% Mizar ND problem: t4_ami_6,ami_6,69,33 fof(dh_c1_4__ami_6,definition, ( ( m1_struct_0(c1_4__ami_6,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( c1_4__ami_6 != A & k11_ami_3(c1_4__ami_6) = k11_ami_3(A) ) ) ) => ! [B] : ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [C] : ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( B != C & k11_ami_3(B) = k11_ami_3(C) ) ) ) ), introduced(definition,[new_symbol(c1_4__ami_6),file(ami_6,c1_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,c1_4__ami_6)]). fof(dh_c2_4__ami_6,definition, ( ( m1_struct_0(c2_4__ami_6,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( c1_4__ami_6 != c2_4__ami_6 & k11_ami_3(c1_4__ami_6) = k11_ami_3(c2_4__ami_6) ) ) => ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( c1_4__ami_6 != A & k11_ami_3(c1_4__ami_6) = k11_ami_3(A) ) ) ), introduced(definition,[new_symbol(c2_4__ami_6),file(ami_6,c2_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,c2_4__ami_6)]). fof(e1_4__ami_6,assumption, ( c1_4__ami_6 != c2_4__ami_6 & k11_ami_3(c1_4__ami_6) = k11_ami_3(c2_4__ami_6) ), introduced(assumption,[file(ami_6,e1_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,e1_4__ami_6)]). 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(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(rc1_fraenkel,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]). 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(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_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_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_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_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), [interesting(0.9),axiom,file(card_3,k4_card_3)]). 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(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(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_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(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_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(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_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_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(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(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(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(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(rc2_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). 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(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). 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_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_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(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(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(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(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(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_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(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_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_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_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(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_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(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(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_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(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(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(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(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_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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). 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_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). 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(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(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_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_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc3_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(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_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(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(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(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_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_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), [interesting(0.9),axiom,file(int_1,fc1_int_1)]). fof(fc1_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), [interesting(0.9),axiom,file(nat_1,fc1_nat_1)]). fof(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). fof(fc1_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]). fof(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_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_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(fc3_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), [interesting(0.9),axiom,file(int_1,fc3_int_1)]). fof(fc3_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), [interesting(0.9),axiom,file(nat_1,fc3_nat_1)]). fof(fc4_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), [interesting(0.9),axiom,file(int_1,fc4_int_1)]). fof(fc4_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), [interesting(0.9),axiom,file(nat_1,fc4_nat_1)]). 