% Mizar ND problem: t5_ami_6,ami_6,82,72 fof(dh_c1_5__ami_6,definition, ( ( m1_ami_3(c1_5__ami_6) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(A,c1_5__ami_6) = k2_ami_3(B,c1_5__ami_6) ) ) ) ) => ! [C] : ( m1_ami_3(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [E] : ( m1_subset_1(E,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(D,E,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(D,C) = k2_ami_3(E,C) ) ) ) ) ), introduced(definition,[new_symbol(c1_5__ami_6),file(ami_6,c1_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,c1_5__ami_6)]). fof(dh_c2_5__ami_6,definition, ( ( m1_subset_1(c2_5__ami_6,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(c2_5__ami_6,A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(A,c1_5__ami_6) ) ) ) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(B,C,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(B,c1_5__ami_6) = k2_ami_3(C,c1_5__ami_6) ) ) ) ), introduced(definition,[new_symbol(c2_5__ami_6),file(ami_6,c2_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,c2_5__ami_6)]). fof(dh_c3_5__ami_6,definition, ( ( m1_subset_1(c3_5__ami_6,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(c2_5__ami_6,c3_5__ami_6,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(c3_5__ami_6,c1_5__ami_6) ) ) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(c2_5__ami_6,A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(A,c1_5__ami_6) ) ) ), introduced(definition,[new_symbol(c3_5__ami_6),file(ami_6,c3_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,c3_5__ami_6)]). fof(e1_5__ami_6,assumption,( r1_funct_7(c2_5__ami_6,c3_5__ami_6,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), introduced(assumption,[file(ami_6,e1_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,e1_5__ami_6)]). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), [interesting(0.9),axiom,file(finseq_1,k13_finseq_1)]). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), [interesting(0.9),axiom,file(funct_2,k1_funct_2)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), [interesting(0.9),axiom,file(tarski,k3_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(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(cc3_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc3_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). fof(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(fc16_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc16_finseq_1)]). 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_fraenkel,theorem,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,fc1_fraenkel)]). fof(fc2_fraenkel,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => ( v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)) ) ) ), file(fraenkel,fc2_fraenkel), [interesting(0.9),axiom,file(fraenkel,fc2_fraenkel)]). fof(fc4_ami_1,theorem,( ! [A,B,C] : ( ( v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( ~ v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)) ) ) ), file(ami_1,fc4_ami_1), [interesting(0.9),axiom,file(ami_1,fc4_ami_1)]). fof(fc9_finseq_1,theorem,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc9_finseq_1)]). fof(rc1_amistd_2,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) & v1_pralg_2(A) & v1_amistd_2(A) ) ), file(amistd_2,rc1_amistd_2), [interesting(0.9),axiom,file(amistd_2,rc1_amistd_2)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(free_g1_ami_1,definition,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ! [I,J,K,L,M,N,O,P] : ( g1_ami_1(A,B,C,D,E,F,G,H) = g1_ami_1(I,J,K,L,M,N,O,P) => ( A = I & B = J & C = K & D = L & E = M & F = N & G = O & H = P ) ) ) ), file(ami_1,g1_ami_1), [interesting(0.9),axiom,file(ami_1,g1_ami_1)]). 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(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(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_g1_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ), file(ami_1,g1_ami_1), [interesting(0.9),axiom,file(ami_1,g1_ami_1)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_u1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u1_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,u1_ami_1), [interesting(0.9),axiom,file(ami_1,u1_ami_1)]). fof(dt_u3_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ~ v1_xboole_0(u3_ami_1(A,B)) ) ), file(ami_1,u3_ami_1), [interesting(0.9),axiom,file(ami_1,u3_ami_1)]). fof(dt_u4_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( ~ v1_xboole_0(u4_ami_1(A,B)) & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ), file(ami_1,u4_ami_1), [interesting(0.9),axiom,file(ami_1,u4_ami_1)]). fof(dt_u6_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u6_ami_1(A,B)) & v1_funct_2(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) & m2_relset_1(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) ) ) ), file(ami_1,u6_ami_1), [interesting(0.9),axiom,file(ami_1,u6_ami_1)]). 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(cc1_amistd_2,theorem,( ! [A] : ( v1_amistd_2(A) => ( v1_fraenkel(A) & v1_pralg_2(A) ) ) ), file(amistd_2,cc1_amistd_2), [interesting(0.9),axiom,file(amistd_2,cc1_amistd_2)]). fof(cc1_fraenkel,theorem,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_setfam_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(setfam_1,cc1_setfam_1), [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]). fof(cc1_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_tex_2(B,k1_zfmisc_1(A)) => ~ v1_xboole_0(B) ) ) ) ), file(tex_2,cc1_tex_2), [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]). 