_struct_0(E)) & m2_relset_1(G,u1_struct_0(E),u1_struct_0(E)) ) => ( ( r1_tarski(F,k1_relat_1(G)) & ! [H] : ( m1_subset_1(H,u1_struct_0(E)) => ( r2_hidden(H,F) => k8_funct_2(u1_struct_0(E),u1_struct_0(E),G,H) = H ) ) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(E),k1_numbers) & m2_relset_1(H,u1_struct_0(E),k1_numbers) ) => ( ( r1_tarski(F,k1_relat_1(H)) & ! [I] : ( m1_subset_1(I,u1_struct_0(E)) => ( r2_hidden(I,F) => k8_funct_2(u1_struct_0(E),k1_numbers,H,I) = k2_bhsp_1(E,I,I) ) ) ) => k2_bhsp_1(E,k5_bhsp_5(u1_struct_0(E),u1_struct_0(E),u1_rlvect_1(E),F,G),k5_bhsp_5(u1_struct_0(E),u1_struct_0(E),u1_rlvect_1(E),F,G)) = k5_bhsp_5(k1_numbers,u1_struct_0(E),k33_binop_2,F,H) ) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_5__bhsp_7),file(bhsp_7,c1_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c1_5__bhsp_7)]). fof(e1_5__bhsp_7,assumption, ( v1_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v2_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v1_setwiseo(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ), introduced(assumption,[file(bhsp_7,e1_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,e1_5__bhsp_7)]). fof(dh_c2_5__bhsp_7,definition, ( ( ( v1_finset_1(c2_5__bhsp_7) & m1_bhsp_5(c2_5__bhsp_7,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(c2_5__bhsp_7) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),A,B) = B ) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,B,C) = k2_bhsp_1(c1_5__bhsp_7,C,C) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,B) ) ) ) ) ) ) => ! [D] : ( ( v1_finset_1(D) & m1_bhsp_5(D,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(E,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(D,k1_relat_1(E)) & ! [F] : ( m1_subset_1(F,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(F,D) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),E,F) = F ) ) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(F,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(D,k1_relat_1(F)) & ! [G] : ( m1_subset_1(G,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(G,D) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,F,G) = k2_bhsp_1(c1_5__bhsp_7,G,G) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),D,E),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),D,E)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,D,F) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_5__bhsp_7),file(bhsp_7,c2_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c2_5__bhsp_7)]). fof(e2_5__bhsp_7,assumption,( ~ v1_xboole_0(c2_5__bhsp_7) ), introduced(assumption,[file(bhsp_7,e2_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,e2_5__bhsp_7)]). fof(dh_c3_5__bhsp_7,definition, ( ( ( v1_funct_1(c3_5__bhsp_7) & v1_funct_2(c3_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(c3_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c3_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A) = A ) ) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,A,B) = k2_bhsp_1(c1_5__bhsp_7,B,B) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,A) ) ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(C,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(D,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),C,D) = D ) ) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(D,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(D)) & ! [E] : ( m1_subset_1(E,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(E,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,D,E) = k2_bhsp_1(c1_5__bhsp_7,E,E) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,C),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,C)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,D) ) ) ) ) ), introduced(definition,[new_symbol(c3_5__bhsp_7),file(bhsp_7,c3_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c3_5__bhsp_7)]). fof(e3_5__bhsp_7,assumption, ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c3_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A) = A ) ) ), introduced(assumption,[file(bhsp_7,e3_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,e3_5__bhsp_7)]). fof(dh_c4_5__bhsp_7,definition, ( ( ( v1_funct_1(c4_5__bhsp_7) & v1_funct_2(c4_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(c4_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c4_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,A) = k2_bhsp_1(c1_5__bhsp_7,A,A) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,c4_5__bhsp_7) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,B,C) = k2_bhsp_1(c1_5__bhsp_7,C,C) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,B) ) ) ), introduced(definition,[new_symbol(c4_5__bhsp_7),file(bhsp_7,c4_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c4_5__bhsp_7)]). fof(e4_5__bhsp_7,assumption, ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c4_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,A) = k2_bhsp_1(c1_5__bhsp_7,A,A) ) ) ), introduced(assumption,[file(bhsp_7,e4_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,e4_5__bhsp_7)]). fof(rc2_finset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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(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(fc10_membered,theorem,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), [interesting(0.9),axiom,file(membered,fc10_membered)]). fof(fc11_membered,theorem,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), [interesting(0.9),axiom,file(membered,fc11_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_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(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(fc9_membered,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), [interesting(0.9),axiom,file(membered,fc9_membered)]). 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(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_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_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_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(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_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(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_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). 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(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(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). 