% Mizar ND problem: t9_rlsub_1,rlsub_1,97,63 fof(dh_c1_7__rlsub_1,definition, ( ( ( ~ v3_struct_0(c1_7__rlsub_1) & v3_rlvect_1(c1_7__rlsub_1) & v4_rlvect_1(c1_7__rlsub_1) & v5_rlvect_1(c1_7__rlsub_1) & v6_rlvect_1(c1_7__rlsub_1) & v7_rlvect_1(c1_7__rlsub_1) & l2_rlvect_1(c1_7__rlsub_1) ) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(A,c1_7__rlsub_1) & v1_rlsub_1(B,c1_7__rlsub_1) & C = a_3_0_rlsub_1(c1_7__rlsub_1,A,B) ) => v1_rlsub_1(C,c1_7__rlsub_1) ) ) ) ) ) => ! [D] : ( ( ~ v3_struct_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v5_rlvect_1(D) & v6_rlvect_1(D) & v7_rlvect_1(D) & l2_rlvect_1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D))) => ( ( v1_rlsub_1(E,D) & v1_rlsub_1(F,D) & G = a_3_0_rlsub_1(D,E,F) ) => v1_rlsub_1(G,D) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_7__rlsub_1),file(rlsub_1,c1_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c1_7__rlsub_1)]). fof(dh_c2_7__rlsub_1,definition, ( ( m1_subset_1(c2_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(A,c1_7__rlsub_1) & B = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,A) ) => v1_rlsub_1(B,c1_7__rlsub_1) ) ) ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(C,c1_7__rlsub_1) & v1_rlsub_1(D,c1_7__rlsub_1) & E = a_3_0_rlsub_1(c1_7__rlsub_1,C,D) ) => v1_rlsub_1(E,c1_7__rlsub_1) ) ) ) ) ), introduced(definition,[new_symbol(c2_7__rlsub_1),file(rlsub_1,c2_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c2_7__rlsub_1)]). fof(dh_c3_7__rlsub_1,definition, ( ( m1_subset_1(c3_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & A = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(A,c1_7__rlsub_1) ) ) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(B,c1_7__rlsub_1) & C = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,B) ) => v1_rlsub_1(C,c1_7__rlsub_1) ) ) ) ), introduced(definition,[new_symbol(c3_7__rlsub_1),file(rlsub_1,c3_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c3_7__rlsub_1)]). fof(dh_c4_7__rlsub_1,definition, ( ( m1_subset_1(c4_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & c4_7__rlsub_1 = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(c4_7__rlsub_1,c1_7__rlsub_1) ) ) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & A = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(A,c1_7__rlsub_1) ) ) ), introduced(definition,[new_symbol(c4_7__rlsub_1),file(rlsub_1,c4_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c4_7__rlsub_1)]). fof(e1_7__rlsub_1,assumption, ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) ), introduced(assumption,[file(rlsub_1,e1_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,e1_7__rlsub_1)]). fof(e2_7__rlsub_1,assumption,( c4_7__rlsub_1 = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ), introduced(assumption,[file(rlsub_1,e2_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,e2_7__rlsub_1)]). 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_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(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(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(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]). fof(dt_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(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_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(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). 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(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc3_struct_0,theorem,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]). fof(rc5_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]). fof(commutativity_k4_rlvect_1,theorem,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(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(redefinition_k4_rlvect_1,definition,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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_k3_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_numbers) ) => m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k3_rlvect_1)]). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_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_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(dt_c1_7__rlsub_1,assumption, ( ~ v3_struct_0(c1_7__rlsub_1) & v3_rlvect_1(c1_7__rlsub_1) & v4_rlvect_1(c1_7__rlsub_1) & v5_rlvect_1(c1_7__rlsub_1) & v6_rlvect_1(c1_7__rlsub_1) & v7_rlvect_1(c1_7__rlsub_1) & l2_rlvect_1(c1_7__rlsub_1) ), introduced(assumption,[file(rlsub_1,c1_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c1_7__rlsub_1)]). fof(dt_c4_7__rlsub_1,assumption,( m1_subset_1(c4_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) ), introduced(assumption,[file(rlsub_1,c4_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c4_7__rlsub_1)]). 