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(cc3_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_tex_2(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc3_tex_2), [interesting(0.9),axiom,file(tex_2,cc3_tex_2)]). fof(cc5_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc5_tex_2), [interesting(0.9),axiom,file(tex_2,cc5_tex_2)]). fof(cc7_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ) ) ), file(tex_2,cc7_tex_2), [interesting(0.9),axiom,file(tex_2,cc7_tex_2)]). 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(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(fc22_membered,theorem,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), [interesting(0.9),axiom,file(membered,fc22_membered)]). fof(fc23_membered,theorem,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), [interesting(0.9),axiom,file(membered,fc23_membered)]). fof(fc24_membered,theorem,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), [interesting(0.9),axiom,file(membered,fc24_membered)]). fof(fc25_membered,theorem,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), [interesting(0.9),axiom,file(membered,fc25_membered)]). fof(fc26_membered,theorem,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), [interesting(0.9),axiom,file(membered,fc26_membered)]). fof(fc2_relat_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) ), file(relat_1,fc2_relat_1), [interesting(0.9),axiom,file(relat_1,fc2_relat_1)]). fof(fc2_xboole_0,theorem,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]). fof(fc3_setfam_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)) ) ) ), file(setfam_1,fc3_setfam_1), [interesting(0.9),axiom,file(setfam_1,fc3_setfam_1)]). fof(fc3_xboole_0,theorem,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]). fof(fc41_membered,theorem,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), [interesting(0.9),axiom,file(membered,fc41_membered)]). fof(fc4_setfam_1,theorem,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_1), [interesting(0.9),axiom,file(setfam_1,fc4_setfam_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(rc1_fraenkel,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]). 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_setfam_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), [interesting(0.9),axiom,file(setfam_1,rc1_setfam_1)]). fof(rc2_tex_2,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ), file(tex_2,rc2_tex_2), [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]). fof(rc3_ami_1,theorem,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) ) ) ), file(ami_1,rc3_ami_1), [interesting(0.9),axiom,file(ami_1,rc3_ami_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(rc3_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc3_tex_2), [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]). fof(rc4_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc4_tex_2), [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]). 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(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(rc6_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc6_tex_2), [interesting(0.9),axiom,file(tex_2,rc6_tex_2)]). fof(rc7_ami_1,theorem,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) ) ), file(ami_1,rc7_ami_1), [interesting(0.9),axiom,file(ami_1,rc7_ami_1)]). fof(rc7_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc7_tex_2), [interesting(0.9),axiom,file(tex_2,rc7_tex_2)]). fof(abstractness_v1_ami_1,theorem,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_ami_1(B,A) => B = g1_ami_1(A,u1_struct_0(B),u1_ami_1(A,B),u2_ami_1(A,B),u3_ami_1(A,B),u4_ami_1(A,B),u5_ami_1(A,B),u6_ami_1(A,B)) ) ) ), file(ami_1,v1_ami_1), [interesting(0.9),axiom,file(ami_1,v1_ami_1)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), [interesting(0.9),axiom,file(card_3,k4_card_3)]). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), [interesting(0.9),axiom,file(ami_1,l1_ami_1)]). fof(dt_m1_ami_3,axiom,( ! [A] : ( m1_ami_3(A) => m1_subset_1(A,u1_struct_0(k1_ami_3)) ) ), file(ami_3,m1_ami_3), [interesting(0.9),axiom,file(ami_3,m1_ami_3)]). 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_u5_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u5_ami_1(A,B)) & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ), file(ami_1,u5_ami_1), [interesting(0.9),axiom,file(ami_1,u5_ami_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(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(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(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_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_int_1,theorem,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_1), [interesting(0.9),axiom,file(int_1,cc1_int_1)]). fof(cc1_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]). fof(cc1_scmring1,theorem,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ) ), file(scmring1,cc1_scmring1), [interesting(0.9),axiom,file(scmring1,cc1_scmring1)]). 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(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc2_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ), file(tex_2,cc2_tex_2), [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), [interesting(0.9),axiom,file(int_1,cc4_int_1)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc4_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_xboole_0(B) => ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc4_tex_2), [interesting(0.9),axiom,file(tex_2,cc4_tex_2)]). fof(cc6_tex_2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & v1_realset1(B) ) => ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc6_tex_2), [interesting(0.9),axiom,file(tex_2,cc6_tex_2)]). fof(cc8_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) ) ) ), file(membered,cc8_membered), [interesting(0.9),axiom,file(membered,cc8_membered)]). 