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_membered,theorem,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), [interesting(0.9),axiom,file(membered,fc7_membered)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_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(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(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(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_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). 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_bhsp_5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : m1_bhsp_5(B,A) ) ), file(bhsp_5,m1_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,m1_bhsp_5)]). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_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_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). 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_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). 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_bhsp_5,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_bhsp_5(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(bhsp_5,m1_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,m1_bhsp_5)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_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_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_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(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_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_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(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(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). 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(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(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_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_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(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(rc1_bhsp_5,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] : ( m1_bhsp_5(B,A) & v1_finset_1(B) ) ) ), file(bhsp_5,rc1_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,rc1_bhsp_5)]). 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_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). 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_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). 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_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(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(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(commutativity_k2_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) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_bhsp_1(A,B,C) = k2_bhsp_1(A,C,B) ) ), file(bhsp_1,k2_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k2_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_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(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_k2_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) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k2_bhsp_1(A,B,C) = k1_bhsp_1(A,B,C) ) ), file(bhsp_1,k2_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k2_bhsp_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_bhsp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_bhsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_bhsp_1(A,B,C),k1_numbers) ) ), file(bhsp_1,k1_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k1_bhsp_1)]). 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_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k2_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) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_bhsp_1(A,B,C),k1_numbers) ) ), file(bhsp_1,k2_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,k2_bhsp_1)]). fof(dt_k2_finsop_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) ) => m1_subset_1(k2_finsop_1(A,B,C),A) ) ), file(finsop_1,k2_finsop_1), [interesting(0.9),axiom,file(finsop_1,k2_finsop_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_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_k33_binop_2,axiom, ( v1_funct_1(k33_binop_2) & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ), file(binop_2,k33_binop_2), [interesting(0.9),axiom,file(binop_2,k33_binop_2)]). fof(dt_k4_bhsp_5,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,B,A) & m1_relset_1(C,B,A) & m1_finseq_1(D,B) ) => m2_finseq_1(k4_bhsp_5(A,B,C,D),A) ) ), file(bhsp_5,k4_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,k4_bhsp_5)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). 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_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_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_u1_bhsp_1,axiom,( ! [A] : ( l1_bhsp_1(A) => ( v1_funct_1(u1_bhsp_1(A)) & v1_funct_2(u1_bhsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_bhsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) ) ) ), file(bhsp_1,u1_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,u1_bhsp_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_5__bhsp_7,assumption, ( ~ v3_struct_0(c1_5__bhsp_7) & v3_rlvect_1(c1_5__bhsp_7) & v4_rlvect_1(c1_5__bhsp_7) & v5_rlvect_1(c1_5__bhsp_7) & v6_rlvect_1(c1_5__bhsp_7) & v7_rlvect_1(c1_5__bhsp_7) & v2_bhsp_1(c1_5__bhsp_7) & l1_bhsp_1(c1_5__bhsp_7) ), introduced(assumption,[file(bhsp_7,c1_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c1_5__bhsp_7)]). fof(dt_c2_5__bhsp_7,assumption, ( v1_finset_1(c2_5__bhsp_7) & m1_bhsp_5(c2_5__bhsp_7,c1_5__bhsp_7) ), introduced(assumption,[file(bhsp_7,c2_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c2_5__bhsp_7)]). fof(dt_c3_5__bhsp_7,assumption, ( v1_funct_1(c3_5__bhsp_7) & v1_funct_2(c3_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(c3_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ), introduced(assumption,[file(bhsp_7,c3_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c3_5__bhsp_7)]). fof(dt_c4_5__bhsp_7,assumption, ( v1_funct_1(c4_5__bhsp_7) & v1_funct_2(c4_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(c4_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),k1_numbers) ), introduced(assumption,[file(bhsp_7,c4_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c4_5__bhsp_7)]). fof(dh_c5_5__bhsp_7,definition, ( ? [A] : ( m2_finseq_1(A,u1_struct_0(c1_5__bhsp_7)) & v2_funct_1(A) & k2_relat_1(A) = c2_5__bhsp_7 & k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7) = k2_finsop_1(u1_struct_0(c1_5__bhsp_7),k4_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A),u1_rlvect_1(c1_5__bhsp_7)) ) => ( m2_finseq_1(c5_5__bhsp_7,u1_struct_0(c1_5__bhsp_7)) & v2_funct_1(c5_5__bhsp_7) & k2_relat_1(c5_5__bhsp_7) = c2_5__bhsp_7 & k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7) = k2_finsop_1(u1_struct_0(c1_5__bhsp_7),k4_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c5_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7)) ) ), introduced(definition,[new_symbol(c5_5__bhsp_7),file(bhsp_7,c5_5__bhsp_7)]), [interesting(0.8),axiom,file(bhsp_7,c5_5__bhsp_7)]). 