% Mizar ND problem: t1_ami_3,ami_3,45,21 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(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), [interesting(0.9),axiom,file(funct_2,k1_funct_2)]). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), [interesting(0.9),axiom,file(card_3,k4_card_3)]). 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_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(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(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(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(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_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_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(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(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(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(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(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(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_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_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(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(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_k10_relat_1,axiom,( $true ), file(relat_1,k10_relat_1), [interesting(0.9),axiom,file(relat_1,k10_relat_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_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), [interesting(0.9),axiom,file(tarski,k3_tarski)]). 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_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_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(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_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(cc1_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_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(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(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). fof(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(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(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(fc9_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]). fof(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_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_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_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). fof(rc5_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(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(redefinition_k3_funct_2,definition,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ) ), file(funct_2,k3_funct_2), [interesting(0.9),axiom,file(funct_2,k3_funct_2)]). 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_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_k3_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)) ) ), file(funct_2,k3_funct_2), [interesting(0.9),axiom,file(funct_2,k3_funct_2)]). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), [interesting(0.9),axiom,file(numbers,k4_numbers)]). 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_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). 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_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_c2_3__ami_3,assumption,( $true ), introduced(assumption,[file(ami_3,c2_3__ami_3)]), [interesting(0.8),axiom,file(ami_3,c2_3__ami_3)]). 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_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]). fof(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(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(d12_ami_1,definition,( ! [A,B] : ( l1_ami_1(B,A) => ( v6_ami_1(B,A) <=> r1_tarski(k3_funct_2(u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))),u5_ami_1(A,B),k1_tarski(u4_ami_1(A,B))),u2_ami_1(A,B)) ) ) ), file(ami_1,d12_ami_1), [interesting(0.9),axiom,file(ami_1,d12_ami_1)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(dh_c2_3__ami_3,definition, ( ~ ( r2_hidden(c2_3__ami_3,k3_funct_2(u1_struct_0(k1_ami_3),k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),u5_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) & ~ r2_hidden(c2_3__ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) => ! [A] : ~ ( r2_hidden(A,k3_funct_2(u1_struct_0(k1_ami_3),k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),u5_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) & ~ r2_hidden(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), introduced(definition,[new_symbol(c2_3__ami_3),file(ami_3,c2_3__ami_3)]), [interesting(0.8),axiom,file(ami_3,c2_3__ami_3)]). fof(e1_3__ami_3,assumption,( r2_hidden(c2_3__ami_3,k10_relat_1(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) ), introduced(assumption,[file(ami_3,e1_3__ami_3)]), [interesting(0.8),axiom,file(ami_3,e1_3__ami_3)]). fof(existence_m1_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]). fof(dt_m1_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), [interesting(0.9),axiom,file(fraenkel,m1_fraenkel)]). 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_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_k1_fraenkel,definition,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]). fof(dt_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). 