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(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc2_ami_1,theorem,( ! [A,B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ~ v1_xboole_0(u2_ami_1(A,B)) ) ), file(ami_1,fc2_ami_1), [interesting(0.9),axiom,file(ami_1,fc2_ami_1)]). fof(fc2_setfam_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)) ) ) ), file(setfam_1,fc2_setfam_1), [interesting(0.9),axiom,file(setfam_1,fc2_setfam_1)]). fof(fc37_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), [interesting(0.9),axiom,file(membered,fc37_membered)]). fof(fc38_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), [interesting(0.9),axiom,file(membered,fc38_membered)]). fof(fc39_membered,theorem,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), [interesting(0.9),axiom,file(membered,fc39_membered)]). fof(fc3_ami_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(ami_1,fc3_ami_1), [interesting(0.9),axiom,file(ami_1,fc3_ami_1)]). fof(fc3_relat_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k4_xboole_0(A,B)) ) ), file(relat_1,fc3_relat_1), [interesting(0.9),axiom,file(relat_1,fc3_relat_1)]). fof(fc40_membered,theorem,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), [interesting(0.9),axiom,file(membered,fc40_membered)]). fof(fc4_amistd_2,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k4_xboole_0(A,B)) & v1_funct_1(k4_xboole_0(A,B)) & v1_setfam_1(k4_xboole_0(A,B)) ) ) ), file(amistd_2,fc4_amistd_2), [interesting(0.9),axiom,file(amistd_2,fc4_amistd_2)]). fof(fc4_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), [interesting(0.9),axiom,file(funct_1,fc4_funct_1)]). fof(fc5_amistd_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_fraenkel(k4_card_3(A)) & v1_amistd_2(k4_card_3(A)) ) ) ), file(amistd_2,fc5_amistd_2), [interesting(0.9),axiom,file(amistd_2,fc5_amistd_2)]). fof(fc5_relat_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]). fof(fc7_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]). fof(rc1_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) ) ), file(ami_1,rc1_ami_1), [interesting(0.9),axiom,file(ami_1,rc1_ami_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_relat_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]). fof(rc1_tex_2,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(tex_2,rc1_tex_2), [interesting(0.9),axiom,file(tex_2,rc1_tex_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_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), [interesting(0.9),axiom,file(ami_1,rc2_ami_1)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc2_int_1,theorem,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), [interesting(0.9),axiom,file(int_1,rc2_int_1)]). fof(rc2_relat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), [interesting(0.9),axiom,file(relat_1,rc2_relat_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(rc5_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) ) ), file(ami_1,rc5_ami_1), [interesting(0.9),axiom,file(ami_1,rc5_ami_1)]). fof(rc5_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) ) ) ), file(tex_2,rc5_tex_2), [interesting(0.9),axiom,file(tex_2,rc5_tex_2)]). fof(rc6_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) ) ), file(ami_1,rc6_ami_1), [interesting(0.9),axiom,file(ami_1,rc6_ami_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc8_ami_1), [interesting(0.9),axiom,file(ami_1,rc8_ami_1)]). fof(rc9_ami_1,theorem,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc9_ami_1), [interesting(0.9),axiom,file(ami_1,rc9_ami_1)]). fof(redefinition_k2_ami_3,definition,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_ami_3(B) ) => k2_ami_3(A,B) = k1_funct_1(A,B) ) ), file(ami_3,k2_ami_3), [interesting(0.9),axiom,file(ami_3,k2_ami_3)]). fof(dt_k1_ami_3,axiom, ( v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & l1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,k1_ami_3), [interesting(0.9),axiom,file(ami_3,k1_ami_3)]). 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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k2_ami_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_ami_3(B) ) => v1_int_1(k2_ami_3(A,B)) ) ), file(ami_3,k2_ami_3), [interesting(0.9),axiom,file(ami_3,k2_ami_3)]). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), [interesting(0.9),axiom,file(numbers,k4_numbers)]). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), [interesting(0.9),axiom,file(relat_1,k7_relat_1)]). fof(dt_u2_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ), file(ami_1,u2_ami_1), [interesting(0.9),axiom,file(ami_1,u2_ami_1)]). fof(dt_c1_5__ami_6,assumption,( m1_ami_3(c1_5__ami_6) ), introduced(assumption,[file(ami_6,c1_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,c1_5__ami_6)]). fof(dt_c2_5__ami_6,assumption,( m1_subset_1(c2_5__ami_6,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ), introduced(assumption,[file(ami_6,c2_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,c2_5__ami_6)]). fof(dt_c3_5__ami_6,assumption,( m1_subset_1(c3_5__ami_6,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ), introduced(assumption,[file(ami_6,c3_5__ami_6)]), [interesting(0.8),axiom,file(ami_6,c3_5__ami_6)]). fof(fc1_ami_3,theorem, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc1_ami_3), [interesting(0.9),axiom,file(ami_3,fc1_ami_3)]). fof(fc1_tex_2,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(tex_2,fc1_tex_2), [interesting(0.9),axiom,file(tex_2,fc1_tex_2)]). fof(fc2_ami_3,theorem, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc2_ami_3), [interesting(0.9),axiom,file(ami_3,fc2_ami_3)]). fof(fc2_ami_5,theorem, ( ~ v1_xboole_0(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), file(ami_5,fc2_ami_5), [interesting(0.9),axiom,file(ami_5,fc2_ami_5)]). fof(fc3_ami_3,theorem, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc3_ami_3), [interesting(0.9),axiom,file(ami_3,fc3_ami_3)]). fof(fc4_membered,theorem, ( ~ v1_xboole_0(k4_numbers) & v1_membered(k4_numbers) & v2_membered(k4_numbers) & v3_membered(k4_numbers) & v4_membered(k4_numbers) ), file(membered,fc4_membered), [interesting(0.9),axiom,file(membered,fc4_membered)]). fof(fc5_ami_3,theorem, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v7_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc5_ami_3), [interesting(0.9),axiom,file(ami_3,fc5_ami_3)]). 