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(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(d5_bhsp_5,definition,( ! [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_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) ) => ( r1_tarski(D,k1_relat_1(E)) => ! [F] : ( m1_subset_1(F,A) => ( F = k5_bhsp_5(A,B,C,D,E) <=> ? [G] : ( m2_finseq_1(G,B) & v2_funct_1(G) & k2_relat_1(G) = D & F = k2_finsop_1(A,k4_bhsp_5(A,B,E,G),C) ) ) ) ) ) ) ) ) ) ) ), file(bhsp_5,d5_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,d5_bhsp_5)]). fof(e5_5__bhsp_7,plain,( ? [A] : ( m2_finseq_1(A,u1_struct_0(c1_5__bhsp_7)) & v2_funct_1(A) & k2_relat_1(A) = c2_5__bhsp_7 & k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7) = k2_finsop_1(u1_struct_0(c1_5__bhsp_7),k4_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A),u1_rlvect_1(c1_5__bhsp_7)) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k1_numbers,dt_k5_ordinal2,dt_l2_rlvect_1,dt_l2_struct_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc6_membered,cc7_xreal_0,fc1_ordinal2,fc2_membered,fc5_membered,rc1_xreal_0,rc4_struct_0,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_bhsp_5,existence_m1_finseq_1,existence_m1_relset_1,redefinition_k5_numbers,dt_k1_funct_1,dt_k1_xboole_0,dt_k5_numbers,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_finseq_1,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,cc9_membered,fc1_struct_0,fc1_xboole_0,fc6_membered,rc1_bhsp_5,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc3_funct_1,rc3_struct_0,rc5_struct_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_k8_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_finsop_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k4_bhsp_5,dt_k5_bhsp_5,dt_k8_funct_2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e1_5__bhsp_7,e3_5__bhsp_7,d5_bhsp_5]), [interesting(0.8),file(bhsp_7,e5_5__bhsp_7),[file(bhsp_7,e5_5__bhsp_7)]]). fof(dt_c5_5__bhsp_7,plain,( m2_finseq_1(c5_5__bhsp_7,u1_struct_0(c1_5__bhsp_7)) ), inference(consider,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[dh_c5_5__bhsp_7,e5_5__bhsp_7]), [interesting(0.8),file(bhsp_7,c5_5__bhsp_7),[file(bhsp_7,c5_5__bhsp_7)]]). fof(fc12_binop_2,theorem, ( v1_funct_1(k33_binop_2) & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_binop_1(k33_binop_2,k1_numbers) & v2_binop_1(k33_binop_2,k1_numbers) & v1_setwiseo(k33_binop_2,k1_numbers) ), file(binop_2,fc12_binop_2), [interesting(0.9),axiom,file(binop_2,fc12_binop_2)]). fof(fc3_binop_2,theorem, ( v1_funct_1(k33_binop_2) & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_binop_1(k33_binop_2,k1_numbers) & v2_binop_1(k33_binop_2,k1_numbers) ), file(binop_2,fc3_binop_2), [interesting(0.9),axiom,file(binop_2,fc3_binop_2)]). fof(d5_tarski,definition,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), [interesting(0.9),axiom,file(tarski,d5_tarski)]). 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_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_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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). 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(dh_c1_5_2__bhsp_7,definition, ( ( m1_subset_1(c1_5_2__bhsp_7,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(c1_5_2__bhsp_7,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,A) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A))) ) ) ), introduced(definition,[new_symbol(c1_5_2__bhsp_7),file(bhsp_7,c1_5_2__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,c1_5_2__bhsp_7)]). fof(dt_c1_5_2__bhsp_7,assumption,( m1_subset_1(c1_5_2__bhsp_7,u1_struct_0(c1_5__bhsp_7)) ), introduced(assumption,[file(bhsp_7,c1_5_2__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,c1_5_2__bhsp_7)]). fof(e1_5_2__bhsp_7,assumption,( r2_hidden(c1_5_2__bhsp_7,c2_5__bhsp_7) ), introduced(assumption,[file(bhsp_7,e1_5_2__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,e1_5_2__bhsp_7)]). fof(e1_5_2_1__bhsp_7,plain,( k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k2_bhsp_1(c1_5__bhsp_7,c1_5_2__bhsp_7,c1_5_2__bhsp_7) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c4_5__bhsp_7,e4_5__bhsp_7,e1_5_2__bhsp_7])],[existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,existence_l1_rlvect_1,dt_l1_rlvect_1,cc1_xreal_0,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,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_l2_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc14_finset_1,fc1_xboole_0,fc6_membered,rc1_membered,rc1_xreal_0,rc3_funct_1,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_bhsp_5,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_bhsp_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,fc1_struct_0,rc1_bhsp_5,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_bhsp_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,dt_k1_numbers,dt_k1_relat_1,dt_k2_bhsp_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c4_5__bhsp_7,fc2_membered,t1_subset,t3_subset,t7_boole,e4_5__bhsp_7,e1_5_2__bhsp_7]), [interesting(0.5),file(bhsp_7,e1_5_2_1__bhsp_7),[file(bhsp_7,e1_5_2_1__bhsp_7)]]). fof(e2_5_2__bhsp_7,plain,( k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7) = c1_5_2__bhsp_7 ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5_2__bhsp_7,e3_5__bhsp_7])],[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,existence_l1_rlvect_1,dt_l1_rlvect_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_l2_rlvect_1,dt_k1_xboole_0,dt_k2_zfmisc_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,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,fc1_xboole_0,fc6_membered,rc1_membered,rc3_funct_1,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_bhsp_5,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_bhsp_5,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k8_funct_2,dt_k1_relat_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,t1_subset,t3_subset,t7_boole,e1_5_2__bhsp_7,e3_5__bhsp_7]), [interesting(0.65),file(bhsp_7,e2_5_2__bhsp_7),[file(bhsp_7,e2_5_2__bhsp_7)]]). fof(d1_bhsp_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bhsp_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers,u1_bhsp_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ), file(bhsp_1,d1_bhsp_1), [interesting(0.9),axiom,file(bhsp_1,d1_bhsp_1)]). fof(e2_5_2_1__bhsp_7,plain,( k2_bhsp_1(c1_5__bhsp_7,c1_5_2__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5_2__bhsp_7,e3_5__bhsp_7])],[reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_l1_rlvect_1,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,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc14_finset_1,fc1_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_finset_1,fc1_struct_0,fc2_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_bhsp_1,existence_l1_bhsp_1,existence_m1_subset_1,redefinition_k1_domain_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,dt_k1_bhsp_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_bhsp_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k8_funct_2,dt_l1_bhsp_1,dt_m1_subset_1,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c3_5__bhsp_7,fc2_membered,d5_tarski,e2_5_2__bhsp_7,d1_bhsp_1]), [interesting(0.5),file(bhsp_7,e2_5_2_1__bhsp_7),[file(bhsp_7,e2_5_2_1__bhsp_7)]]). fof(e3_5_2__bhsp_7,plain,( k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ), inference(iterative_eq,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5_2__bhsp_7,e3_5__bhsp_7])],[dt_l2_struct_0,rc4_struct_0,dt_l1_rlvect_1,cc1_xreal_0,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_k1_zfmisc_1,dt_l2_rlvect_1,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,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,fc14_finset_1,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,redefinition_m2_relset_1,dt_k1_bhsp_1,dt_k2_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,commutativity_k2_bhsp_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,dt_k1_funct_1,dt_k1_numbers,dt_k2_bhsp_1,dt_k4_tarski,dt_k8_funct_2,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,fc2_membered,e1_5_2_1__bhsp_7,e2_5_2_1__bhsp_7]), [interesting(0.65),file(bhsp_7,e3_5_2__bhsp_7),[file(bhsp_7,e3_5_2__bhsp_7)]]). fof(e4_5_2__bhsp_7,plain,( k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ), inference(mizar_by,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5_2__bhsp_7,e3_5__bhsp_7])],[existence_l2_struct_0,dt_l2_struct_0,rc4_struct_0,reflexivity_r1_tarski,existence_l1_rlvect_1,dt_l1_rlvect_1,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_l2_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_l2_rlvect_1,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,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc14_finset_1,fc1_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_k2_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_finset_1,fc1_struct_0,fc2_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,redefinition_k8_funct_2,dt_k1_funct_1,dt_k1_numbers,dt_k4_tarski,dt_k8_funct_2,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,fc2_membered,d5_tarski,e3_5_2__bhsp_7]), [interesting(0.65),file(bhsp_7,e4_5_2__bhsp_7),[file(bhsp_7,e4_5_2__bhsp_7)]]). fof(i3_5_2__bhsp_7,theorem,( $true ), introduced(tautology,[file(bhsp_7,i3_5_2__bhsp_7)]), [interesting(0.65),trivial,file(bhsp_7,i3_5_2__bhsp_7)]). fof(i2_5_2__bhsp_7,plain,( k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ), inference(conclusion,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5_2__bhsp_7,e3_5__bhsp_7])],[dt_l2_struct_0,rc4_struct_0,dt_l1_rlvect_1,cc1_xreal_0,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_k1_zfmisc_1,dt_l2_rlvect_1,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,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,fc14_finset_1,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,redefinition_k8_funct_2,dt_k1_funct_1,dt_k1_numbers,dt_k4_tarski,dt_k8_funct_2,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,fc2_membered,e4_5_2__bhsp_7,i3_5_2__bhsp_7]), [interesting(0.65),file(bhsp_7,i2_5_2__bhsp_7),[file(bhsp_7,i2_5_2__bhsp_7)]]). fof(i2_5_2_tmp__bhsp_7,plain, ( r2_hidden(c1_5_2__bhsp_7,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[e1_5_2__bhsp_7])],[e1_5_2__bhsp_7,i2_5_2__bhsp_7]), [interesting(0.65),i1_5_2__bhsp_7]). fof(i1_5_2__bhsp_7,plain, ( r2_hidden(c1_5_2__bhsp_7,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7])],[i2_5_2_tmp__bhsp_7,dt_l2_struct_0,rc4_struct_0,dt_l1_rlvect_1,cc1_xreal_0,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_k1_zfmisc_1,dt_l2_rlvect_1,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,cc2_xreal_0,cc3_membered,cc6_membered,cc7_xreal_0,rc1_membered,rc1_xreal_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_struct_0,rc1_bhsp_5,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,antisymmetry_r2_hidden,redefinition_k8_funct_2,dt_k1_funct_1,dt_k1_numbers,dt_k4_tarski,dt_k8_funct_2,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_2__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,fc2_membered]), [interesting(0.65),file(bhsp_7,i1_5_2__bhsp_7),[file(bhsp_7,i1_5_2__bhsp_7)]]). fof(i1_5_2_tmp__bhsp_7,plain, ( m1_subset_1(c1_5_2__bhsp_7,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(c1_5_2__bhsp_7,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,c1_5_2__bhsp_7) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_2__bhsp_7))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[dt_c1_5_2__bhsp_7])],[dt_c1_5_2__bhsp_7,i1_5_2__bhsp_7]), [interesting(0.8),e9_5__bhsp_7]). fof(e9_5__bhsp_7,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,A) = k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A))) ) ) ), inference(let,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7])],[i1_5_2_tmp__bhsp_7,dh_c1_5_2__bhsp_7]), [interesting(0.8),file(bhsp_7,e9_5__bhsp_7),[file(bhsp_7,e9_5__bhsp_7)]]). fof(e6_5__bhsp_7,plain, ( v2_funct_1(c5_5__bhsp_7) & k2_relat_1(c5_5__bhsp_7) = c2_5__bhsp_7 & k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7) = k2_finsop_1(u1_struct_0(c1_5__bhsp_7),k4_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c5_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7)) ), inference(consider,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[dh_c5_5__bhsp_7,e5_5__bhsp_7]), [interesting(0.8),file(bhsp_7,e6_5__bhsp_7),[file(bhsp_7,e6_5__bhsp_7)]]). fof(dh_c1_5_1__bhsp_7,definition, ( ( m1_subset_1(c1_5_1__bhsp_7,u1_struct_0(c1_5__bhsp_7)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(A,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = A | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A))) = 0 ) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(B,c2_5__bhsp_7) & r2_hidden(C,c2_5__bhsp_7) ) => ( B = C | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,B),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,C))) = 0 ) ) ) ) ), introduced(definition,[new_symbol(c1_5_1__bhsp_7),file(bhsp_7,c1_5_1__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,c1_5_1__bhsp_7)]). fof(dh_c2_5_1__bhsp_7,definition, ( ( m1_subset_1(c2_5_1__bhsp_7,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(c2_5_1__bhsp_7,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = c2_5_1__bhsp_7 | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7))) = 0 ) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(A,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = A | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A))) = 0 ) ) ) ), introduced(definition,[new_symbol(c2_5_1__bhsp_7),file(bhsp_7,c2_5_1__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,c2_5_1__bhsp_7)]). fof(dt_c1_5_1__bhsp_7,assumption,( m1_subset_1(c1_5_1__bhsp_7,u1_struct_0(c1_5__bhsp_7)) ), introduced(assumption,[file(bhsp_7,c1_5_1__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,c1_5_1__bhsp_7)]). fof(dt_c2_5_1__bhsp_7,assumption,( m1_subset_1(c2_5_1__bhsp_7,u1_struct_0(c1_5__bhsp_7)) ), introduced(assumption,[file(bhsp_7,c2_5_1__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,c2_5_1__bhsp_7)]). fof(e1_5_1__bhsp_7,assumption, ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(c2_5_1__bhsp_7,c2_5__bhsp_7) & c1_5_1__bhsp_7 != c2_5_1__bhsp_7 ), introduced(assumption,[file(bhsp_7,e1_5_1__bhsp_7)]), [interesting(0.65),axiom,file(bhsp_7,e1_5_1__bhsp_7)]). fof(d8_bhsp_5,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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_bhsp_5(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => ( C = D | k2_bhsp_1(A,C,D) = 0 ) ) ) ) ) ) ) ), file(bhsp_5,d8_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,d8_bhsp_5)]). fof(e3_5_1__bhsp_7,plain,( k2_bhsp_1(c1_5__bhsp_7,c1_5_1__bhsp_7,c2_5_1__bhsp_7) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,e1_5_1__bhsp_7])],[cc4_xreal_0,cc5_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_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,rc4_struct_0,existence_l1_rlvect_1,dt_k1_xboole_0,dt_k5_ordinal2,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_membered,cc3_membered,cc4_membered,fc1_ordinal2,fc1_xboole_0,fc5_membered,fc6_membered,rc1_membered,reflexivity_r1_tarski,existence_l1_struct_0,existence_l2_rlvect_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_bhsp_1,dt_k1_numbers,dt_k5_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc6_membered,cc9_membered,fc1_struct_0,fc2_membered,rc1_bhsp_5,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t1_numerals,t2_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_bhsp_1,antisymmetry_r2_hidden,existence_l1_bhsp_1,existence_m1_bhsp_5,existence_m1_subset_1,redefinition_k2_bhsp_1,dt_k1_zfmisc_1,dt_k2_bhsp_1,dt_l1_bhsp_1,dt_m1_bhsp_5,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,t1_subset,t3_subset,t4_subset,t7_boole,spc0_boole,spc0_numerals,e1_5_1__bhsp_7,d8_bhsp_5]), [interesting(0.65),file(bhsp_7,e3_5_1__bhsp_7),[file(bhsp_7,e3_5_1__bhsp_7)]]). fof(e2_5_1__bhsp_7,plain, ( k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7) = c1_5_1__bhsp_7 & k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7) = c2_5_1__bhsp_7 ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,e1_5_1__bhsp_7,e3_5__bhsp_7])],[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,existence_l1_rlvect_1,dt_l1_rlvect_1,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_l2_rlvect_1,dt_k1_xboole_0,dt_k2_zfmisc_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,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc14_finset_1,fc1_xboole_0,fc6_membered,rc1_membered,rc3_funct_1,existence_l1_bhsp_1,existence_l1_struct_0,existence_m1_bhsp_5,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_bhsp_5,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k8_funct_2,dt_k1_relat_1,dt_k8_funct_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,t1_subset,t3_subset,t7_boole,e1_5_1__bhsp_7,e3_5__bhsp_7]), [interesting(0.65),file(bhsp_7,e2_5_1__bhsp_7),[file(bhsp_7,e2_5_1__bhsp_7)]]). fof(e4_5_1__bhsp_7,plain,( k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7))) = 0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,e1_5_1__bhsp_7,e3_5__bhsp_7])],[reflexivity_r1_tarski,existence_l2_struct_0,dt_l2_struct_0,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_finset_1,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,antisymmetry_r2_hidden,existence_l1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_rlvect_1,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,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc12_membered,fc13_membered,fc14_finset_1,fc1_ordinal2,fc1_xboole_0,fc5_membered,fc6_membered,fc7_membered,fc8_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k5_numbers,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_finset_1,fc1_struct_0,fc2_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_bhsp_1,existence_l1_bhsp_1,existence_m1_subset_1,redefinition_k1_domain_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,dt_k1_bhsp_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_bhsp_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k8_funct_2,dt_l1_bhsp_1,dt_m1_subset_1,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,fc2_membered,d5_tarski,spc0_boole,spc0_numerals,e3_5_1__bhsp_7,e2_5_1__bhsp_7,d1_bhsp_1]), [interesting(0.65),file(bhsp_7,e4_5_1__bhsp_7),[file(bhsp_7,e4_5_1__bhsp_7)]]). fof(i4_5_1__bhsp_7,theorem,( $true ), introduced(tautology,[file(bhsp_7,i4_5_1__bhsp_7)]), [interesting(0.65),trivial,file(bhsp_7,i4_5_1__bhsp_7)]). fof(i3_5_1__bhsp_7,plain,( k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7))) = 0 ), inference(conclusion,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,e1_5_1__bhsp_7,e3_5__bhsp_7])],[dt_l2_struct_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,dt_l1_rlvect_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,rc2_finset_1,dt_k1_zfmisc_1,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_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc5_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k5_numbers,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_membered,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,redefinition_k8_funct_2,dt_k1_funct_1,dt_k4_tarski,dt_k8_funct_2,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,spc0_boole,spc0_numerals,e4_5_1__bhsp_7,i4_5_1__bhsp_7]), [interesting(0.65),file(bhsp_7,i3_5_1__bhsp_7),[file(bhsp_7,i3_5_1__bhsp_7)]]). fof(i3_5_1_tmp__bhsp_7,plain, ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(c2_5_1__bhsp_7,c2_5__bhsp_7) & c1_5_1__bhsp_7 != c2_5_1__bhsp_7 ) => k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7))) = 0 ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[e1_5_1__bhsp_7])],[e1_5_1__bhsp_7,i3_5_1__bhsp_7]), [interesting(0.65),i2_5_1__bhsp_7]). fof(i2_5_1__bhsp_7,plain, ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(c2_5_1__bhsp_7,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = c2_5_1__bhsp_7 | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7))) = 0 ) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7])],[i3_5_1_tmp__bhsp_7,dt_l2_struct_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,dt_l1_rlvect_1,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,rc2_finset_1,dt_k1_zfmisc_1,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_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_membered,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc5_struct_0,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k5_numbers,dt_l1_bhsp_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_struct_0,fc2_membered,rc1_bhsp_5,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_struct_0,antisymmetry_r2_hidden,redefinition_k8_funct_2,dt_k1_funct_1,dt_k4_tarski,dt_k8_funct_2,dt_u1_bhsp_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c2_5_1__bhsp_7,dt_c3_5__bhsp_7,spc0_boole,spc0_numerals]), [interesting(0.65),file(bhsp_7,i2_5_1__bhsp_7),[file(bhsp_7,i2_5_1__bhsp_7)]]). fof(i2_5_1_tmp__bhsp_7,plain, ( m1_subset_1(c2_5_1__bhsp_7,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(c2_5_1__bhsp_7,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = c2_5_1__bhsp_7 | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c2_5_1__bhsp_7))) = 0 ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[dt_c2_5_1__bhsp_7])],[dt_c2_5_1__bhsp_7,i2_5_1__bhsp_7]), [interesting(0.65),i1_5_1__bhsp_7]). fof(i1_5_1__bhsp_7,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(A,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = A | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A))) = 0 ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c1_5_1__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7])],[i2_5_1_tmp__bhsp_7,dh_c2_5_1__bhsp_7]), [interesting(0.65),file(bhsp_7,i1_5_1__bhsp_7),[file(bhsp_7,i1_5_1__bhsp_7)]]). fof(i1_5_1_tmp__bhsp_7,plain, ( m1_subset_1(c1_5_1__bhsp_7,u1_struct_0(c1_5__bhsp_7)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(c1_5_1__bhsp_7,c2_5__bhsp_7) & r2_hidden(A,c2_5__bhsp_7) ) => ( c1_5_1__bhsp_7 = A | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c1_5_1__bhsp_7),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A))) = 0 ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[dt_c1_5_1__bhsp_7])],[dt_c1_5_1__bhsp_7,i1_5_1__bhsp_7]), [interesting(0.8),e8_5__bhsp_7]). fof(e8_5__bhsp_7,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( ( r2_hidden(A,c2_5__bhsp_7) & r2_hidden(B,c2_5__bhsp_7) ) => ( A = B | k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A),k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,B))) = 0 ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7])],[i1_5_1_tmp__bhsp_7,dh_c1_5_1__bhsp_7]), [interesting(0.8),file(bhsp_7,e8_5__bhsp_7),[file(bhsp_7,e8_5__bhsp_7)]]). fof(t9_bhsp_5,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_xboole_0(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,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => ( D = E | k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E))) = 0 ) ) ) ) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k1_numbers) & m2_relset_1(D,u1_struct_0(A),k1_numbers) ) => ( ( r1_tarski(B,k1_relat_1(D)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => k1_funct_1(D,E) = k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(C,E),k1_funct_1(C,E))) ) ) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( ( v2_funct_1(E) & k2_relat_1(E) = B ) => k1_funct_1(u1_bhsp_1(A),k4_tarski(k2_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),C,E),u1_rlvect_1(A)),k2_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),C,E),u1_rlvect_1(A)))) = k2_finsop_1(k1_numbers,k4_bhsp_5(k1_numbers,u1_struct_0(A),D,E),k33_binop_2) ) ) ) ) ) ) ) ) ), file(bhsp_5,t9_bhsp_5), [interesting(0.9),axiom,file(bhsp_5,t9_bhsp_5)]). fof(e10_5__bhsp_7,plain,( k1_funct_1(u1_bhsp_1(c1_5__bhsp_7),k4_tarski(k2_finsop_1(u1_struct_0(c1_5__bhsp_7),k4_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c5_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7)),k2_finsop_1(u1_struct_0(c1_5__bhsp_7),k4_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,c5_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7)))) = k2_finsop_1(k1_numbers,k4_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),c4_5__bhsp_7,c5_5__bhsp_7),k33_binop_2) ), inference(mizar_by,[status(thm),assumptions([dt_c4_5__bhsp_7,e2_5__bhsp_7,e4_5__bhsp_7,e1_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e3_5__bhsp_7])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_l2_struct_0,dt_k5_ordinal2,dt_l2_struct_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_ordinal2,fc5_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,rc4_struct_0,commutativity_k2_tarski,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_bhsp_5,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_bhsp_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k2_zfmisc_1,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_bhsp_5,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc9_membered,fc14_finset_1,fc1_finset_1,fc1_struct_0,fc1_xboole_0,fc2_finset_1,fc6_membered,rc1_bhsp_5,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc3_funct_1,rc3_struct_0,rc5_struct_0,t1_numerals,commutativity_k2_bhsp_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_bhsp_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_bhsp_1,dt_k2_finsop_1,dt_k2_relat_1,dt_k33_binop_2,dt_k4_bhsp_5