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(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). fof(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(rc3_rlvect_1,theorem,( ? [A] : ( l2_rlvect_1(A) & ~ v3_struct_0(A) ) ), file(rlvect_1,rc3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,rc3_rlvect_1)]). fof(d1_rlsub_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(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) ) => r2_hidden(k4_rlvect_1(A,C,D),B) ) ) ) & ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k3_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) ), file(rlsub_1,d1_rlsub_1), [interesting(0.9),axiom,file(rlsub_1,d1_rlsub_1)]). fof(dh_c1_7_1__rlsub_1,definition, ( ( m1_subset_1(c1_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(A,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,A),c4_7__rlsub_1) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(B,c4_7__rlsub_1) & r2_hidden(C,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,B,C),c4_7__rlsub_1) ) ) ) ), introduced(definition,[new_symbol(c1_7_1__rlsub_1),file(rlsub_1,c1_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c1_7_1__rlsub_1)]). fof(dh_c2_7_1__rlsub_1,definition, ( ( m1_subset_1(c2_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(c2_7_1__rlsub_1,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1),c4_7__rlsub_1) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(A,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,A),c4_7__rlsub_1) ) ) ), introduced(definition,[new_symbol(c2_7_1__rlsub_1),file(rlsub_1,c2_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c2_7_1__rlsub_1)]). fof(e1_7_1__rlsub_1,assumption,( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) ), introduced(assumption,[file(rlsub_1,e1_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,e1_7_1__rlsub_1)]). fof(e2_7_1__rlsub_1,assumption,( r2_hidden(c2_7_1__rlsub_1,c4_7__rlsub_1) ), introduced(assumption,[file(rlsub_1,e2_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,e2_7_1__rlsub_1)]). fof(cc1_realset1,theorem,( ! [A] : ( ~ v1_realset1(A) => ~ v1_xboole_0(A) ) ), file(realset1,cc1_realset1), [interesting(0.9),axiom,file(realset1,cc1_realset1)]). fof(rc1_realset1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(realset1,rc1_realset1), [interesting(0.9),axiom,file(realset1,rc1_realset1)]). fof(rc2_realset1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ), file(realset1,rc2_realset1), [interesting(0.9),axiom,file(realset1,rc2_realset1)]). 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(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). 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(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(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(fc2_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]). fof(fc3_realset1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ), file(realset1,fc3_realset1), [interesting(0.9),axiom,file(realset1,fc3_realset1)]). fof(fc3_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). 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(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(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(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_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_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_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). 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_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(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(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(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(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). 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_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). fof(redefinition_k1_domain_1,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(redefinition_k8_funct_2,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_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(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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(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(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_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_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(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(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(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(d3_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ), file(rlvect_1,d3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d3_rlvect_1)]). fof(dt_c1_7_1__rlsub_1,assumption,( m1_subset_1(c1_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), introduced(assumption,[file(rlsub_1,c1_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c1_7_1__rlsub_1)]). fof(dt_c2_7__rlsub_1,assumption,( m1_subset_1(c2_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) ), introduced(assumption,[file(rlsub_1,c2_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c2_7__rlsub_1)]). fof(dt_c2_7_1__rlsub_1,assumption,( m1_subset_1(c2_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), introduced(assumption,[file(rlsub_1,c2_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c2_7_1__rlsub_1)]). fof(dt_c3_7__rlsub_1,assumption,( m1_subset_1(c3_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) ), introduced(assumption,[file(rlsub_1,c3_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c3_7__rlsub_1)]). fof(dh_c3_7_1__rlsub_1,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) & c1_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,A,B) & r2_hidden(A,c2_7__rlsub_1) & r2_hidden(B,c3_7__rlsub_1) ) ) => ( m1_subset_1(c3_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) & ? [C] : ( m1_subset_1(C,u1_struct_0(c1_7__rlsub_1)) & c1_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,C) & r2_hidden(c3_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(C,c3_7__rlsub_1) ) ) ), introduced(definition,[new_symbol(c3_7_1__rlsub_1),file(rlsub_1,c3_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c3_7_1__rlsub_1)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(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