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(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(fc13_relat_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)) ) ) ), file(relat_1,fc13_relat_1), [interesting(0.9),axiom,file(relat_1,fc13_relat_1)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc3_relat_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]). fof(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(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_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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(fc12_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]). 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(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc35_membered,theorem,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), [interesting(0.9),axiom,file(membered,fc35_membered)]). fof(fc36_membered,theorem,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), [interesting(0.9),axiom,file(membered,fc36_membered)]). fof(fc4_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), [interesting(0.9),axiom,file(relat_1,fc4_relat_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(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). fof(t2_boole,theorem,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), [interesting(0.9),axiom,file(boole,t2_boole)]). fof(t3_boole,theorem,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), [interesting(0.9),axiom,file(boole,t3_boole)]). fof(t4_boole,theorem,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), [interesting(0.9),axiom,file(boole,t4_boole)]). fof(existence_l1_ami_1,axiom,( ! [A] : ? [B] : l1_ami_1(B,A) ), file(ami_1,l1_ami_1), [interesting(0.9),axiom,file(ami_1,l1_ami_1)]). fof(existence_m1_ami_3,axiom,( ? [A] : m1_ami_3(A) ), file(ami_3,m1_ami_3), [interesting(0.9),axiom,file(ami_3,m1_ami_3)]). 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(fc27_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), [interesting(0.9),axiom,file(membered,fc27_membered)]). fof(fc28_membered,theorem,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), [interesting(0.9),axiom,file(membered,fc28_membered)]). fof(fc29_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), [interesting(0.9),axiom,file(membered,fc29_membered)]). fof(fc30_membered,theorem,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), [interesting(0.9),axiom,file(membered,fc30_membered)]). fof(fc31_membered,theorem,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), [interesting(0.9),axiom,file(membered,fc31_membered)]). fof(fc32_membered,theorem,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), [interesting(0.9),axiom,file(membered,fc32_membered)]). fof(fc33_membered,theorem,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), [interesting(0.9),axiom,file(membered,fc33_membered)]). fof(fc34_membered,theorem,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), [interesting(0.9),axiom,file(membered,fc34_membered)]). 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(commutativity_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(idempotence_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). 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(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(fc1_relat_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_1), [interesting(0.9),axiom,file(relat_1,fc1_relat_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(t1_ami_6,theorem,( ! [A] : ( m1_ami_3(A) => ~ r2_hidden(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_6,t1_ami_6), [interesting(0.9),axiom,file(ami_6,t1_ami_6)]). fof(e4_5__ami_6,plain,( ~ r2_hidden(c1_5__ami_6,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6])],[rc1_amistd_2,cc1_amistd_2,cc1_fraenkel,rc1_fraenkel,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_card_3,dt_m1_relset_1,dt_m2_relset_1,cc1_finseq_1,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_fraenkel,fc2_relat_1,fc2_xboole_0,fc3_ami_1,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc4_setfam_1,fc5_amistd_2,fc9_finseq_1,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,t1_boole,free_g1_ami_1,reflexivity_r1_tarski,existence_l1_struct_0,dt_g1_ami_1,dt_k1_xboole_0,dt_l1_struct_0,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc1_tex_2,cc20_membered,cc2_funct_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc12_relat_1,fc1_struct_0,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_membered,rc1_relat_1,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_tex_2,rc3_ami_1,rc3_struct_0,rc3_tex_2,rc4_tex_2,rc5_struct_0,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t8_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_ami_1,dt_m1_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc2_ami_1,fc2_setfam_1,rc1_ami_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc5_ami_1,rc5_tex_2,rc6_ami_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_ami