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_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_int_1,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), [interesting(0.9),axiom,file(int_1,fc2_int_1)]). fof(fc2_nat_1,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(nat_1,fc2_nat_1), [interesting(0.9),axiom,file(nat_1,fc2_nat_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(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(fc7_int_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), [interesting(0.9),axiom,file(int_1,fc7_int_1)]). 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(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(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(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(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_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), [interesting(0.9),axiom,file(real,t2_real)]). fof(t3_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), [interesting(0.9),axiom,file(real,t3_real)]). fof(t5_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), [interesting(0.9),axiom,file(real,t5_real)]). fof(t6_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), [interesting(0.9),axiom,file(real,t6_real)]). fof(t7_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), [interesting(0.9),axiom,file(real,t7_real)]). fof(t8_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), [interesting(0.9),axiom,file(real,t8_real)]). 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(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_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_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_k17_ami_2,axiom, ( v1_funct_1(k17_ami_2) & v1_funct_2(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) & m2_relset_1(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) ), file(ami_2,k17_ami_2), [interesting(0.9),axiom,file(ami_2,k17_ami_2)]). fof(dt_k1_gr_cy_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( ~ v1_xboole_0(k1_gr_cy_1(A)) & m1_subset_1(k1_gr_cy_1(A),k1_zfmisc_1(k5_numbers)) ) ) ), file(gr_cy_1,k1_gr_cy_1), [interesting(0.9),axiom,file(gr_cy_1,k1_gr_cy_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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_ami_2,axiom,( m1_subset_1(k4_ami_2,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ), file(ami_2,k4_ami_2), [interesting(0.9),axiom,file(ami_2,k4_ami_2)]). fof(dt_k5_ami_2,axiom, ( v1_funct_1(k5_ami_2) & v1_funct_2(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) & m2_relset_1(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) ), file(ami_2,k5_ami_2), [interesting(0.9),axiom,file(ami_2,k5_ami_2)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(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(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(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(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(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(fc3_ami_2,theorem, ( v1_relat_1(k4_ami_2) & ~ v1_xboole_0(k4_ami_2) ), file(ami_2,fc3_ami_2), [interesting(0.9),axiom,file(ami_2,fc3_ami_2)]). 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(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(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_r7_r7,theorem,( k2_xcmplx_0(0,7) = 7 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r7_r7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r7_r7)]). fof(rqRealAdd__k2_xcmplx_0__r0_r8_r8,theorem,( k2_xcmplx_0(0,8) = 8 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r8_r8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r8_r8)]). fof(rqRealAdd__k2_xcmplx_0__r0_r9_r9,theorem,( k2_xcmplx_0(0,9) = 9 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r9_r9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r9_r9)]). 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__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_r7_r8,theorem,( k2_xcmplx_0(1,7) = 8 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r7_r8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r7_r8)]). fof(rqRealAdd__k2_xcmplx_0__r1_r8_r9,theorem,( k2_xcmplx_0(1,8) = 9 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r8_r9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r8_r9)]). 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_rm9_rm8,theorem,( k2_xcmplx_0(1,k4_xcmplx_0(9)) = k4_xcmplx_0(8) ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm9_rm8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_rm9_rm8)]). 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_r7_r9,theorem,( k2_xcmplx_0(2,7) = 9 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_r7_r9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r7_r9)]). 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__r2_rm9_rm7,theorem,( k2_xcmplx_0(2,k4_xcmplx_0(9)) = k4_xcmplx_0(7) ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm9_rm7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_rm9_rm7)]). fof(rqRealAdd__k2_xcmplx_0__r7_r0_r7,theorem,( k2_xcmplx_0(7,0) = 7 ), file(arithm,rqRealAdd__k2_xcmplx_0__r7_r0_r7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r7_r0_r7)]). fof(rqRealAdd__k2_xcmplx_0__r7_r1_r8,theorem,( k2_xcmplx_0(7,1) = 8 ), file(arithm,rqRealAdd__k2_xcmplx_0__r7_r1_r8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r7_r1_r8)]). fof(rqRealAdd__k2_xcmplx_0__r7_r2_r9,theorem,( k2_xcmplx_0(7,2) = 9 ), file(arithm,rqRealAdd__k2_xcmplx_0__r7_r2_r9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r7_r2_r9)]). fof(rqRealAdd__k2_xcmplx_0__r8_r0_r8,theorem,( k2_xcmplx_0(8,0) = 8 ), file(arithm,rqRealAdd__k2_xcmplx_0__r8_r0_r8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r8_r0_r8)]). fof(rqRealAdd__k2_xcmplx_0__r8_r1_r9,theorem,( k2_xcmplx_0(8,1) = 9 ), file(arithm,rqRealAdd__k2_xcmplx_0__r8_r1_r9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r8_r1_r9)]). fof(rqRealAdd__k2_xcmplx_0__r8_rm1_r7,theorem,( k2_xcmplx_0(8,k4_xcmplx_0(1)) = 7 ), file(arithm,rqRealAdd__k2_xcmplx_0__r8_rm1_r7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r8_rm1_r7)]). fof(rqRealAdd__k2_xcmplx_0__r8_rm8_r0,theorem,( k2_xcmplx_0(8,k4_xcmplx_0(8)) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r8_rm8_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r8_rm8_r0)]). fof(rqRealAdd__k2_xcmplx_0__r9_r0_r9,theorem,( k2_xcmplx_0(9,0) = 9 ), file(arithm,rqRealAdd__k2_xcmplx_0__r9_r0_r9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r9_r0_r9)]). fof(rqRealAdd__k2_xcmplx_0__r9_rm1_r8,theorem,( k2_xcmplx_0(9,k4_xcmplx_0(1)) = 8 ), file(arithm,rqRealAdd__k2_xcmplx_0__r9_rm1_r8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r9_rm1_r8)]). fof(rqRealAdd__k2_xcmplx_0__r9_rm2_r7,theorem,( k2_xcmplx_0(9,k4_xcmplx_0(2)) = 7 ), file(arithm,rqRealAdd__k2_xcmplx_0__r9_rm2_r7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r9_rm2_r7)]). 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_r8_r7,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),8) = 7 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r8_r7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_r8_r7)]). 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_rm7_rm8,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(7)) = k4_xcmplx_0(8) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm7_rm8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm7_rm8)]). fof(rqRealAdd__k2_xcmplx_0__rm1_rm8_rm9,theorem,( k2_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(8)) = k4_xcmplx_0(9) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm8_rm9), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm1_rm8_rm9)]). 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__rm2_r9_r7,theorem,( k2_xcmplx_0(k4_xcmplx_0(2),9) = 7 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r9_r7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm2_r9_r7)]). fof(rqRealAdd__k2_xcmplx_0__rm7_rm1_rm8,theorem,( k2_xcmplx_0(k4_xcmplx_0(7),k4_xcmplx_0(1)) = k4_xcmplx_0(8) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm7_rm1_rm8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm7_rm1_rm8)]). fof(rqRealAdd__k2_xcmplx_0__rm8_r8_r0,theorem,( k2_xcmplx_0(k4_xcmplx_0(8),8) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__rm8_r8_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm8_r8_r0)]). fof(rqRealAdd__k2_xcmplx_0__rm9_r1_rm8,theorem,( k2_xcmplx_0(k4_xcmplx_0(9),1) = k4_xcmplx_0(8) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm9_r1_rm8), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm9_r1_rm8)]). fof(rqRealAdd__k2_xcmplx_0__rm9_r2_rm7,theorem,( k2_xcmplx_0(k4_xcmplx_0(9),2) = k4_xcmplx_0(7) ), file(arithm,rqRealAdd__k2_xcmplx_0__rm9_r2_rm7), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__rm9_r2_rm7)]). 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(spc2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) ), file(arithm,spc2_arithm), [interesting(0.9),axiom,file(arithm,spc2_arithm)]). fof(spc5_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ), file(arithm,spc5_arithm), [interesting(0.9),axiom,file(arithm,spc5_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc7_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(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(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(t1_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), [interesting(0.9),axiom,file(real,t1_real)]). fof(t2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), [interesting(0.9),axiom,file(arithm,t2_arithm)]). 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_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), [interesting(0.9),axiom,file(arithm,t3_arithm)]). fof(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_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(t4_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), [interesting(0.9),axiom,file(real,t4_real)]). 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_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_nat_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) ), file(nat_1,k2_nat_1), [interesting(0.9),axiom,file(nat_1,k2_nat_1)]). fof(commutativity_k3_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(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(reflexivity_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(connectedness_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_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(redefinition_k2_nat_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ), file(nat_1,k2_nat_1), [interesting(0.9),axiom,file(nat_1,k2_nat_1)]). 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_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k2_nat_1), [interesting(0.9),axiom,file(nat_1,k2_nat_1)]). 