(t2_tarski,theorem,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), [interesting(0.9),axiom,file(tarski,t2_tarski)]). fof(fraenkel_a_3_0_rlsub_1,definition,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_rlsub_1(B,C,D)) <=> ? [E,F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k4_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ), file(rlsub_1,a_3_0_rlsub_1), [interesting(0.9),axiom,file(rlsub_1,a_3_0_rlsub_1)]). fof(e3_7_1__rlsub_1,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) & c1_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,A,B) & r2_hidden(A,c2_7__rlsub_1) & r2_hidden(B,c3_7__rlsub_1) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e1_7_1__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,d5_tarski,reflexivity_r1_tarski,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc4_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,cc15_membered,cc1_funct_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_rlvect_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_3_0_rlsub_1,e2_7__rlsub_1,e1_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e3_7_1__rlsub_1),[file(rlsub_1,e3_7_1__rlsub_1)]]). fof(dt_c3_7_1__rlsub_1,plain,( m1_subset_1(c3_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e1_7_1__rlsub_1])],[dh_c3_7_1__rlsub_1,e3_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,c3_7_1__rlsub_1),[file(rlsub_1,c3_7_1__rlsub_1)]]). fof(dh_c4_7_1__rlsub_1,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & c1_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,A) & r2_hidden(c3_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(A,c3_7__rlsub_1) ) => ( m1_subset_1(c4_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) & c1_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c4_7_1__rlsub_1) & r2_hidden(c3_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(c4_7_1__rlsub_1,c3_7__rlsub_1) ) ), introduced(definition,[new_symbol(c4_7_1__rlsub_1),file(rlsub_1,c4_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c4_7_1__rlsub_1)]). fof(dt_c4_7_1__rlsub_1,plain,( m1_subset_1(c4_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e1_7_1__rlsub_1])],[dh_c3_7_1__rlsub_1,dh_c4_7_1__rlsub_1,e3_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,c4_7_1__rlsub_1),[file(rlsub_1,c4_7_1__rlsub_1)]]). fof(dh_c5_7_1__rlsub_1,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) & c2_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,A,B) & r2_hidden(A,c2_7__rlsub_1) & r2_hidden(B,c3_7__rlsub_1) ) ) => ( m1_subset_1(c5_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) & ? [C] : ( m1_subset_1(C,u1_struct_0(c1_7__rlsub_1)) & c2_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c5_7_1__rlsub_1,C) & r2_hidden(c5_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(C,c3_7__rlsub_1) ) ) ), introduced(definition,[new_symbol(c5_7_1__rlsub_1),file(rlsub_1,c5_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c5_7_1__rlsub_1)]). fof(e6_7_1__rlsub_1,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) & c2_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,A,B) & r2_hidden(A,c2_7__rlsub_1) & r2_hidden(B,c3_7__rlsub_1) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,d5_tarski,reflexivity_r1_tarski,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc4_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,cc15_membered,cc1_funct_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_rlvect_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_3_0_rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e6_7_1__rlsub_1),[file(rlsub_1,e6_7_1__rlsub_1)]]). fof(dt_c5_7_1__rlsub_1,plain,( m1_subset_1(c5_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[dh_c5_7_1__rlsub_1,e6_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,c5_7_1__rlsub_1),[file(rlsub_1,c5_7_1__rlsub_1)]]). fof(dh_c6_7_1__rlsub_1,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & c2_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c5_7_1__rlsub_1,A) & r2_hidden(c5_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(A,c3_7__rlsub_1) ) => ( m1_subset_1(c6_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) & c2_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c5_7_1__rlsub_1,c6_7_1__rlsub_1) & r2_hidden(c5_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(c6_7_1__rlsub_1,c3_7__rlsub_1) ) ), introduced(definition,[new_symbol(c6_7_1__rlsub_1),file(rlsub_1,c6_7_1__rlsub_1)]), [interesting(0.65),axiom,file(rlsub_1,c6_7_1__rlsub_1)]). fof(dt_c6_7_1__rlsub_1,plain,( m1_subset_1(c6_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[dh_c5_7_1__rlsub_1,dh_c6_7_1__rlsub_1,e6_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,c6_7_1__rlsub_1),[file(rlsub_1,c6_7_1__rlsub_1)]]). fof(e4_7_1__rlsub_1,plain,( c1_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c4_7_1__rlsub_1) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e1_7_1__rlsub_1])],[dh_c3_7_1__rlsub_1,dh_c4_7_1__rlsub_1,e3_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e4_7_1__rlsub_1),[file(rlsub_1,e4_7_1__rlsub_1)]]). fof(e7_7_1__rlsub_1,plain,( c2_7_1__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c5_7_1__rlsub_1,c6_7_1__rlsub_1) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[dh_c5_7_1__rlsub_1,dh_c6_7_1__rlsub_1,e6_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e7_7_1__rlsub_1),[file(rlsub_1,e7_7_1__rlsub_1)]]). fof(d6_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ( v4_rlvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ), file(rlvect_1,d6_