_3,dt_k1_ami_3,dt_k1_tarski,dt_k4_numbers,dt_m1_ami_3,dt_u2_ami_1,dt_c1_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc4_membered,fc5_ami_3,t1_subset,t7_boole,t1_ami_6]), [interesting(0.8),file(ami_6,e4_5__ami_6),[file(ami_6,e4_5__ami_6)]]). fof(t36_ami_3,theorem,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k1_relat_1(C) = u1_struct_0(B) ) ) ) ), file(ami_3,t36_ami_3), [interesting(0.9),axiom,file(ami_3,t36_ami_3)]). fof(e2_5__ami_6,plain,( k1_relat_1(c2_5__ami_6) = u1_struct_0(k1_ami_3) ), inference(mizar_by,[status(thm),assumptions([dt_c2_5__ami_6])],[cc1_finseq_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_xboole_0,cc14_membered,cc1_membered,cc1_tex_2,cc20_membered,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc1_fraenkel,fc1_xboole_0,fc26_membered,fc2_finseq_1,fc2_fraenkel,fc4_relat_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,rc6_finseq_1,rc6_tex_2,rc7_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,free_g1_ami_1,existence_m1_relset_1,dt_g1_ami_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u6_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_membered,cc4_int_1,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc10_membered,fc15_membered,fc16_finseq_1,fc17_finseq_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc5_relat_1,fc7_relat_1,fc9_finseq_1,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_tex_2,rc1_xboole_0,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,rc5_struct_0,rc5_tex_2,rc7_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,abstractness_v1_ami_1,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k4_numbers,dt_l1_struct_0,dt_m2_relset_1,dt_u2_ami_1,dt_u4_ami_1,cc1_int_1,fc1_struct_0,fc1_tex_2,fc2_ami_1,fc2_ami_5,fc2_relat_1,fc3_ami_1,fc4_membered,fc4_setfam_1,fc5_amistd_2,rc1_ami_1,rc1_funct_1,rc2_ami_1,rc3_ami_1,rc3_struct_0,rc5_ami_1,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,existence_l1_ami_1,existence_m1_subset_1,dt_k1_ami_3,dt_k1_relat_1,dt_k4_card_3,dt_l1_ami_1,dt_m1_subset_1,dt_u1_struct_0,dt_u5_ami_1,dt_c2_5__ami_6,fc1_ami_3,fc2_ami_3,fc3_ami_3,fc5_ami_3,t36_ami_3]), [interesting(0.8),file(ami_6,e2_5__ami_6),[file(ami_6,e2_5__ami_6)]]). fof(d4_xboole_0,definition,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]). fof(e5_5__ami_6,plain,( r2_hidden(c1_5__ami_6,k4_xboole_0(k1_relat_1(c2_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6,dt_c2_5__ami_6])],[rc1_amistd_2,existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_amistd_2,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc1_tex_2,cc20_membered,cc2_funct_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc17_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_ami_1,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_amistd_2,fc4_relat_1,fc4_setfam_1,fc5_amistd_2,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_membered,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_tex_2,rc3_ami_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t1_boole,t3_boole,t4_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_3,dt_m1_subset_1,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc1_struct_0,fc2_ami_1,fc2_setfam_1,fc37_membered,fc38_membered,fc39_membered,fc3_relat_1,fc40_membered,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_ami_1,rc5_struct_0,rc5_tex_2,rc6_ami_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_ami_3,dt_k1_relat_1,dt_k1_tarski,dt_k4_numbers,dt_k4_xboole_0,dt_u1_struct_0,dt_u2_ami_1,dt_c1_5__ami_6,dt_c2_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc4_membered,fc5_ami_3,t1_subset,t7_boole,e4_5__ami_6,e2_5__ami_6,d4_xboole_0]), [interesting(0.8),file(ami_6,e5_5__ami_6),[file(ami_6,e5_5__ami_6)]]). fof(d3_xboole_0,definition,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]). fof(e6_5__ami_6,plain,( r2_hidden(c1_5__ami_6,k3_xboole_0(k1_relat_1(c2_5__ami_6),k4_xboole_0(k1_relat_1(c2_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6,dt_c2_5__ami_6])],[rc1_amistd_2,existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_amistd_2,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc1_tex_2,cc20_membered,cc2_funct_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc17_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc35_membered,fc36_membered,fc3_ami_1,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_amistd_2,fc4_relat_1,fc4_setfam_1,fc5_amistd_2,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_membered,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_tex_2,rc3_ami_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t1_boole,t2_boole,t3_boole,t4_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_3,dt_m1_subset_1,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc1_relat_1,fc1_struct_0,fc27_membered,fc28_membered,fc29_membered,fc2_ami_1,fc2_setfam_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc37_membered,fc38_membered,fc39_membered,fc3_relat_1,fc40_membered,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_ami_1,rc5_struct_0,rc5_tex_2,rc6_ami_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_ami_3,dt_k1_relat_1,dt_k1_tarski,dt_k3_xboole_0,dt_k4_numbers,dt_k4_xboole_0,dt_u1_struct_0,dt_u2_ami_1,dt_c1_5__ami_6,dt_c2_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc4_membered,fc5_ami_3,t1_subset,t7_boole,e5_5__ami_6,e2_5__ami_6,d3_xboole_0]), [interesting(0.8),file(ami_6,e6_5__ami_6),[file(ami_6,e6_5__ami_6)]]). fof(t71_funct_1,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t71_funct_1), [interesting(0.9),axiom,file(funct_1,t71_funct_1)]). fof(e1_5_1__ami_6,plain,( k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k1_funct_1(k7_relat_1(c2_5__ami_6,k4_xboole_0(k1_