,dt_k4_tarski,dt_k5_bhsp_5,dt_k8_funct_2,dt_l1_bhsp_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_u1_bhsp_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,dt_c5_5__bhsp_7,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc6_membered,fc12_binop_2,fc2_membered,fc3_binop_2,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc4_finset_1,spc0_boole,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d5_tarski,spc0_boole,spc0_numerals,e9_5__bhsp_7,e2_5__bhsp_7,e3_5__bhsp_7,e4_5__bhsp_7,e6_5__bhsp_7,e8_5__bhsp_7,t9_bhsp_5]), [interesting(0.8),file(bhsp_7,e10_5__bhsp_7),[file(bhsp_7,e10_5__bhsp_7)]]). fof(e7_5__bhsp_7,plain,( k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,c4_5__bhsp_7) = k2_finsop_1(k1_numbers,k4_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),c4_5__bhsp_7,c5_5__bhsp_7),k33_binop_2) ), inference(mizar_by,[status(thm),assumptions([dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_finset_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k5_ordinal2,dt_l2_rlvect_1,dt_l2_struct_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc1_ordinal2,fc5_membered,rc1_xreal_0,rc4_struct_0,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_bhsp_5,existence_m1_finseq_1,existence_m1_relset_1,redefinition_k5_numbers,dt_k1_bhsp_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k5_numbers,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_bhsp_5,dt_m1_finseq_1,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,cc9_membered,fc1_struct_0,fc1_xboole_0,fc6_membered,rc1_bhsp_5,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc3_funct_1,rc3_struct_0,rc5_struct_0,commutativity_k2_bhsp_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_bhsp_1,dt_k2_finsop_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k33_binop_2,dt_k4_bhsp_5,dt_k5_bhsp_5,dt_k8_funct_2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,dt_c5_5__bhsp_7,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_finset_1,cc6_membered,fc12_binop_2,fc14_finset_1,fc2_membered,fc3_binop_2,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e4_5__bhsp_7,e6_5__bhsp_7,d5_bhsp_5]), [interesting(0.8),file(bhsp_7,e7_5__bhsp_7),[file(bhsp_7,e7_5__bhsp_7)]]). fof(e11_5__bhsp_7,plain,( k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,c4_5__bhsp_7) ), inference(mizar_by,[status(thm),assumptions([e2_5__bhsp_7,dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[rc2_finset_1,dt_k5_ordinal2,cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc1_ordinal2,fc5_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l2_struct_0,redefinition_k5_numbers,dt_k1_xboole_0,dt_k5_numbers,dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,cc9_membered,fc12_membered,fc13_membered,fc1_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc4_struct_0,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_m1_bhsp_5,existence_m1_finseq_1,existence_m1_relset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_m1_bhsp_5,dt_m1_finseq_1,dt_m1_relset_1,dt_m2_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,fc14_finset_1,fc1_finset_1,fc1_struct_0,fc2_finset_1,rc1_bhsp_5,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_finset_1,rc3_funct_1,rc3_struct_0,rc4_finset_1,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_bhsp_1,existence_l1_bhsp_1,existence_m1_subset_1,redefinition_k1_domain_1,redefinition_k2_bhsp_1,redefinition_k8_funct_2,dt_k1_bhsp_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k2_bhsp_1,dt_k2_finsop_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k33_binop_2,dt_k4_bhsp_5,dt_k4_tarski,dt_k5_bhsp_5,dt_k8_funct_2,dt_l1_bhsp_1,dt_m1_subset_1,dt_u1_bhsp_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,dt_c4_5__bhsp_7,dt_c5_5__bhsp_7,fc12_binop_2,fc2_membered,fc3_binop_2,d5_tarski,e10_5__bhsp_7,e6_5__bhsp_7,e7_5__bhsp_7,d1_bhsp_1]), [interesting(0.8),file(bhsp_7,e11_5__bhsp_7),[file(bhsp_7,e11_5__bhsp_7)]]). fof(i9_5__bhsp_7,theorem,( $true ), introduced(tautology,[file(bhsp_7,i9_5__bhsp_7)]), [interesting(0.8),trivial,file(bhsp_7,i9_5__bhsp_7)]). fof(i8_5__bhsp_7,plain,( k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,c4_5__bhsp_7) ), inference(conclusion,[status(thm),assumptions([e2_5__bhsp_7,dt_c4_5__bhsp_7,e4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[e11_5__bhsp_7,i9_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i8_5__bhsp_7),[file(bhsp_7,i8_5__bhsp_7)]]). fof(i7_5__bhsp_7,plain, ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c4_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,A) = k2_bhsp_1(c1_5__bhsp_7,A,A) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,c4_5__bhsp_7) ), inference(discharge_asm,[status(thm),assumptions([e2_5__bhsp_7,dt_c4_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[e4_5__bhsp_7])],[e4_5__bhsp_7,i8_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i7_5__bhsp_7),[file(bhsp_7,i7_5__bhsp_7)]]). fof(i7_5_tmp__bhsp_7,plain, ( ( v1_funct_1(c4_5__bhsp_7) & v1_funct_2(c4_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(c4_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c4_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,c4_5__bhsp_7,A) = k2_bhsp_1(c1_5__bhsp_7,A,A) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,c4_5__bhsp_7) ) ), inference(discharge_asm,[status(thm),assumptions([e2_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7]),discharge_asm(discharge,[dt_c4_5__bhsp_7])],[dt_c4_5__bhsp_7,i7_5__bhsp_7]), [interesting(0.8),i6_5__bhsp_7]). fof(i6_5__bhsp_7,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,A,B) = k2_bhsp_1(c1_5__bhsp_7,B,B) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,A) ) ) ), inference(let,[status(thm),assumptions([e2_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7,e3_5__bhsp_7])],[i7_5_tmp__bhsp_7,dh_c4_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i6_5__bhsp_7),[file(bhsp_7,i6_5__bhsp_7)]]). fof(i5_5__bhsp_7,plain, ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c3_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A) = A ) ) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,A,B) = k2_bhsp_1(c1_5__bhsp_7,B,B) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,A) ) ) ), inference(discharge_asm,[status(thm),assumptions([e2_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,dt_c3_5__bhsp_7,e1_5__bhsp_7]),discharge_asm(discharge,[e3_5__bhsp_7])],[e3_5__bhsp_7,i6_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i5_5__bhsp_7),[file(bhsp_7,i5_5__bhsp_7)]]). fof(i5_5_tmp__bhsp_7,plain, ( ( v1_funct_1(c3_5__bhsp_7) & v1_funct_2(c3_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(c3_5__bhsp_7,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(c3_5__bhsp_7)) & ! [A] : ( m1_subset_1(A,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(A,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),c3_5__bhsp_7,A) = A ) ) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,A,B) = k2_bhsp_1(c1_5__bhsp_7,B,B) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,c3_5__bhsp_7)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,A) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([e2_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,e1_5__bhsp_7]),discharge_asm(discharge,[dt_c3_5__bhsp_7])],[dt_c3_5__bhsp_7,i5_5__bhsp_7]), [interesting(0.8),i4_5__bhsp_7]). fof(i4_5__bhsp_7,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),A,B) = B ) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,B,C) = k2_bhsp_1(c1_5__bhsp_7,C,C) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,B) ) ) ) ) ), inference(let,[status(thm),assumptions([e2_5__bhsp_7,dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,e1_5__bhsp_7])],[i5_5_tmp__bhsp_7,dh_c3_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i4_5__bhsp_7),[file(bhsp_7,i4_5__bhsp_7)]]). fof(i3_5__bhsp_7,plain, ( ~ v1_xboole_0(c2_5__bhsp_7) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),A,B) = B ) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,B,C) = k2_bhsp_1(c1_5__bhsp_7,C,C) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,B) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bhsp_7,dt_c2_5__bhsp_7,e1_5__bhsp_7]),discharge_asm(discharge,[e2_5__bhsp_7])],[e2_5__bhsp_7,i4_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i3_5__bhsp_7),[file(bhsp_7,i3_5__bhsp_7)]]). fof(i3_5_tmp__bhsp_7,plain, ( ( v1_finset_1(c2_5__bhsp_7) & m1_bhsp_5(c2_5__bhsp_7,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(c2_5__bhsp_7) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(A,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(B,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),A,B) = B ) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(c2_5__bhsp_7,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,c2_5__bhsp_7) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,B,C) = k2_bhsp_1(c1_5__bhsp_7,C,C) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),c2_5__bhsp_7,A)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,c2_5__bhsp_7,B) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bhsp_7,e1_5__bhsp_7]),discharge_asm(discharge,[dt_c2_5__bhsp_7])],[dt_c2_5__bhsp_7,i3_5__bhsp_7]), [interesting(0.8),i2_5__bhsp_7]). fof(i2_5__bhsp_7,plain,( ! [A] : ( ( v1_finset_1(A) & m1_bhsp_5(A,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(A,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),B,C) = C ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(A,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(D,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,C,D) = k2_bhsp_1(c1_5__bhsp_7,D,D) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,A,C) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__bhsp_7,e1_5__bhsp_7])],[i3_5_tmp__bhsp_7,dh_c2_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i2_5__bhsp_7),[file(bhsp_7,i2_5__bhsp_7)]]). fof(i1_5__bhsp_7,plain, ( ( v1_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v2_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v1_setwiseo(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ! [A] : ( ( v1_finset_1(A) & m1_bhsp_5(A,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(A,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),B,C) = C ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(A,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(D,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,C,D) = k2_bhsp_1(c1_5__bhsp_7,D,D) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,A,C) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__bhsp_7]),discharge_asm(discharge,[e1_5__bhsp_7])],[e1_5__bhsp_7,i2_5__bhsp_7]), [interesting(0.8),file(bhsp_7,i1_5__bhsp_7),[file(bhsp_7,i1_5__bhsp_7)]]). fof(i1_5_tmp__bhsp_7,plain, ( ( ~ v3_struct_0(c1_5__bhsp_7) & v3_rlvect_1(c1_5__bhsp_7) & v4_rlvect_1(c1_5__bhsp_7) & v5_rlvect_1(c1_5__bhsp_7) & v6_rlvect_1(c1_5__bhsp_7) & v7_rlvect_1(c1_5__bhsp_7) & v2_bhsp_1(c1_5__bhsp_7) & l1_bhsp_1(c1_5__bhsp_7) ) => ( ( v1_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v2_binop_1(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & v1_setwiseo(u1_rlvect_1(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ! [A] : ( ( v1_finset_1(A) & m1_bhsp_5(A,c1_5__bhsp_7) ) => ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) & m2_relset_1(B,u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7)) ) => ( ( r1_tarski(A,k1_relat_1(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(C,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),B,C) = C ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) & m2_relset_1(C,u1_struct_0(c1_5__bhsp_7),k1_numbers) ) => ( ( r1_tarski(A,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(c1_5__bhsp_7)) => ( r2_hidden(D,A) => k8_funct_2(u1_struct_0(c1_5__bhsp_7),k1_numbers,C,D) = k2_bhsp_1(c1_5__bhsp_7,D,D) ) ) ) => k2_bhsp_1(c1_5__bhsp_7,k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B),k5_bhsp_5(u1_struct_0(c1_5__bhsp_7),u1_struct_0(c1_5__bhsp_7),u1_rlvect_1(c1_5__bhsp_7),A,B)) = k5_bhsp_5(k1_numbers,u1_struct_0(c1_5__bhsp_7),k33_binop_2,A,C) ) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__bhsp_7])],[dt_c1_5__bhsp_7,i1_5__bhsp_7]), [interesting(1),t2_bhsp_7]). fof(t2_bhsp_7,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_bhsp_5(B,A) ) => ( ~ v1_xboole_0(B) => ! [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,k1_relat_1(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = D ) ) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k1_numbers) & m2_relset_1(D,u1_struct_0(A),k1_numbers) ) => ( ( r1_tarski(B,k1_relat_1(D)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => k8_funct_2(u1_struct_0(A),k1_numbers,D,E) = k2_bhsp_1(A,E,E) ) ) ) => k2_bhsp_1(A,k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C),k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C)) = k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,B,D) ) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_5_tmp__bhsp_7,dh_c1_5__bhsp_7]), [interesting(1),file(bhsp_7,t2_bhsp_7),[file(bhsp_7,t2_bhsp_7)]]).