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d6_rlvect_1)]). fof(e1_7_1_1__rlsub_1,plain,( k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1) = k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c4_7_1__rlsub_1),c5_7_1__rlsub_1),c6_7_1__rlsub_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[reflexivity_r1_tarski,cc1_realset1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_realset1,rc2_realset1,rc3_funct_1,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,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,fc1_subset_1,fc2_subset_1,fc3_realset1,fc3_subset_1,fc6_membered,rc1_funct_1,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,d5_tarski,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,fc1_struct_0,rc3_rlvect_1,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7_1__rlsub_1,dt_c4_7_1__rlsub_1,dt_c5_7_1__rlsub_1,dt_c6_7_1__rlsub_1,d3_rlvect_1,e4_7_1__rlsub_1,e7_7_1__rlsub_1,d6_rlvect_1]), [interesting(0.5),file(rlsub_1,e1_7_1_1__rlsub_1),[file(rlsub_1,e1_7_1_1__rlsub_1)]]). fof(e2_7_1_1__rlsub_1,plain,( k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c4_7_1__rlsub_1),c5_7_1__rlsub_1),c6_7_1__rlsub_1) = k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c5_7_1__rlsub_1),c4_7_1__rlsub_1),c6_7_1__rlsub_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[reflexivity_r1_tarski,cc1_realset1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_realset1,rc2_realset1,rc3_funct_1,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,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,fc1_subset_1,fc2_subset_1,fc3_realset1,fc3_subset_1,fc6_membered,rc1_funct_1,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,d5_tarski,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,fc1_struct_0,rc3_rlvect_1,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c3_7_1__rlsub_1,dt_c4_7_1__rlsub_1,dt_c5_7_1__rlsub_1,dt_c6_7_1__rlsub_1,d3_rlvect_1,d6_rlvect_1]), [interesting(0.5),file(rlsub_1,e2_7_1_1__rlsub_1),[file(rlsub_1,e2_7_1_1__rlsub_1)]]). fof(e3_7_1_1__rlsub_1,plain,( k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c5_7_1__rlsub_1),c4_7_1__rlsub_1),c6_7_1__rlsub_1) = k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c5_7_1__rlsub_1),k4_rlvect_1(c1_7__rlsub_1,c4_7_1__rlsub_1,c6_7_1__rlsub_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[reflexivity_r1_tarski,cc1_realset1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_realset1,rc2_realset1,rc3_funct_1,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,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,fc1_subset_1,fc2_subset_1,fc3_realset1,fc3_subset_1,fc6_membered,rc1_funct_1,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,d5_tarski,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,fc1_struct_0,rc3_rlvect_1,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c3_7_1__rlsub_1,dt_c4_7_1__rlsub_1,dt_c5_7_1__rlsub_1,dt_c6_7_1__rlsub_1,d3_rlvect_1,d6_rlvect_1]), [interesting(0.5),file(rlsub_1,e3_7_1_1__rlsub_1),[file(rlsub_1,e3_7_1_1__rlsub_1)]]). fof(e10_7_1__rlsub_1,plain,( k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1) = k4_rlvect_1(c1_7__rlsub_1,k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c5_7_1__rlsub_1),k4_rlvect_1(c1_7__rlsub_1,c4_7_1__rlsub_1,c6_7_1__rlsub_1)) ), inference(iterative_eq,[status(thm),assumptions([dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[e1_7_1_1__rlsub_1,e2_7_1_1__rlsub_1,e3_7_1_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e10_7_1__rlsub_1),[file(rlsub_1,e10_7_1__rlsub_1)]]). fof(dt_u2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => ( v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,u2_rlvect_1)]). fof(d4_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_numbers) => k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) ) ) ) ), file(rlvect_1,d4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d4_rlvect_1)]). fof(e5_7_1__rlsub_1,plain, ( r2_hidden(c3_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(c4_7_1__rlsub_1,c3_7__rlsub_1) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e1_7_1__rlsub_1])],[dh_c3_7_1__rlsub_1,dh_c4_7_1__rlsub_1,e3_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e5_7_1__rlsub_1),[file(rlsub_1,e5_7_1__rlsub_1)]]). fof(e8_7_1__rlsub_1,plain, ( r2_hidden(c5_7_1__rlsub_1,c2_7__rlsub_1) & r2_hidden(c6_7_1__rlsub_1,c3_7__rlsub_1) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[dh_c5_7_1__rlsub_1,dh_c6_7_1__rlsub_1,e6_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e8_7_1__rlsub_1),[file(rlsub_1,e8_7_1__rlsub_1)]]). fof(e9_7_1__rlsub_1,plain, ( r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c3_7_1__rlsub_1,c5_7_1__rlsub_1),c2_7__rlsub_1) & r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c4_7_1__rlsub_1,c6_7_1__rlsub_1),c3_7__rlsub_1) ), inference(mizar_by,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k4_tarski,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,fc6_membered,rc1_funct_1,rc1_membered,rc2_funct_1,rc4_struct_0,d5_tarski,reflexivity_r1_tarski,existence_l1_rlvect_1,existence_l1_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_rlvect_1,dt_l1_struct_0,dt_u2_rlvect_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_funct_1,cc1_relset_1,cc4_membered,fc1_struct_0,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c3_7_1__rlsub_1,dt_c4_7_1__rlsub_1,dt_c5_7_1__rlsub_1,dt_c6_7_1__rlsub_1,cc6_membered,fc1_subset_1,fc2_membered,rc3_rlvect_1,t1_subset,t3_subset,t4_subset,t7_boole,d4_rlvect_1,e1_7__rlsub_1,e5_7_1__rlsub_1,e8_7_1__rlsub_1,d1_rlsub_1]), [interesting(0.65),file(rlsub_1,e9_7_1__rlsub_1),[file(rlsub_1,e9_7_1__rlsub_1)]]). fof(e11_7_1__rlsub_1,plain,( r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1),c4_7__rlsub_1) ), inference(mizar_by,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,d5_tarski,reflexivity_r1_tarski,existence_l1_struct_0,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_struct_0,dt_u1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc4_subset_1,fc6_membered,rc1_membered,rc3_struct_0,rc4_struct_0,rc5_struct_0,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_rlvect_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,redefinition_k4_rlvect_1,dt_k4_rlvect_1,dt_c1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c3_7_1__rlsub_1,dt_c4_7__rlsub_1,dt_c4_7_1__rlsub_1,dt_c5_7_1__rlsub_1,dt_c6_7_1__rlsub_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_3_0_rlsub_1,e10_7_1__rlsub_1,e2_7__rlsub_1,e9_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,e11_7_1__rlsub_1),[file(rlsub_1,e11_7_1__rlsub_1)]]). fof(i4_7_1__rlsub_1,theorem,( $true ), introduced(tautology,[file(rlsub_1,i4_7_1__rlsub_1)]), [interesting(0.65),trivial,file(rlsub_1,i4_7_1__rlsub_1)]). fof(i3_7_1__rlsub_1,plain,( r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1),c4_7__rlsub_1) ), inference(conclusion,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7_1__rlsub_1,e1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1,e2_7_1__rlsub_1])],[e11_7_1__rlsub_1,i4_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,i3_7_1__rlsub_1),[file(rlsub_1,i3_7_1__rlsub_1)]]). fof(i2_7_1__rlsub_1,plain, ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(c2_7_1__rlsub_1,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1),c4_7__rlsub_1) ), inference(discharge_asm,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c2_7_1__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1]),discharge_asm(discharge,[e1_7_1__rlsub_1,e2_7_1__rlsub_1])],[e1_7_1__rlsub_1,e2_7_1__rlsub_1,i3_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,i2_7_1__rlsub_1),[file(rlsub_1,i2_7_1__rlsub_1)]]). fof(i2_7_1_tmp__rlsub_1,plain, ( m1_subset_1(c2_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(c2_7_1__rlsub_1,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,c2_7_1__rlsub_1),c4_7__rlsub_1) ) ), inference(discharge_asm,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1]),discharge_asm(discharge,[dt_c2_7_1__rlsub_1])],[dt_c2_7_1__rlsub_1,i2_7_1__rlsub_1]), [interesting(0.65),i1_7_1__rlsub_1]). fof(i1_7_1__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(A,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,A),c4_7__rlsub_1) ) ) ), inference(let,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7_1__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1])],[i2_7_1_tmp__rlsub_1,dh_c2_7_1__rlsub_1]), [interesting(0.65),file(rlsub_1,i1_7_1__rlsub_1),[file(rlsub_1,i1_7_1__rlsub_1)]]). fof(i1_7_1_tmp__rlsub_1,plain, ( m1_subset_1(c1_7_1__rlsub_1,u1_struct_0(c1_7__rlsub_1)) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(c1_7_1__rlsub_1,c4_7__rlsub_1) & r2_hidden(A,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,c1_7_1__rlsub_1,A),c4_7__rlsub_1) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1]),discharge_asm(discharge,[dt_c1_7_1__rlsub_1])],[dt_c1_7_1__rlsub_1,i1_7_1__rlsub_1]), [interesting(0.8),e3_7__rlsub_1]). fof(e3_7__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) => ( ( r2_hidden(A,c4_7__rlsub_1) & r2_hidden(B,c4_7__rlsub_1) ) => r2_hidden(k4_rlvect_1(c1_7__rlsub_1,A,B),c4_7__rlsub_1) ) ) ) ), inference(let,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1])],[i1_7_1_tmp__rlsub_1,dh_c1_7_1__rlsub_1]), [interesting(0.8),file(rlsub_1,e3_7__rlsub_1),[file(rlsub_1,e3_7__rlsub_1)]]). fof(dh_c5_7__rlsub_1,definition, ( ( m1_subset_1(c5_7__rlsub_1,k1_numbers) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(A,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,A,c5_7__rlsub_1),c4_7__rlsub_1) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(C,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,C,B),c4_7__rlsub_1) ) ) ) ), introduced(definition,[new_symbol(c5_7__rlsub_1),file(rlsub_1,c5_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c5_7__rlsub_1)]). fof(dh_c6_7__rlsub_1,definition, ( ( m1_subset_1(c6_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(c6_7__rlsub_1,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c6_7__rlsub_1,c5_7__rlsub_1),c4_7__rlsub_1) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(A,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,A,c5_7__rlsub_1),c4_7__rlsub_1) ) ) ), introduced(definition,[new_symbol(c6_7__rlsub_1),file(rlsub_1,c6_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c6_7__rlsub_1)]). fof(e4_7__rlsub_1,assumption,( r2_hidden(c6_7__rlsub_1,c4_7__rlsub_1) ), introduced(assumption,[file(rlsub_1,e4_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,e4_7__rlsub_1)]). fof(dt_c5_7__rlsub_1,assumption,( m1_subset_1(c5_7__rlsub_1,k1_numbers) ), introduced(assumption,[file(rlsub_1,c5_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c5_7__rlsub_1)]). fof(dt_c6_7__rlsub_1,assumption,( m1_subset_1(c6_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), introduced(assumption,[file(rlsub_1,c6_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c6_7__rlsub_1)]). fof(dh_c7_7__rlsub_1,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) & c6_7__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,A,B) & r2_hidden(A,c2_7__rlsub_1) & r2_hidden(B,c3_7__rlsub_1) ) ) => ( m1_subset_1(c7_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) & ? [C] : ( m1_subset_1(C,u1_struct_0(c1_7__rlsub_1)) & c6_7__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c7_7__rlsub_1,C) & r2_hidden(c7_7__rlsub_1,c2_7__rlsub_1) & r2_hidden(C,c3_7__rlsub_1) ) ) ), introduced(definition,[new_symbol(c7_7__rlsub_1),file(rlsub_1,c7_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c7_7__rlsub_1)]). fof(e5_7__rlsub_1,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) & c6_7__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,A,B) & r2_hidden(A,c2_7__rlsub_1) & r2_hidden(B,c3_7__rlsub_1) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,d5_tarski,reflexivity_r1_tarski,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l2_struct_0,dt_u1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc4_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,cc15_membered,cc1_funct_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_rlvect_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k4_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_3_0_rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1]), [interesting(0.8),file(rlsub_1,e5_7__rlsub_1),[file(rlsub_1,e5_7__rlsub_1)]]). fof(dt_c7_7__rlsub_1,plain,( m1_subset_1(c7_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[dh_c7_7__rlsub_1,e5_7__rlsub_1]), [interesting(0.8),file(rlsub_1,c7_7__rlsub_1),[file(rlsub_1,c7_7__rlsub_1)]]). fof(dh_c8_7__rlsub_1,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) & c6_7__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c7_7__rlsub_1,A) & r2_hidden(c7_7__rlsub_1,c2_7__rlsub_1) & r2_hidden(A,c3_7__rlsub_1) ) => ( m1_subset_1(c8_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) & c6_7__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c7_7__rlsub_1,c8_7__rlsub_1) & r2_hidden(c7_7__rlsub_1,c2_7__rlsub_1) & r2_hidden(c8_7__rlsub_1,c3_7__rlsub_1) ) ), introduced(definition,[new_symbol(c8_7__rlsub_1),file(rlsub_1,c8_7__rlsub_1)]), [interesting(0.8),axiom,file(rlsub_1,c8_7__rlsub_1)]). fof(dt_c8_7__rlsub_1,plain,( m1_subset_1(c8_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[dh_c7_7__rlsub_1,dh_c8_7__rlsub_1,e5_7__rlsub_1]), [interesting(0.8),file(rlsub_1,c8_7__rlsub_1),[file(rlsub_1,c8_7__rlsub_1)]]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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(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(spc5_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ), file(arithm,spc5_arithm), [interesting(0.9),axiom,file(arithm,spc5_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc7_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t3_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), [interesting(0.9),axiom,file(arithm,t3_arithm)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(commutativity_k3_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). 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_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). 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_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_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_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(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,( k3_xcmplx_0(1,1) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]). fof(commutativity_k3_real_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), [interesting(0.9),axiom,file(real_1,k3_real_1)]). fof(commutativity_k4_real_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), [interesting(0.9),axiom,file(real_1,k4_real_1)]). fof(redefinition_k3_real_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), [interesting(0.9),axiom,file(real_1,k3_real_1)]). fof(redefinition_k4_real_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_1), [interesting(0.9),axiom,file(real_1,k4_real_1)]). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), [interesting(0.9),axiom,file(real_1,k3_real_1)]). fof(dt_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), [interesting(0.9),axiom,file(real_1,k4_real_1)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(e6_7__rlsub_1,plain,( c6_7__rlsub_1 = k4_rlvect_1(c1_7__rlsub_1,c7_7__rlsub_1,c8_7__rlsub_1) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[dh_c7_7__rlsub_1,dh_c8_7__rlsub_1,e5_7__rlsub_1]), [interesting(0.8),file(rlsub_1,e6_7__rlsub_1),[file(rlsub_1,e6_7__rlsub_1)]]). fof(d9_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) ) => ( v7_rlvect_1(A) <=> ( ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_rlvect_1(A,B,1) = B ) ) ) ) ), file(rlvect_1,d9_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d9_rlvect_1)]). fof(e9_7__rlsub_1,plain,( k3_rlvect_1(c1_7__rlsub_1,c6_7__rlsub_1,c5_7__rlsub_1) = k4_rlvect_1(c1_7__rlsub_1,k3_rlvect_1(c1_7__rlsub_1,c7_7__rlsub_1,c5_7__rlsub_1),k3_rlvect_1(c1_7__rlsub_1,c8_7__rlsub_1,c5_7__rlsub_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c5_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,rc3_funct_1,commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,cc2_funct_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc2_funct_1,antisymmetry_r2_hidden,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_k5_ordinal2,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc4_struct_0,rc5_struct_0,spc5_arithm,spc6_arithm,spc7_arithm,t1_subset,t3_arithm,t3_subset,t4_subset,t5_subset,d5_tarski,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_m2_subset_1,redefinition_k1_domain_