relat_1(c2_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),c1_5__ami_6) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6,dt_c2_5__ami_6])],[existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc13_relat_1,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_amistd_2,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_l1_struct_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_amistd_2,cc1_fraenkel,cc1_membered,cc1_tex_2,cc20_membered,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc1_struct_0,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc35_membered,fc36_membered,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_relat_1,fc4_setfam_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_fraenkel,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_struct_0,rc3_tex_2,rc4_tex_2,rc5_struct_0,rc6_finseq_1,rc6_tex_2,rc7_tex_2,t1_boole,t2_boole,t3_boole,t4_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_m1_ami_3,dt_m1_subset_1,dt_u1_struct_0,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_membered,cc4_int_1,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc10_membered,fc17_finseq_1,fc27_membered,fc28_membered,fc29_membered,fc2_ami_1,fc2_setfam_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc37_membered,fc38_membered,fc39_membered,fc3_ami_1,fc40_membered,fc5_amistd_2,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_setfam_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,rc3_ami_1,rc5_ami_1,rc5_tex_2,rc6_ami_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_ami_3,dt_k1_ami_3,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_ami_3,dt_k3_xboole_0,dt_k4_numbers,dt_k4_xboole_0,dt_k7_relat_1,dt_u2_ami_1,dt_c1_5__ami_6,dt_c2_5__ami_6,fc1_ami_3,fc1_relat_1,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc3_relat_1,fc4_amistd_2,fc4_funct_1,fc4_membered,fc5_ami_3,rc1_funct_1,t1_subset,t7_boole,e6_5__ami_6,t71_funct_1]), [interesting(0.65),file(ami_6,e1_5_1__ami_6),[file(ami_6,e1_5_1__ami_6)]]). fof(d2_funct_7,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_funct_7(A,B,C) <=> k7_relat_1(A,k4_xboole_0(k1_relat_1(A),C)) = k7_relat_1(B,k4_xboole_0(k1_relat_1(B),C)) ) ) ) ), file(funct_7,d2_funct_7), [interesting(0.9),axiom,file(funct_7,d2_funct_7)]). fof(e2_5_1__ami_6,plain,( k1_funct_1(k7_relat_1(c2_5__ami_6,k4_xboole_0(k1_relat_1(c2_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),c1_5__ami_6) = k1_funct_1(k7_relat_1(c3_5__ami_6,k4_xboole_0(k1_relat_1(c3_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),c1_5__ami_6) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6,dt_c2_5__ami_6,dt_c3_5__ami_6,e1_5__ami_6])],[existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc13_relat_1,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_amistd_2,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_l1_struct_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_amistd_2,cc1_fraenkel,cc1_membered,cc1_tex_2,cc20_membered,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc1_struct_0,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_relat_1,fc4_setfam_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_fraenkel,rc1_membered,rc2_int_1,rc2_tex_2,rc3_funct_1,rc3_struct_0,rc3_tex_2,rc4_tex_2,rc5_struct_0,rc6_finseq_1,rc6_tex_2,rc7_tex_2,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_m1_ami_3,dt_m1_subset_1,dt_u1_struct_0,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc17_finseq_1,fc2_ami_1,fc2_setfam_1,fc37_membered,fc38_membered,fc39_membered,fc3_ami_1,fc40_membered,fc5_amistd_2,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_setfam_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_ami_1,rc5_ami_1,rc5_tex_2,rc6_ami_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,dt_k1_ami_3,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k4_numbers,dt_k4_xboole_0,dt_k7_relat_1,dt_u2_ami_1,dt_c1_5__ami_6,dt_c2_5__ami_6,dt_c3_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc3_relat_1,fc4_amistd_2,fc4_funct_1,fc4_membered,fc5_ami_3,rc1_funct_1,e1_5__ami_6,d2_funct_7]), [interesting(0.65),file(ami_6,e2_5_1__ami_6),[file(ami_6,e2_5_1__ami_6)]]). fof(e3_5__ami_6,plain,( k1_relat_1(c3_5__ami_6) = u1_struct_0(k1_ami_3) ), inference(mizar_by,[status(thm),assumptions([dt_c3_5__ami_6])],[cc1_finseq_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_membered,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_xboole_0,cc14_membered,cc1_membered,cc1_tex_2,cc20_membered,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc1_fraenkel,fc1_xboole_0,fc26_membered,fc2_finseq_1,fc2_fraenkel,fc4_relat_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_amistd_2,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,rc6_finseq_1,rc6_tex_2,rc7_tex_2,t1_boole,t1_subset,t4_subset,t5_subset,free_g1_ami_1,existence_m1_relset_1,dt_g1_ami_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u6_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_amistd_2,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_membered,cc4_int_1,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc10_membered,fc15_membered,fc16_finseq_1,fc17_finseq_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc5_relat_1,fc7_relat_1,fc9_finseq_1,rc1_fraenkel,rc1_relat_1,rc1_setfam_1,rc1_tex_2,rc1_xboole_0,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,rc5_struct_0,rc5_tex_2,rc7_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,abstractness_v1_ami_1,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k4_numbers,dt_l1_struct_0,dt_m2_relset_1,dt_u2_ami_1,dt_u4_ami_1,cc1_int_1,fc1_struct_0,fc1_tex_2,fc2_ami_1,fc2_ami_5,fc2_relat_1,fc3_ami_1,fc4_membered,fc4_setfam_1,fc5_amistd_2,rc1_ami_1,rc