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(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(fc6_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), [interesting(0.9),axiom,file(int_1,fc6_int_1)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(fc8_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), [interesting(0.9),axiom,file(int_1,fc8_int_1)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_membered)]). fof(rc1_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_int_1,theorem,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), [interesting(0.9),axiom,file(int_1,rc1_int_1)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(rc1_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_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(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(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_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), [interesting(0.9),axiom,file(nat_1,rc2_nat_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(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_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), [interesting(0.9),axiom,file(nat_1,rc3_nat_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_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_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(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_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_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(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(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(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), [interesting(0.9),axiom,file(struct_0,m1_struct_0)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_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_m1_struct_0,definition,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), [interesting(0.9),axiom,file(struct_0,m1_struct_0)]). fof(redefinition_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k1_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_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k3_ami_2,axiom,( m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k3_ami_2), [interesting(0.9),axiom,file(ami_2,k3_ami_2)]). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), [interesting(0.9),axiom,file(numbers,k4_numbers)]). 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_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), [interesting(0.9),axiom,file(struct_0,m1_struct_0)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_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(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc1_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_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), [interesting(0.9),axiom,file(nat_1,cc1_nat_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(cc2_int_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), [interesting(0.9),axiom,file(int_1,cc2_int_1)]). fof(cc2_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]). 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(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(fc2_scmring1,theorem, ( ~ v1_xboole_0(k3_ami_2) & ~ v1_finset_1(k3_ami_2) & ~ v1_realset1(k3_ami_2) & v1_membered(k3_ami_2) & v2_membered(k3_ami_2) & v3_membered(k3_ami_2) & v4_membered(k3_ami_2) & v5_membered(k3_ami_2) ), file(scmring1,fc2_scmring1), [interesting(0.9),axiom,file(scmring1,fc2_scmring1)]). 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(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(fc5_int_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), [interesting(0.9),axiom,file(int_1,fc5_int_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(fc9_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), [interesting(0.9),axiom,file(int_1,fc9_int_1)]). 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_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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(commutativity_k1_nat_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(commutativity_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(involutiveness_k4_xcmplx_0,theorem,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(redefinition_k1_nat_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k11_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => m1_struct_0(k11_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k11_ami_3), [interesting(0.9),axiom,file(ami_3,k11_ami_3)]). fof(dt_k15_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k3_ami_2) => m2_subset_1(k15_ami_2(A),k5_numbers,k3_ami_2) ) ), file(ami_2,k15_ami_2), [interesting(0.9),axiom,file(ami_2,k15_ami_2)]). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]). fof(dt_c1_4__ami_6,assumption,( m1_struct_0(c1_4__ami_6,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), introduced(assumption,[file(ami_6,c1_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,c1_4__ami_6)]). fof(dt_c2_4__ami_6,assumption,( m1_struct_0(c2_4__ami_6,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), introduced(assumption,[file(ami_6,c2_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,c2_4__ami_6)]). fof(dh_c3_4__ami_6,definition, ( ? [A] : ( m2_subset_1(A,k5_numbers,k3_ami_2) & A = c1_4__ami_6 & k11_ami_3(c1_4__ami_6) = k15_ami_2(A) ) => ( m2_subset_1(c3_4__ami_6,k5_numbers,k3_ami_2) & c3_4__ami_6 = c1_4__ami_6 & k11_ami_3(c1_4__ami_6) = k15_ami_2(c3_4__ami_6) ) ), introduced(definition,[new_symbol(c3_4__ami_6),file(ami_6,c3_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,c3_4__ami_6)]). fof(d11_ami_3,definition,( ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ( B = k11_ami_3(A) <=> ? [C] : ( m2_subset_1(C,k5_numbers,k3_ami_2) & C = A & B = k15_ami_2(C) ) ) ) ) ), file(ami_3,d11_ami_3), [interesting(0.9),axiom,file(ami_3,d11_ami_3)]). fof(e2_4__ami_6,plain,( ? [A] : ( m2_subset_1(A,k5_numbers,k3_ami_2) & A = c1_4__ami_6 & k11_ami_3(c1_4__ami_6) = k15_ami_2(A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__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,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,rc2_finseq_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,antisymmetry_r2_hidden,dt_g1_ami_1,dt_k1_xboole_0,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,cc1_setfam_1,cc1_tex_2,cc2_funct_1,cc3_int_1,cc3_nat_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc11_membered,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_relat_1,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_relat_1,rc2_tex_2,rc3_ami_1,rc3_nat_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t1_subset,t4_subset,t5_subset,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc20_membered,cc2_int_1,cc2_membered,cc2_nat_1,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_membered,cc6_tex_2,cc8_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc2_ami_1,fc2_membered,fc2_setfam_1,fc5_membered,rc1_ami_1,rc1_membered,rc1_tex_2,rc1_xboole_0,rc2_ami_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,t6_boole,t7_boole,t8_boole,existence_m1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k11_ami_3,dt_k15_ami_2,dt_k1_ami_3,dt_k1_tarski,dt_k3_ami_2,dt_k4_numbers,dt_k5_numbers,dt_m1_struct_0,dt_m2_subset_1,dt_u2_ami_1,dt_c1_4__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc2_scmring1,fc3_ami_3,fc4_membered,fc5_ami_3,d11_ami_3]), [interesting(0.8),file(ami_6,e2_4__ami_6),[file(ami_6,e2_4__ami_6)]]). fof(dt_c3_4__ami_6,plain,( m2_subset_1(c3_4__ami_6,k5_numbers,k3_ami_2) ), inference(consider,[status(thm),assumptions([dt_c1_4__ami_6])],[dh_c3_4__ami_6,e2_4__ami_6]), [interesting(0.8),file(ami_6,c3_4__ami_6),[file(ami_6,c3_4__ami_6)]]). fof(dh_c4_4__ami_6,definition, ( ? [A] : ( m2_subset_1(A,k5_numbers,k3_ami_2) & A = c2_4__ami_6 & k11_ami_3(c2_4__ami_6) = k15_ami_2(A) ) => ( m2_subset_1(c4_4__ami_6,k5_numbers,k3_ami_2) & c4_4__ami_6 = c2_4__ami_6 & k11_ami_3(c2_4__ami_6) = k15_ami_2(c4_4__ami_6) ) ), introduced(definition,[new_symbol(c4_4__ami_6),file(ami_6,c4_4__ami_6)]), [interesting(0.8),axiom,file(ami_6,c4_4__ami_6)]). fof(e4_4__ami_6,plain,( ? [A] : ( m2_subset_1(A,k5_numbers,k3_ami_2) & A = c2_4__ami_6 & k11_ami_3(c2_4__ami_6) = k15_ami_2(A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__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,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,rc2_finseq_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,antisymmetry_r2_hidden,dt_g1_ami_1,dt_k1_xboole_0,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,cc1_setfam_1,cc1_tex_2,cc2_funct_1,cc3_int_1,cc3_nat_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc10_membered,fc11_membered,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc4_relat_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_relat_1,rc1_setfam_1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_relat_1,rc2_tex_2,rc3_ami_1,rc3_nat_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_ami_1,rc7_finseq_1,rc7_tex_2,t1_subset,t4_subset,t5_subset,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc20_membered,cc2_int_1,cc2_membered,cc2_nat_1,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_membered,cc6_tex_2,cc8_membered,cc9_membered,fc1_ordinal2,fc1_struct_0,fc2_ami_1,fc2_membered,fc2_setfam_1,fc5_membered,rc1_ami_1,rc1_membered,rc1_tex_2,rc1_xboole_0,rc2_ami_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,t6_boole,t7_boole,t8_boole,existence_m1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k11_ami_3,dt_k15_ami_2,dt_k1_ami_3,dt_k1_tarski,dt_k3_ami_2,dt_k4_numbers,dt_k5_numbers,dt_m1_struct_0,dt_m2_subset_1,dt_u2_ami_1,dt_c2_4__ami_6,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc2_scmring1,fc3_ami_3,fc4_membered,fc5_ami_3,d11_ami_3]), [interesting(0.8),file(ami_6,e4_4__ami_6),[file(ami_6,e4_4__ami_6)]]). fof(dt_c4_4__ami_6,plain,( m2_subset_1(c4_4__ami_6,k5_numbers,k3_ami_2) ), inference(consider,[status(thm),assumptions([dt_c2_4__ami_6])],[dh_c4_4__ami_6,e4_4__ami_6]), [interesting(0.8),file(ami_6,c4_4__ami_6),[file(ami_6,c4_4__ami_6)]]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2,theorem,( k2_xcmplx_0(0,2) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,theorem,( k2_xcmplx_0(0,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,theorem,( k2_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,theorem,( k2_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,( k2_xcmplx_0(1,0) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,( k2_xcmplx_0(1,1) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]). fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]). fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,theorem,( k2_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2,theorem,( k2_xcmplx_0(2,0) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)]). fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),1) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),2) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]). fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),2) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(1)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]). fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,theorem,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(1,2) ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]). fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,theorem,( k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ), file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,( k6_xcmplx_0(0,0) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,( k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,( k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,( k6_xcmplx_0(1,0) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,( k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]). fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,( k6_xcmplx_0(2,0) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,( k6_xcmplx_0(2,1) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,( k7_xcmplx_0(0,1) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,( k7_xcmplx_0(0,2) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,( k7_xcmplx_0(1,1) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]). fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,( k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,( k7_xcmplx_0(2,1) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,( k7_xcmplx_0(2,2) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]). fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,( k4_xcmplx_0(0) = 0 ), file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]). fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]). fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]). fof(spc1_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) ), file(arithm,spc1_arithm), [interesting(0.9),axiom,file(arithm,spc1_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(spc8_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) ), file(arithm,spc8_arithm), [interesting(0.9),axiom,file(arithm,spc8_arithm)]). fof(spc9_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ), file(arithm,spc9_arithm), [interesting(0.9),axiom,file(arithm,spc9_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(t4_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), [interesting(0.9),axiom,file(arithm,t4_arithm)]). fof(t5_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), [interesting(0.9),axiom,file(arithm,t5_arithm)]). fof(t6_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), [interesting(0.9),axiom,file(arithm,t6_arithm)]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc2_numerals,theorem, ( v2_xreal_0(2) & m2_subset_1(2,k1_numbers,k5_numbers) & m1_subset_1(2,k5_numbers) & m1_subset_1(2,k1_numbers) ), file(numerals,spc2_numerals), [interesting(0.9),axiom,file(numerals,spc2_numerals)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(d15_ami_2,definition,( ! [A] : ( m2_subset_1(A,k5_numbers,k3_ami_2) => k15_ami_2(A) = k1_nat_1(A,2) ) ), file(ami_2,d15_ami_2), [interesting(0.9),axiom,file(ami_2,d15_ami_2)]). fof(e6_4__ami_6,plain, ( k15_ami_2(c3_4__ami_6) = k1_nat_1(c3_4__ami_6,2) & k15_ami_2(c4_4__ami_6) = k1_nat_1(c4_4__ami_6,2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__ami_6,dt_c2_4__ami_6])],[cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_tex_2,cc2_funct_1,cc3_int_1,cc3_nat_1,cc3_tex_2,cc4_int_1,cc5_tex_2,cc7_tex_2,fc12_relat_1,fc1_int_1,fc1_nat_1,fc1_xboole_0,fc2_finseq_1,fc3_nat_1,fc4_nat_1,fc4_relat_1,fc6_int_1,fc6_membered,rc1_funct_1,rc1_int_1,rc1_nat_1,rc1_relat_1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_relat_1,rc2_tex_2,rc3_nat_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_finseq_1,rc7_tex_2,spc6_arithm,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_scmring1,cc20_membered,cc2_int_1,cc2_membered,cc2_nat_1,cc2_tex_2,cc3_membered,cc4_membered,cc4_tex_2,cc6_membered,cc6_tex_2,cc9_membered,fc1_ordinal2,fc2_membered,fc5_membered,rc1_membered,rc1_tex_2,rc1_xboole_0,rc2_xboole_0,rc5_tex_2,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_ami_2,dt_k1_nat_1,dt_k3_ami_2,dt_k5_numbers,dt_m2_subset_1,dt_c3_4__ami_6,dt_c4_4__ami_6,fc2_scmring1,spc2_numerals,spc2_boole,d15_ami_2]), [interesting(0.8),file(ami_6,e6_4__ami_6),[file(ami_6,e6_4__ami_6)]]). fof(e3_4__ami_6,plain, ( c3_4__ami_6 = c1_4__ami_6 & k11_ami_3(c1_4__ami_6) = k15_ami_2(c3_4__ami_6) ), inference(consider,[status(thm),assumptions([dt_c1_4__ami_6])],[dh_c3_4__ami_6,e2_4__ami_6]), [interesting(0.8),file(ami_6,e3_4__ami_6),[file(ami_6,e3_4__ami_6)]]). fof(e5_4__ami_6,plain, ( c4_4__ami_6 = c2_4__ami_6 & k11_ami_3(c2_4__ami_6) = k15_ami_2(c4_4__ami_6) ), inference(consider,[status(thm),assumptions([dt_c2_4__ami_6])],[dh_c4_4__ami_6,e4_4__ami_6]), [interesting(0.8),file(ami_6,e5_4__ami_6),[file(ami_6,e5_4__ami_6)]]). fof(t2_xcmplx_1,theorem,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B) => A = C ) ) ) ) ), file(xcmplx_1,t2_xcmplx_1), [interesting(0.9),axiom,file(xcmplx_1,t2_xcmplx_1)]). fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,( k4_xcmplx_0(1) = k4_xcmplx_0(1) ), file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]). fof(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,( k4_xcmplx_0(2) = k4_xcmplx_0(2) ), file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,( k6_xcmplx_0(1,1) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]). fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,( k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,( k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,( k6_xcmplx_0(2,2) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]). fof(e7_4__ami_6,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([e1_4__ami_6,dt_c1_4__ami_6,dt_c2_4__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_relset_1,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,rc2_finseq_1,t1_boole,free_g1_ami_1,reflexivity_r1_tarski,dt_g1_ami_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,cc1_finseq_1,cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc9_membered,rc1_finseq_1,rc2_tex_2,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc3_tex_2,rc4_funct_1,rc4_tex_2,rc6_finseq_1,rc6_tex_2,rc7_tex_2,rc8_finseq_1,antisymmetry_r2_hidden,abstractness_v1_ami_1,existence_l1_ami_1,existence_l1_struct_0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_ami_1,dt_l1_struct_0,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_scmring1,cc1_setfam_1,cc20_membered,cc2_funct_1,cc2_membered,cc2_tex_2,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,cc4_tex_2,cc6_membered,cc6_tex_2,cc8_membered,cc9_membered,fc10_membered,fc11_membered,fc12_relat_1,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_struct_0,fc1_xboole_0,fc2_ami_1,fc2_finseq_1,fc3_int_1,fc3_nat_1,fc4_int_1,fc4_nat_1,fc4_relat_1,fc5_membered,fc6_int_1,fc6_membered,fc8_int_1,fc8_membered,rc1_ami_1,rc1_funct_1,rc1_int_1,rc1_membered,rc1_nat_1,rc1_relat_1,rc1_setfam_1,rc1_tex_2,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_relat_1,rc3_ami_1,rc3_nat_1,rc3_struct_0,rc5_ami_1,rc5_struct_0,rc5_tex_2,rc6_ami_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc9_ami_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m1_struct_0,redefinition_m2_subset_1,dt_k1_ami_3,dt_k1_numbers,dt_k1_tarski,dt_k3_ami_2,dt_k4_numbers,dt_k5_numbers,dt_m1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u2_ami_1,cc15_membered,cc1_funct_1,cc1_int_1,cc1_nat_1,cc1_relat_1,cc2_int_1,cc2_nat_1,fc1_ami_3,fc1_tex_2,fc2_ami_3,fc2_ami_5,fc2_membered,fc2_scmring1,fc2_setfam_1,fc3_ami_3,fc4_membered,fc5_ami_3,fc5_int_1,fc7_membered,fc9_int_1,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k1_nat_1,dt_k11_ami_3,dt_k15_ami_2,dt_k1_nat_1,dt_k2_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c1_4__ami_6,dt_c2_4__ami_6,dt_c3_4__ami_6,dt_c4_4__ami_6,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__rm1_r0_rm1,rqRealAdd__k2_xcmplx_0__rm1_r1_r0,rqRealAdd__k2_xcmplx_0__rm1_r2_r1,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2,rqRealAdd__k2_xcmplx_0__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2,rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1,rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2,rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0,rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,spc1_arithm,spc6_arithm,spc8_arithm,spc9_arithm,t1_arithm,t4_arithm,t5_arithm,t6_arithm,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e6_4__ami_6,e1_4__ami_6,e3_4__ami_6,e5_4__ami_6,t2_xcmplx_1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealDiff__k6_xcmplx_0__r2_r2_r0]), [interesting(0.8),file(ami_6,e7_4__ami_6),[file(ami_6,e7_4__ami_6)]]). fof(i4_4__ami_6,theorem,( $true ), introduced(tautology,[file(ami_6,i4_4__ami_6)]), [interesting(0.8),trivial,file(ami_6,i4_4__ami_6)]). fof(i3_4__ami_6,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([e1_4__ami_6,dt_c1_4__ami_6,dt_c2_4__ami_6])],[e7_4__ami_6,i4_4__ami_6]), [interesting(0.8),file(ami_6,i3_4__ami_6),[file(ami_6,i3_4__ami_6)]]). fof(i2_4__ami_6,plain,( ~ ( c1_4__ami_6 != c2_4__ami_6 & k11_ami_3(c1_4__ami_6) = k11_ami_3(c2_4__ami_6) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4__ami_6,dt_c2_4__ami_6]),discharge_asm(discharge,[e1_4__ami_6])],[e1_4__ami_6,i3_4__ami_6]), [interesting(0.8),file(ami_6,i2_4__ami_6),[file(ami_6,i2_4__ami_6)]]). fof(i2_4_tmp__ami_6,plain, ( m1_struct_0(c2_4__ami_6,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( c1_4__ami_6 != c2_4__ami_6 & k11_ami_3(c1_4__ami_6) = k11_ami_3(c2_4__ami_6) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4__ami_6]),discharge_asm(discharge,[dt_c2_4__ami_6])],[dt_c2_4__ami_6,i2_4__ami_6]), [interesting(0.8),i1_4__ami_6]). fof(i1_4__ami_6,plain,( ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( c1_4__ami_6 != A & k11_ami_3(c1_4__ami_6) = k11_ami_3(A) ) ) ), inference(let,[status(thm),assumptions([dt_c1_4__ami_6])],[i2_4_tmp__ami_6,dh_c2_4__ami_6]), [interesting(0.8),file(ami_6,i1_4__ami_6),[file(ami_6,i1_4__ami_6)]]). fof(i1_4_tmp__ami_6,plain, ( m1_struct_0(c1_4__ami_6,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( c1_4__ami_6 != A & k11_ami_3(c1_4__ami_6) = k11_ami_3(A) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__ami_6])],[dt_c1_4__ami_6,i1_4__ami_6]), [interesting(1),t4_ami_6]). fof(t4_ami_6,theorem,( ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ~ ( A != B & k11_ami_3(A) = k11_ami_3(B) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_4_tmp__ami_6,dh_c1_4__ami_6]), [interesting(1),file(ami_6,t4_ami_6),[file(ami_6,t4_ami_6)]]).