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_domain_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_xcmplx_0,dt_k5_numbers,dt_k8_funct_2,dt_l1_rlvect_1,dt_l1_struct_0,dt_m2_subset_1,dt_u1_rlvect_1,dt_u2_rlvect_1,cc10_membered,cc11_membered,cc15_membered,cc1_funct_1,cc4_membered,fc1_struct_0,fc4_subset_1,rc3_struct_0,rqRealMult__k3_xcmplx_0__r1_r1_r1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_real_1,commutativity_k4_real_1,commutativity_k4_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k2_rlvect_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k4_real_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c5_7__rlsub_1,dt_c6_7__rlsub_1,dt_c7_7__rlsub_1,dt_c8_7__rlsub_1,fc2_membered,rc3_rlvect_1,d3_rlvect_1,d4_rlvect_1,spc1_numerals,spc1_boole,e6_7__rlsub_1,d9_rlvect_1]), [interesting(0.8),file(rlsub_1,e9_7__rlsub_1),[file(rlsub_1,e9_7__rlsub_1)]]). fof(e7_7__rlsub_1,plain, ( r2_hidden(c7_7__rlsub_1,c2_7__rlsub_1) & r2_hidden(c8_7__rlsub_1,c3_7__rlsub_1) ), inference(consider,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[dh_c7_7__rlsub_1,dh_c8_7__rlsub_1,e5_7__rlsub_1]), [interesting(0.8),file(rlsub_1,e7_7__rlsub_1),[file(rlsub_1,e7_7__rlsub_1)]]). fof(e8_7__rlsub_1,plain, ( r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c7_7__rlsub_1,c5_7__rlsub_1),c2_7__rlsub_1) & r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c8_7__rlsub_1,c5_7__rlsub_1),c3_7__rlsub_1) ), inference(mizar_by,[status(thm),assumptions([dt_c5_7__rlsub_1,e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k4_tarski,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u1_rlvect_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,fc6_membered,rc1_funct_1,rc1_membered,rc2_funct_1,rc4_struct_0,d5_tarski,reflexivity_r1_tarski,existence_l1_rlvect_1,existence_l1_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_rlvect_1,dt_l1_struct_0,dt_u2_rlvect_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_funct_1,cc1_relset_1,cc4_membered,fc1_struct_0,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c5_7__rlsub_1,dt_c7_7__rlsub_1,dt_c8_7__rlsub_1,cc6_membered,fc1_subset_1,fc2_membered,rc3_rlvect_1,t1_subset,t3_subset,t4_subset,t7_boole,d4_rlvect_1,e1_7__rlsub_1,e7_7__rlsub_1,d1_rlsub_1]), [interesting(0.8),file(rlsub_1,e8_7__rlsub_1),[file(rlsub_1,e8_7__rlsub_1)]]). fof(e10_7__rlsub_1,plain,( r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c6_7__rlsub_1,c5_7__rlsub_1),c4_7__rlsub_1) ), inference(mizar_by,[status(thm),assumptions([dt_c5_7__rlsub_1,e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[cc1_realset1,rc1_realset1,rc2_realset1,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc2_subset_1,fc3_realset1,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_funct_1,reflexivity_r1_tarski,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k4_tarski,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u1_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_funct_1,cc2_membered,cc3_membered,cc4_membered,fc1_struct_0,fc6_membered,rc1_funct_1,rc1_membered,rc2_funct_1,rc3_struct_0,rc4_struct_0,rc5_struct_0,d5_tarski,existence_l1_rlvect_1,existence_l2_rlvect_1,existence_m1_subset_1,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_u2_rlvect_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc6_membered,fc1_subset_1,fc2_membered,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_rlvect_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_rlvect_1,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,redefinition_k4_rlvect_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c5_7__rlsub_1,dt_c6_7__rlsub_1,dt_c7_7__rlsub_1,dt_c8_7__rlsub_1,t1_subset,t7_boole,t2_tarski,fraenkel_a_3_0_rlsub_1,d4_rlvect_1,e9_7__rlsub_1,e2_7__rlsub_1,e8_7__rlsub_1]), [interesting(0.8),file(rlsub_1,e10_7__rlsub_1),[file(rlsub_1,e10_7__rlsub_1)]]). fof(i10_7__rlsub_1,theorem,( $true ), introduced(tautology,[file(rlsub_1,i10_7__rlsub_1)]), [interesting(0.8),trivial,file(rlsub_1,i10_7__rlsub_1)]). fof(i9_7__rlsub_1,plain,( r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c6_7__rlsub_1,c5_7__rlsub_1),c4_7__rlsub_1) ), inference(conclusion,[status(thm),assumptions([dt_c5_7__rlsub_1,e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e4_7__rlsub_1,e2_7__rlsub_1])],[e10_7__rlsub_1,i10_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i9_7__rlsub_1),[file(rlsub_1,i9_7__rlsub_1)]]). fof(i8_7__rlsub_1,plain, ( r2_hidden(c6_7__rlsub_1,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c6_7__rlsub_1,c5_7__rlsub_1),c4_7__rlsub_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_7__rlsub_1,e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,dt_c6_7__rlsub_1,e2_7__rlsub_1]),discharge_asm(discharge,[e4_7__rlsub_1])],[e4_7__rlsub_1,i9_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i8_7__rlsub_1),[file(rlsub_1,i8_7__rlsub_1)]]). fof(i8_7_tmp__rlsub_1,plain, ( m1_subset_1(c6_7__rlsub_1,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(c6_7__rlsub_1,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,c6_7__rlsub_1,c5_7__rlsub_1),c4_7__rlsub_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_7__rlsub_1,e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1]),discharge_asm(discharge,[dt_c6_7__rlsub_1])],[dt_c6_7__rlsub_1,i8_7__rlsub_1]), [interesting(0.8),i7_7__rlsub_1]). fof(i7_7__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(A,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,A,c5_7__rlsub_1),c4_7__rlsub_1) ) ) ), inference(let,[status(thm),assumptions([dt_c5_7__rlsub_1,e