1_funct_1,rc2_ami_1,rc3_ami_1,rc3_struct_0,rc5_ami_1,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,existence_l1_ami_1,existence_m1_subset_1,dt_k1_ami_3,dt_k1_relat_1,dt_k4_card_3,dt_l1_ami_1,dt_m1_subset_1,dt_u1_struct_0,dt_u5_ami_1,dt_c3_5__ami_6,fc1_ami_3,fc2_ami_3,fc3_ami_3,fc5_ami_3,t36_ami_3]), [interesting(0.8),file(ami_6,e3_5__ami_6),[file(ami_6,e3_5__ami_6)]]). fof(e7_5__ami_6,plain,( r2_hidden(c1_5__ami_6,k4_xboole_0(k1_relat_1(c3_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ), inference(mizar_by,[status(thm),assumptions([dt_c3_5__ami_6,dt_c1_5__ami_6])],[rc1_amistd_2,existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_amistd_2,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc1_tex_2,cc20_membered,cc2_funct_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc17_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc3_ami_1,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_amistd_2,fc4_relat_1,fc4_setfam_1,fc5_amistd_2,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_membered,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_tex_2,rc3_ami_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t1_boole,t3_boole,t4_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_3,dt_m1_subset_1,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc1_struct_0,fc2_ami_1,fc2_setfam_1,fc37_membered,fc38_membered,fc39_membered,fc3_relat_1,fc40_membered,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_ami_1,rc5_struct_0,rc5_tex_2,rc6_ami_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_ami_3,dt_k1_relat_1,dt_k1_tarski,dt_k4_numbers,dt_k4_xboole_0,dt_u1_struct_0,dt_u2_ami_1,dt_c1_5__ami_6,dt_c3_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc4_membered,fc5_ami_3,t1_subset,t7_boole,e3_5__ami_6,e4_5__ami_6,d4_xboole_0]), [interesting(0.8),file(ami_6,e7_5__ami_6),[file(ami_6,e7_5__ami_6)]]). fof(e8_5__ami_6,plain,( r2_hidden(c1_5__ami_6,k3_xboole_0(k1_relat_1(c3_5__ami_6),k4_xboole_0(k1_relat_1(c3_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6,dt_c3_5__ami_6])],[rc1_amistd_2,existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_amistd_2,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_finseq_1,rc1_fraenkel,rc1_nat_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc1_tex_2,cc20_membered,cc2_funct_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc17_finseq_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc35_membered,fc36_membered,fc3_ami_1,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_amistd_2,fc4_relat_1,fc4_setfam_1,fc5_amistd_2,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_membered,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_tex_2,rc3_ami_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t1_boole,t2_boole,t3_boole,t4_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_3,dt_m1_subset_1,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc2_membered,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc1_relat_1,fc1_struct_0,fc27_membered,fc28_membered,fc29_membered,fc2_ami_1,fc2_setfam_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc37_membered,fc38_membered,fc39_membered,fc3_relat_1,fc40_membered,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_relat_1,rc2_xboole_0,rc3_struct_0,rc5_ami_1,rc5_struct_0,rc5_tex_2,rc6_ami_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_ami_3,dt_k1_relat_1,dt_k1_tarski,dt_k3_xboole_0,dt_k4_numbers,dt_k4_xboole_0,dt_u1_struct_0,dt_u2_ami_1,dt_c1_5__ami_6,dt_c3_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc4_membered,fc5_ami_3,t1_subset,t7_boole,e7_5__ami_6,e3_5__ami_6,d3_xboole_0]), [interesting(0.8),file(ami_6,e8_5__ami_6),[file(ami_6,e8_5__ami_6)]]). fof(e3_5_1__ami_6,plain,( k1_funct_1(k7_relat_1(c3_5__ami_6,k4_xboole_0(k1_relat_1(c3_5__ami_6),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),c1_5__ami_6) = k2_ami_3(c3_5__ami_6,c1_5__ami_6) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__ami_6,dt_c3_5__ami_6])],[existence_m1_relset_1,dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc13_relat_1,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_amistd_2,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc3_relat_1,rc4_funct_1,rc8_finseq_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_ami_1,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_l1_struct_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_amistd_2,cc1_fraenkel,cc1_membered,cc1_tex_2,cc20_membered,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc12_membered,fc12_relat_1,fc13_membered,fc14_membered,fc15_membered,fc1_struct_0,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_relat_1,fc2_xboole_0,fc35_membered,fc36_membered,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_relat_1,fc4_setfam_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_fraenkel,rc1_membered,rc2_tex_2,rc3_funct_1,rc3_struct_0,rc3_tex_2,rc4_tex_2,rc5_struct_0,rc6_finseq_1,rc6_tex_2,rc7_tex_2,t1_boole,t2_boole,t3_boole,t4_boole,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_ami_3,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_m1_ami_3,dt_m1_subset_1,dt_u1_struct_0,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc1_setfam_1,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_membered,cc4_int_1,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc10_membered,fc17_finseq_1,fc27_membered,fc28_membered,fc29_membered,fc2_ami_1,fc2_setfam_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc37_membered,fc38_membered,fc39_membered,fc3_ami_1,fc40_membered,fc5_amistd_2,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_relat_1,rc1_setfam_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,rc3_ami_1,rc5_ami