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1])],[i8_7_tmp__rlsub_1,dh_c6_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i7_7__rlsub_1),[file(rlsub_1,i7_7__rlsub_1)]]). fof(i7_7_tmp__rlsub_1,plain, ( m1_subset_1(c5_7__rlsub_1,k1_numbers) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(A,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,A,c5_7__rlsub_1),c4_7__rlsub_1) ) ) ), inference(discharge_asm,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1]),discharge_asm(discharge,[dt_c5_7__rlsub_1])],[dt_c5_7__rlsub_1,i7_7__rlsub_1]), [interesting(0.8),i6_7__rlsub_1]). fof(i6_7__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_7__rlsub_1)) => ( r2_hidden(B,c4_7__rlsub_1) => r2_hidden(k3_rlvect_1(c1_7__rlsub_1,B,A),c4_7__rlsub_1) ) ) ) ), inference(let,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1])],[i7_7_tmp__rlsub_1,dh_c5_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i6_7__rlsub_1),[file(rlsub_1,i6_7__rlsub_1)]]). fof(i5_7__rlsub_1,plain,( v1_rlsub_1(c4_7__rlsub_1,c1_7__rlsub_1) ), inference(conclusion,[status(thm),assumptions([e1_7__rlsub_1,dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1,e2_7__rlsub_1])],[dt_l2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,rc1_membered,rc4_struct_0,dt_k2_rlvect_1,dt_l1_rlvect_1,dt_l1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_funct_1,cc4_membered,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,commutativity_k4_rlvect_1,antisymmetry_r2_hidden,redefinition_k4_rlvect_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_rlvect_1,dt_k4_rlvect_1,dt_l2_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_7__rlsub_1,dt_c4_7__rlsub_1,cc6_membered,fc1_subset_1,fc2_membered,rc3_rlvect_1,d1_rlsub_1,e3_7__rlsub_1,i6_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i5_7__rlsub_1),[file(rlsub_1,i5_7__rlsub_1)]]). fof(i4_7__rlsub_1,plain, ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & c4_7__rlsub_1 = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(c4_7__rlsub_1,c1_7__rlsub_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1,dt_c4_7__rlsub_1]),discharge_asm(discharge,[e1_7__rlsub_1,e2_7__rlsub_1])],[e1_7__rlsub_1,e2_7__rlsub_1,i5_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i4_7__rlsub_1),[file(rlsub_1,i4_7__rlsub_1)]]). fof(i4_7_tmp__rlsub_1,plain, ( m1_subset_1(c4_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & c4_7__rlsub_1 = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(c4_7__rlsub_1,c1_7__rlsub_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1]),discharge_asm(discharge,[dt_c4_7__rlsub_1])],[dt_c4_7__rlsub_1,i4_7__rlsub_1]), [interesting(0.8),i3_7__rlsub_1]). fof(i3_7__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & A = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(A,c1_7__rlsub_1) ) ) ), inference(let,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1,dt_c3_7__rlsub_1])],[i4_7_tmp__rlsub_1,dh_c4_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i3_7__rlsub_1),[file(rlsub_1,i3_7__rlsub_1)]]). fof(i3_7_tmp__rlsub_1,plain, ( m1_subset_1(c3_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(c3_7__rlsub_1,c1_7__rlsub_1) & A = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,c3_7__rlsub_1) ) => v1_rlsub_1(A,c1_7__rlsub_1) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1]),discharge_asm(discharge,[dt_c3_7__rlsub_1])],[dt_c3_7__rlsub_1,i3_7__rlsub_1]), [interesting(0.8),i2_7__rlsub_1]). fof(i2_7__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(A,c1_7__rlsub_1) & B = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,A) ) => v1_rlsub_1(B,c1_7__rlsub_1) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_7__rlsub_1,dt_c2_7__rlsub_1])],[i3_7_tmp__rlsub_1,dh_c3_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i2_7__rlsub_1),[file(rlsub_1,i2_7__rlsub_1)]]). fof(i2_7_tmp__rlsub_1,plain, ( m1_subset_1(c2_7__rlsub_1,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(c2_7__rlsub_1,c1_7__rlsub_1) & v1_rlsub_1(A,c1_7__rlsub_1) & B = a_3_0_rlsub_1(c1_7__rlsub_1,c2_7__rlsub_1,A) ) => v1_rlsub_1(B,c1_7__rlsub_1) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_7__rlsub_1]),discharge_asm(discharge,[dt_c2_7__rlsub_1])],[dt_c2_7__rlsub_1,i2_7__rlsub_1]), [interesting(0.8),i1_7__rlsub_1]). fof(i1_7__rlsub_1,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(A,c1_7__rlsub_1) & v1_rlsub_1(B,c1_7__rlsub_1) & C = a_3_0_rlsub_1(c1_7__rlsub_1,A,B) ) => v1_rlsub_1(C,c1_7__rlsub_1) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_7__rlsub_1])],[i2_7_tmp__rlsub_1,dh_c2_7__rlsub_1]), [interesting(0.8),file(rlsub_1,i1_7__rlsub_1),[file(rlsub_1,i1_7__rlsub_1)]]). fof(i1_7_tmp__rlsub_1,plain, ( ( ~ v3_struct_0(c1_7__rlsub_1) & v3_rlvect_1(c1_7__rlsub_1) & v4_rlvect_1(c1_7__rlsub_1) & v5_rlvect_1(c1_7__rlsub_1) & v6_rlvect_1(c1_7__rlsub_1) & v7_rlvect_1(c1_7__rlsub_1) & l2_rlvect_1(c1_7__rlsub_1) ) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_7__rlsub_1))) => ( ( v1_rlsub_1(A,c1_7__rlsub_1) & v1_rlsub_1(B,c1_7__rlsub_1) & C = a_3_0_rlsub_1(c1_7__rlsub_1,A,B) ) => v1_rlsub_1(C,c1_7__rlsub_1) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__rlsub_1])],[dt_c1_7__rlsub_1,i1_7__rlsub_1]), [interesting(1),t9_rlsub_1]). fof(t9_rlsub_1,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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_rlsub_1(B,A) & v1_rlsub_1(C,A) & D = a_3_0_rlsub_1(A,B,C) ) => v1_rlsub_1(D,A) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_7_tmp__rlsub_1,dh_c1_7__rlsub_1]), [interesting(1),file(rlsub_1,t9_rlsub_1),[file(rlsub_1,t9_rlsub_1)]]).