_1,rc5_tex_2,rc6_ami_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc9_ami_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k2_ami_3,dt_k1_ami_3,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_ami_3,dt_k3_xboole_0,dt_k4_numbers,dt_k4_xboole_0,dt_k7_relat_1,dt_u2_ami_1,dt_c1_5__ami_6,dt_c3_5__ami_6,fc1_ami_3,fc1_relat_1,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc3_relat_1,fc4_amistd_2,fc4_funct_1,fc4_membered,fc5_ami_3,rc1_funct_1,t1_subset,t7_boole,e8_5__ami_6,t71_funct_1]), [interesting(0.65),file(ami_6,e3_5_1__ami_6),[file(ami_6,e3_5_1__ami_6)]]). fof(e9_5__ami_6,plain,( k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(c3_5__ami_6,c1_5__ami_6) ), inference(iterative_eq,[status(thm),assumptions([dt_c2_5__ami_6,e1_5__ami_6,dt_c1_5__ami_6,dt_c3_5__ami_6])],[dt_k13_finseq_1,dt_k1_funct_2,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,cc1_relset_1,cc3_int_1,cc3_nat_1,fc11_membered,fc16_finseq_1,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc4_ami_1,fc9_finseq_1,rc1_amistd_2,rc1_nat_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,redefinition_m2_relset_1,dt_g1_ami_1,dt_k2_tarski,dt_k2_xboole_0,dt_l1_struct_0,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u6_ami_1,cc14_membered,cc1_amistd_2,cc1_fraenkel,cc1_membered,cc1_setfam_1,cc1_tex_2,cc20_membered,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc1_struct_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_relat_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc41_membered,fc4_setfam_1,fc7_membered,fc8_membered,fc9_membered,rc1_fraenkel,rc1_membered,rc1_setfam_1,rc2_tex_2,rc3_ami_1,rc3_funct_1,rc3_struct_0,rc3_tex_2,rc4_tex_2,rc5_struct_0,rc6_finseq_1,rc6_tex_2,rc7_ami_1,rc7_tex_2,abstractness_v1_ami_1,dt_k1_zfmisc_1,dt_k4_card_3,dt_l1_ami_1,dt_m1_ami_3,dt_m1_subset_1,dt_u1_struct_0,dt_u5_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_relat_1,cc1_scmring1,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_membered,cc4_int_1,cc4_membered,cc4_tex_2,cc6_tex_2,cc8_membered,fc10_membered,fc17_finseq_1,fc2_ami_1,fc2_setfam_1,fc37_membered,fc38_membered,fc39_membered,fc3_ami_1,fc3_relat_1,fc40_membered,fc4_amistd_2,fc4_funct_1,fc5_amistd_2,fc5_relat_1,fc7_relat_1,rc1_ami_1,rc1_funct_1,rc1_relat_1,rc1_tex_2,rc1_xboole_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_relat_1,rc2_xboole_0,rc5_ami_1,rc5_tex_2,rc6_ami_1,rc7_finseq_1,rc8_ami_1,rc9_ami_1,redefinition_k2_ami_3,dt_k1_ami_3,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_ami_3,dt_k4_numbers,dt_k4_xboole_0,dt_k7_relat_1,dt_u2_ami_1,dt_c1_5__ami_6,dt_c2_5__ami_6,dt_c3_5__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc3_ami_3,fc4_membered,fc5_ami_3,e1_5_1__ami_6,e2_5_1__ami_6,e3_5_1__ami_6]), [interesting(0.8),file(ami_6,e9_5__ami_6),[file(ami_6,e9_5__ami_6)]]). fof(i5_5__ami_6,theorem,( $true ), introduced(tautology,[file(ami_6,i5_5__ami_6)]), [interesting(0.8),trivial,file(ami_6,i5_5__ami_6)]). fof(i4_5__ami_6,plain,( k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(c3_5__ami_6,c1_5__ami_6) ), inference(conclusion,[status(thm),assumptions([dt_c2_5__ami_6,e1_5__ami_6,dt_c1_5__ami_6,dt_c3_5__ami_6])],[e9_5__ami_6,i5_5__ami_6]), [interesting(0.8),file(ami_6,i4_5__ami_6),[file(ami_6,i4_5__ami_6)]]). fof(i3_5__ami_6,plain, ( r1_funct_7(c2_5__ami_6,c3_5__ami_6,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(c3_5__ami_6,c1_5__ami_6) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__ami_6,dt_c1_5__ami_6,dt_c3_5__ami_6]),discharge_asm(discharge,[e1_5__ami_6])],[e1_5__ami_6,i4_5__ami_6]), [interesting(0.8),file(ami_6,i3_5__ami_6),[file(ami_6,i3_5__ami_6)]]). fof(i3_5_tmp__ami_6,plain, ( m1_subset_1(c3_5__ami_6,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(c2_5__ami_6,c3_5__ami_6,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(c3_5__ami_6,c1_5__ami_6) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_5__ami_6,dt_c1_5__ami_6]),discharge_asm(discharge,[dt_c3_5__ami_6])],[dt_c3_5__ami_6,i3_5__ami_6]), [interesting(0.8),i2_5__ami_6]). fof(i2_5__ami_6,plain,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(c2_5__ami_6,A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(A,c1_5__ami_6) ) ) ), inference(let,[status(thm),assumptions([dt_c2_5__ami_6,dt_c1_5__ami_6])],[i3_5_tmp__ami_6,dh_c3_5__ami_6]), [interesting(0.8),file(ami_6,i2_5__ami_6),[file(ami_6,i2_5__ami_6)]]). fof(i2_5_tmp__ami_6,plain, ( m1_subset_1(c2_5__ami_6,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(c2_5__ami_6,A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(c2_5__ami_6,c1_5__ami_6) = k2_ami_3(A,c1_5__ami_6) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__ami_6]),discharge_asm(discharge,[dt_c2_5__ami_6])],[dt_c2_5__ami_6,i2_5__ami_6]), [interesting(0.8),i1_5__ami_6]). fof(i1_5__ami_6,plain,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(A,c1_5__ami_6) = k2_ami_3(B,c1_5__ami_6) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__ami_6])],[i2_5_tmp__ami_6,dh_c2_5__ami_6]), [interesting(0.8),file(ami_6,i1_5__ami_6),[file(ami_6,i1_5__ami_6)]]). fof(i1_5_tmp__ami_6,plain, ( m1_ami_3(c1_5__ami_6) => ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(A,c1_5__ami_6) = k2_ami_3(B,c1_5__ami_6) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__ami_6])],[dt_c1_5__ami_6,i1_5__ami_6]), [interesting(1),t5_ami_6]). fof(t5_ami_6,theorem,( ! [A] : ( m1_ami_3(A) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( r1_funct_7(B,C,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k2_ami_3(B,A) = k2_ami_3(C,A) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_5_tmp__ami_6,dh_c1_5__ami_6]), [interesting(1),file(ami_6,t5_ami_6),[file(ami_6,t5_ami_6)]]).