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_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_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(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(de_c3_3__ami_3,definition,( c3_3__ami_3 = c2_3__ami_3 ), introduced(definition,[new_symbol(c3_3__ami_3),file(ami_3,c3_3__ami_3)]), [interesting(0.8),axiom,file(ami_3,c3_3__ami_3)]). fof(fc2_ami_2,theorem, ( ~ v1_xboole_0(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(ami_2,fc2_ami_2), [interesting(0.9),axiom,file(ami_2,fc2_ami_2)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc9_boole,theorem,( ~ v1_xboole_0(9) ), file(boole,spc9_boole), [interesting(0.9),axiom,file(boole,spc9_boole)]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(spc9_numerals,theorem, ( v2_xreal_0(9) & m2_subset_1(9,k1_numbers,k5_numbers) & m1_subset_1(9,k5_numbers) & m1_subset_1(9,k1_numbers) ), file(numerals,spc9_numerals), [interesting(0.9),axiom,file(numerals,spc9_numerals)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(d1_ami_3,definition,( k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,0,k3_ami_2,k1_gr_cy_1(9),k4_ami_2,k5_ami_2,k17_ami_2) ), file(ami_3,d1_ami_3), [interesting(0.9),axiom,file(ami_3,d1_ami_3)]). fof(t46_funct_2,theorem,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( B != k1_xboole_0 => ! [E] : ( r2_hidden(E,k10_relat_1(D,C)) <=> ( r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ), file(funct_2,t46_funct_2), [interesting(0.9),axiom,file(funct_2,t46_funct_2)]). fof(e2_3__ami_3,plain,( m2_subset_1(c2_3__ami_3,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[existence_m1_fraenkel,dt_m1_fraenkel,cc1_fraenkel,rc1_fraenkel,reflexivity_r1_tarski,existence_l1_struct_0,redefinition_k1_fraenkel,dt_k1_fraenkel,dt_k1_funct_2,dt_k4_card_3,dt_l1_struct_0,dt_u1_ami_1,dt_u6_ami_1,cc1_setfam_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc3_ami_1,fc4_ami_1,fc4_setfam_1,fc7_membered,fc8_membered,fc9_membered,rc1_int_1,rc1_nat_1,rc1_setfam_1,rc2_int_1,rc2_nat_1,rc3_nat_1,free_g1_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_relset_1,existence_m1_subset_1,dt_g1_ami_1,dt_k13_finseq_1,dt_k17_ami_2,dt_k1_gr_cy_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ami_2,dt_k3_tarski,dt_k4_ami_2,dt_k5_ami_2,dt_k5_ordinal2,dt_l1_ami_1,dt_m1_relset_1,dt_m1_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc8_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_ami_1,fc2_ami_2,fc2_finset_1,fc2_setfam_1,fc2_xboole_0,fc3_ami_2,fc3_setfam_1,fc3_xboole_0,fc5_membered,fc9_finset_1,rc1_ami_1,rc1_finset_1,rc1_membered,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,spc0_boole,spc9_boole,t1_boole,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,spc0_numerals,spc9_numerals,spc0_boole,spc9_boole,antisymmetry_r2_hidden,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_relat_1,dt_k1_ami_3,dt_k1_funct_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k4_numbers,dt_k5_numbers,dt_m2_relset_1,dt_m2_subset_1,dt_u4_ami_1,dt_u5_ami_1,dt_c2_3__ami_3,fc1_ami_3,fc1_finset_1,fc1_xboole_0,fc2_membered,fc4_membered,fc6_membered,t1_subset,t6_boole,t7_boole,d1_ami_3,e1_3__ami_3,t46_funct_2]), [interesting(0.8),file(ami_3,e2_3__ami_3),[file(ami_3,e2_3__ami_3)]]). fof(dt_c3_3__ami_3,plain,( m2_subset_1(c3_3__ami_3,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,fc1_xboole_0,fc6_membered,rc1_finset_1,rc1_int_1,rc1_membered,rc1_nat_1,rc2_int_1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_nat_1,cc2_int_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c2_3__ami_3,fc2_membered,de_c3_3__ami_3,e2_3__ami_3]), [interesting(0.8),file(ami_3,c3_3__ami_3),[file(ami_3,c3_3__ami_3)]]). fof(dh_c4_3__ami_3,definition, ( ? [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) & c3_3__ami_3 = k1_nat_1(k2_nat_1(2,A),k2_nat_1(2,1)) ) => ( m2_subset_1(c4_3__ami_3,k1_numbers,k5_numbers) & c3_3__ami_3 = k1_nat_1(k2_nat_1(2,c4_3__ami_3),k2_nat_1(2,1)) ) ), introduced(definition,[new_symbol(c4_3__ami_3),file(ami_3,c4_3__ami_3)]), [interesting(0.8),axiom,file(ami_3,c4_3__ami_3)]). fof(rqRealMult__k3_xcmplx_0__r1_r9_r9,theorem,( k3_xcmplx_0(1,9) = 9 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r9_r9), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r9_r9)]). fof(rqRealMult__k3_xcmplx_0__r9_r1_r9,theorem,( k3_xcmplx_0(9,1) = 9 ), file(arithm,rqRealMult__k3_xcmplx_0__r9_r1_r9), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r9_r1_r9)]). fof(redefinition_k8_funct_2,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(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(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(e3_3__ami_3,plain,( r2_hidden(k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,c3_3__ami_3),k1_tarski(k4_ami_2)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[existence_m1_fraenkel,dt_m1_fraenkel,cc1_fraenkel,rc1_fraenkel,reflexivity_r1_tarski,existence_l1_struct_0,redefinition_k1_fraenkel,dt_k1_fraenkel,dt_k1_funct_2,dt_k4_card_3,dt_l1_struct_0,dt_u1_ami_1,dt_u6_ami_1,cc1_setfam_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc3_ami_1,fc4_ami_1,fc4_setfam_1,fc7_membered,fc8_membered,fc9_membered,rc1_int_1,rc1_nat_1,rc1_setfam_1,rc2_int_1,rc2_nat_1,rc3_nat_1,free_g1_ami_1,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_g1_ami_1,dt_k13_finseq_1,dt_k17_ami_2,dt_k1_gr_cy_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_k5_ordinal2,dt_l1_ami_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc8_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_ami_1,fc2_membered,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc5_membered,fc9_finset_1,rc1_ami_1,rc1_finset_1,rc1_membered,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,spc0_boole,spc9_boole,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,spc0_numerals,spc9_numerals,spc0_boole,spc9_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_ami_3,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_k3_ami_2,dt_k4_ami_2,dt_k4_numbers,dt_k5_ami_2,dt_k5_numbers,dt_k8_funct_2,dt_m2_relset_1,dt_u4_ami_1,dt_u5_ami_1,dt_c2_3__ami_3,dt_c3_3__ami_3,de_c3_3__ami_3,fc1_ami_3,fc1_finset_1,fc1_xboole_0,fc2_ami_2,fc2_finset_1,fc3_ami_2,fc4_membered,fc6_membered,t1_boole,t1_subset,t6_boole,t7_boole,d1_ami_3,e1_3__ami_3,t46_funct_2]), [interesting(0.8),file(ami_3,e3_3__ami_3),[file(ami_3,e3_3__ami_3)]]). fof(d1_tarski,definition,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), [interesting(0.9),axiom,file(tarski,d1_tarski)]). fof(e4_3__ami_3,plain,( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,c3_3__ami_3) = k4_ami_2 ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_setfam_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_xboole_0,fc4_setfam_1,fc6_membered,fc7_membered,fc8_membered,fc9_membered,rc1_int_1,rc1_nat_1,rc1_setfam_1,rc2_int_1,rc2_nat_1,rc3_nat_1,t1_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_gr_cy_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_c2_3__ami_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc8_membered,cc9_membered,fc14_finset_1,fc1_ordinal2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_membered,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc5_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc4_finset_1,spc9_boole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,spc9_numerals,spc9_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k8_funct_2,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k3_ami_2,dt_k4_ami_2,dt_k4_numbers,dt_k5_ami_2,dt_k5_numbers,dt_k8_funct_2,dt_c3_3__ami_3,de_c3_3__ami_3,fc1_finset_1,fc2_ami_2,fc2_finset_1,fc3_ami_2,fc4_membered,t1_subset,t7_boole,e3_3__ami_3,d1_tarski]), [interesting(0.8),file(ami_3,e4_3__ami_3),[file(ami_3,e4_3__ami_3)]]). fof(t9_ami_2,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_ami_2 <=> ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & A = k1_nat_1(k2_nat_1(2,B),2) ) ) ) ), file(ami_2,t9_ami_2), [interesting(0.9),axiom,file(ami_2,t9_ami_2)]). fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,( k3_xcmplx_0(1,1) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]). fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,( k3_xcmplx_0(1,2) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]). fof(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,( k3_xcmplx_0(2,1) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]). fof(e5_3__ami_3,plain,( ? [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) & c3_3__ami_3 = k1_nat_1(k2_nat_1(2,A),k2_nat_1(2,1)) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_setfam_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_int_1,fc1_nat_1,fc1_xboole_0,fc2_int_1,fc2_nat_1,fc3_nat_1,fc4_nat_1,fc4_setfam_1,fc6_int_1,fc6_membered,fc7_int_1,fc8_membered,fc9_membered,rc1_int_1,rc1_nat_1,rc1_setfam_1,rc2_int_1,rc2_nat_1,rc3_nat_1,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_gr_cy_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_c2_3__ami_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc8_membered,cc9_membered,fc12_membered,fc14_finset_1,fc1_ordinal2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc5_membered,fc7_membered,fc9_finset_1,rc1_finset_1,rc1_membered,rc1_xboole_0,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r1_r9_r9,rqRealMult__k3_xcmplx_0__r9_r1_r9,spc5_arithm,spc6_arithm,spc7_arithm,spc9_boole,spc9_numerals,t2_subset,t3_arithm,t3_subset,t6_boole,t7_boole,t8_boole,spc9_numerals,spc9_boole,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xcmplx_0,existence_m2_subset_1,redefinition_k1_nat_1,redefinition_k2_nat_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m2_subset_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k2_nat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k3_ami_2,dt_k3_xcmplx_0,dt_k4_ami_2,dt_k4_numbers,dt_k5_ami_2,dt_k5_numbers,dt_k8_funct_2,dt_m2_subset_1,dt_c3_3__ami_3,de_c3_3__ami_3,fc1_finset_1,fc2_ami_2,fc2_finset_1,fc2_membered,fc3_ami_2,fc4_membered,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e4_3__ami_3,t9_ami_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.8),file(ami_3,e5_3__ami_3),[file(ami_3,e5_3__ami_3)]]). fof(dt_c4_3__ami_3,plain,( m2_subset_1(c4_3__ami_3,k1_numbers,k5_numbers) ), inference(consider,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[dh_c4_3__ami_3,e5_3__ami_3]), [interesting(0.8),file(ami_3,c4_3__ami_3),[file(ami_3,c4_3__ami_3)]]). fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,( r1_xreal_0(0,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]). fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,( r1_xreal_0(0,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]). fof(rqLessOrEqual__r1_xreal_0__r0_r2,theorem,( r1_xreal_0(0,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r2)]). fof(rqLessOrEqual__r1_xreal_0__r0_r7,theorem,( r1_xreal_0(0,7) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r7)]). fof(rqLessOrEqual__r1_xreal_0__r0_r8,theorem,( r1_xreal_0(0,8) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r8)]). fof(rqLessOrEqual__r1_xreal_0__r0_r9,theorem,( r1_xreal_0(0,9) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r9)]). fof(rqLessOrEqual__r1_xreal_0__r0_rm1,theorem,( ~ r1_xreal_0(0,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r0_rm2,theorem,( ~ r1_xreal_0(0,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r0_rm7,theorem,( ~ r1_xreal_0(0,k4_xcmplx_0(7)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_rm7)]). fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,( r1_xreal_0(1,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r2,theorem,( r1_xreal_0(1,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2)]). fof(rqLessOrEqual__r1_xreal_0__r1_r7,theorem,( r1_xreal_0(1,7) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r7)]). fof(rqLessOrEqual__r1_xreal_0__r1_r8,theorem,( r1_xreal_0(1,8) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r8)]). fof(rqLessOrEqual__r1_xreal_0__r1_r9,theorem,( r1_xreal_0(1,9) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r9)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm1,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm2,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm7,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(7)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm7)]). fof(rqLessOrEqual__r1_xreal_0__r1_rm8,theorem,( ~ r1_xreal_0(1,k4_xcmplx_0(8)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_rm8)]). fof(rqLessOrEqual__r1_xreal_0__r2_r2,theorem,( r1_xreal_0(2,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2)]). fof(rqLessOrEqual__r1_xreal_0__r2_r7,theorem,( r1_xreal_0(2,7) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r7)]). fof(rqLessOrEqual__r1_xreal_0__r2_r8,theorem,( r1_xreal_0(2,8) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r8)]). fof(rqLessOrEqual__r1_xreal_0__r2_r9,theorem,( r1_xreal_0(2,9) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r9)]). fof(rqLessOrEqual__r1_xreal_0__r2_rm1,theorem,( ~ r1_xreal_0(2,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r2_rm2,theorem,( ~ r1_xreal_0(2,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r2_rm7,theorem,( ~ r1_xreal_0(2,k4_xcmplx_0(7)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm7)]). fof(rqLessOrEqual__r1_xreal_0__r2_rm8,theorem,( ~ r1_xreal_0(2,k4_xcmplx_0(8)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_rm8)]). fof(rqLessOrEqual__r1_xreal_0__r7_r0,theorem,( ~ r1_xreal_0(7,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_r0)]). fof(rqLessOrEqual__r1_xreal_0__r7_r1,theorem,( ~ r1_xreal_0(7,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_r1)]). fof(rqLessOrEqual__r1_xreal_0__r7_r2,theorem,( ~ r1_xreal_0(7,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_r2)]). fof(rqLessOrEqual__r1_xreal_0__r7_r7,theorem,( r1_xreal_0(7,7) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_r7)]). fof(rqLessOrEqual__r1_xreal_0__r7_r8,theorem,( r1_xreal_0(7,8) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_r8)]). fof(rqLessOrEqual__r1_xreal_0__r7_r9,theorem,( r1_xreal_0(7,9) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_r9)]). fof(rqLessOrEqual__r1_xreal_0__r7_rm1,theorem,( ~ r1_xreal_0(7,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r7_rm2,theorem,( ~ r1_xreal_0(7,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r7_rm7,theorem,( ~ r1_xreal_0(7,k4_xcmplx_0(7)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r7_rm7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r7_rm7)]). fof(rqLessOrEqual__r1_xreal_0__r8_r0,theorem,( ~ r1_xreal_0(8,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_r0)]). fof(rqLessOrEqual__r1_xreal_0__r8_r1,theorem,( ~ r1_xreal_0(8,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_r1)]). fof(rqLessOrEqual__r1_xreal_0__r8_r2,theorem,( ~ r1_xreal_0(8,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_r2)]). fof(rqLessOrEqual__r1_xreal_0__r8_r7,theorem,( ~ r1_xreal_0(8,7) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_r7)]). fof(rqLessOrEqual__r1_xreal_0__r8_r8,theorem,( r1_xreal_0(8,8) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_r8)]). fof(rqLessOrEqual__r1_xreal_0__r8_r9,theorem,( r1_xreal_0(8,9) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_r9)]). fof(rqLessOrEqual__r1_xreal_0__r8_rm1,theorem,( ~ r1_xreal_0(8,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r8_rm2,theorem,( ~ r1_xreal_0(8,k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_rm2)]). fof(rqLessOrEqual__r1_xreal_0__r8_rm8,theorem,( ~ r1_xreal_0(8,k4_xcmplx_0(8)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r8_rm8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r8_rm8)]). fof(rqLessOrEqual__r1_xreal_0__r9_r7,theorem,( ~ r1_xreal_0(9,7) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_r7)]). fof(rqLessOrEqual__r1_xreal_0__r9_r8,theorem,( ~ r1_xreal_0(9,8) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_r8)]). fof(rqLessOrEqual__r1_xreal_0__r9_r9,theorem,( r1_xreal_0(9,9) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_r9)]). fof(rqLessOrEqual__r1_xreal_0__r9_rm1,theorem,( ~ r1_xreal_0(9,k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_rm1)]). fof(rqLessOrEqual__r1_xreal_0__r9_rm7,theorem,( ~ r1_xreal_0(9,k4_xcmplx_0(7)) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_rm7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_rm7)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r0,theorem,( r1_xreal_0(k4_xcmplx_0(1),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r1,theorem,( r1_xreal_0(k4_xcmplx_0(1),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r2,theorem,( r1_xreal_0(k4_xcmplx_0(1),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r2)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r7,theorem,( r1_xreal_0(k4_xcmplx_0(1),7) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r7)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r8,theorem,( r1_xreal_0(k4_xcmplx_0(1),8) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r8)]). fof(rqLessOrEqual__r1_xreal_0__rm1_r9,theorem,( r1_xreal_0(k4_xcmplx_0(1),9) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_r9)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rm1,theorem,( r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rm1_rm2,theorem,( ~ r1_xreal_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm1_rm2)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r0,theorem,( r1_xreal_0(k4_xcmplx_0(2),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r1,theorem,( r1_xreal_0(k4_xcmplx_0(2),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r2,theorem,( r1_xreal_0(k4_xcmplx_0(2),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r2)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r7,theorem,( r1_xreal_0(k4_xcmplx_0(2),7) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r7)]). fof(rqLessOrEqual__r1_xreal_0__rm2_r8,theorem,( r1_xreal_0(k4_xcmplx_0(2),8) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_r8)]). fof(rqLessOrEqual__r1_xreal_0__rm2_rm1,theorem,( r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm1)]). fof(rqLessOrEqual__r1_xreal_0__rm2_rm2,theorem,( r1_xreal_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm2_rm2)]). fof(rqLessOrEqual__r1_xreal_0__rm7_r0,theorem,( r1_xreal_0(k4_xcmplx_0(7),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm7_r1,theorem,( r1_xreal_0(k4_xcmplx_0(7),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm7_r2,theorem,( r1_xreal_0(k4_xcmplx_0(7),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r2)]). fof(rqLessOrEqual__r1_xreal_0__rm7_r7,theorem,( r1_xreal_0(k4_xcmplx_0(7),7) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r7)]). fof(rqLessOrEqual__r1_xreal_0__rm7_r9,theorem,( r1_xreal_0(k4_xcmplx_0(7),9) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r9), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm7_r9)]). fof(rqLessOrEqual__r1_xreal_0__rm7_rm7,theorem,( r1_xreal_0(k4_xcmplx_0(7),k4_xcmplx_0(7)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm7_rm7), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm7_rm7)]). fof(rqLessOrEqual__r1_xreal_0__rm8_r0,theorem,( r1_xreal_0(k4_xcmplx_0(8),0) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r0)]). fof(rqLessOrEqual__r1_xreal_0__rm8_r1,theorem,( r1_xreal_0(k4_xcmplx_0(8),1) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r1)]). fof(rqLessOrEqual__r1_xreal_0__rm8_r2,theorem,( r1_xreal_0(k4_xcmplx_0(8),2) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r2)]). fof(rqLessOrEqual__r1_xreal_0__rm8_r8,theorem,( r1_xreal_0(k4_xcmplx_0(8),8) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm8_r8)]). fof(rqLessOrEqual__r1_xreal_0__rm8_rm2,theorem,( r1_xreal_0(k4_xcmplx_0(8),k4_xcmplx_0(2)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm8_rm2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm8_rm2)]). fof(rqLessOrEqual__r1_xreal_0__rm8_rm8,theorem,( r1_xreal_0(k4_xcmplx_0(8),k4_xcmplx_0(8)) ), file(arithm,rqLessOrEqual__r1_xreal_0__rm8_rm8), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__rm8_rm8)]). 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_r7_rm7,theorem,( k6_xcmplx_0(0,7) = k4_xcmplx_0(7) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r7_rm7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r7_rm7)]). fof(rqRealDiff__k6_xcmplx_0__r0_r8_rm8,theorem,( k6_xcmplx_0(0,8) = k4_xcmplx_0(8) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r8_rm8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r8_rm8)]). 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_rm7_r7,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(7)) = 7 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm7_r7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm7_r7)]). fof(rqRealDiff__k6_xcmplx_0__r1_r8_rm7,theorem,( k6_xcmplx_0(1,8) = k4_xcmplx_0(7) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r8_rm7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r8_rm7)]). 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_rm7_r8,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(7)) = 8 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm7_r8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm7_r8)]). fof(rqRealDiff__k6_xcmplx_0__r1_rm8_r9,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(8)) = 9 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm8_r9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm8_r9)]). fof(rqRealDiff__k6_xcmplx_0__r7_r0_r7,theorem,( k6_xcmplx_0(7,0) = 7 ), file(arithm,rqRealDiff__k6_xcmplx_0__r7_r0_r7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r7_r0_r7)]). fof(rqRealDiff__k6_xcmplx_0__r7_r7_r0,theorem,( k6_xcmplx_0(7,7) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r7_r7_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r7_r7_r0)]). fof(rqRealDiff__k6_xcmplx_0__r7_r8_rm1,theorem,( k6_xcmplx_0(7,8) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r7_r8_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r7_r8_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r7_r9_rm2,theorem,( k6_xcmplx_0(7,9) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r7_r9_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r7_r9_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r7_rm1_r8,theorem,( k6_xcmplx_0(7,k4_xcmplx_0(1)) = 8 ), file(arithm,rqRealDiff__k6_xcmplx_0__r7_rm1_r8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r7_rm1_r8)]). fof(rqRealDiff__k6_xcmplx_0__r7_rm2_r9,theorem,( k6_xcmplx_0(7,k4_xcmplx_0(2)) = 9 ), file(arithm,rqRealDiff__k6_xcmplx_0__r7_rm2_r9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r7_rm2_r9)]). fof(rqRealDiff__k6_xcmplx_0__r8_r0_r8,theorem,( k6_xcmplx_0(8,0) = 8 ), file(arithm,rqRealDiff__k6_xcmplx_0__r8_r0_r8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r8_r0_r8)]). fof(rqRealDiff__k6_xcmplx_0__r8_r1_r7,theorem,( k6_xcmplx_0(8,1) = 7 ), file(arithm,rqRealDiff__k6_xcmplx_0__r8_r1_r7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r8_r1_r7)]). fof(rqRealDiff__k6_xcmplx_0__r8_r7_r1,theorem,( k6_xcmplx_0(8,7) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r8_r7_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r8_r7_r1)]). fof(rqRealDiff__k6_xcmplx_0__r8_r8_r0,theorem,( k6_xcmplx_0(8,8) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r8_r8_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r8_r8_r0)]). fof(rqRealDiff__k6_xcmplx_0__r8_r9_rm1,theorem,( k6_xcmplx_0(8,9) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r8_r9_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r8_r9_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r8_rm1_r9,theorem,( k6_xcmplx_0(8,k4_xcmplx_0(1)) = 9 ), file(arithm,rqRealDiff__k6_xcmplx_0__r8_rm1_r9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r8_rm1_r9)]). fof(rqRealDiff__k6_xcmplx_0__r9_r0_r9,theorem,( k6_xcmplx_0(9,0) = 9 ), file(arithm,rqRealDiff__k6_xcmplx_0__r9_r0_r9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r9_r0_r9)]). fof(rqRealDiff__k6_xcmplx_0__r9_r1_r8,theorem,( k6_xcmplx_0(9,1) = 8 ), file(arithm,rqRealDiff__k6_xcmplx_0__r9_r1_r8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r9_r1_r8)]). fof(rqRealDiff__k6_xcmplx_0__r9_r2_r7,theorem,( k6_xcmplx_0(9,2) = 7 ), file(arithm,rqRealDiff__k6_xcmplx_0__r9_r2_r7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r9_r2_r7)]). fof(rqRealDiff__k6_xcmplx_0__r9_r7_r2,theorem,( k6_xcmplx_0(9,7) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r9_r7_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r9_r7_r2)]). fof(rqRealDiff__k6_xcmplx_0__r9_r8_r1,theorem,( k6_xcmplx_0(9,8) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r9_r8_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r9_r8_r1)]). fof(rqRealDiff__k6_xcmplx_0__r9_r9_r0,theorem,( k6_xcmplx_0(9,9) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r9_r9_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r9_r9_r0)]). 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_r7_rm8,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),7) = k4_xcmplx_0(8) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r7_rm8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r7_rm8)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r8_rm9,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),8) = k4_xcmplx_0(9) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r8_rm9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r8_rm9)]). 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(rqRealDiff__k6_xcmplx_0__rm1_rm8_r7,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(8)) = 7 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm8_r7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm8_r7)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm9_r8,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(9)) = 8 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm9_r8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm9_r8)]). 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_r7_rm9,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),7) = k4_xcmplx_0(9) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r7_rm9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r7_rm9)]). 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__rm2_rm9_r7,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(9)) = 7 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm9_r7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm9_r7)]). fof(rqRealDiff__k6_xcmplx_0__rm7_r1_rm8,theorem,( k6_xcmplx_0(k4_xcmplx_0(7),1) = k4_xcmplx_0(8) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm7_r1_rm8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm7_r1_rm8)]). fof(rqRealDiff__k6_xcmplx_0__rm7_r2_rm9,theorem,( k6_xcmplx_0(k4_xcmplx_0(7),2) = k4_xcmplx_0(9) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm7_r2_rm9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm7_r2_rm9)]). fof(rqRealDiff__k6_xcmplx_0__rm7_rm7_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(7),k4_xcmplx_0(7)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm7_rm7_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm7_rm7_r0)]). fof(rqRealDiff__k6_xcmplx_0__rm7_rm8_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(7),k4_xcmplx_0(8)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm7_rm8_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm7_rm8_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm7_rm9_r2,theorem,( k6_xcmplx_0(k4_xcmplx_0(7),k4_xcmplx_0(9)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm7_rm9_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm7_rm9_r2)]). fof(rqRealDiff__k6_xcmplx_0__rm8_r0_rm8,theorem,( k6_xcmplx_0(k4_xcmplx_0(8),0) = k4_xcmplx_0(8) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm8_r0_rm8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm8_r0_rm8)]). fof(rqRealDiff__k6_xcmplx_0__rm8_r1_rm9,theorem,( k6_xcmplx_0(k4_xcmplx_0(8),1) = k4_xcmplx_0(9) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm8_r1_rm9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm8_r1_rm9)]). fof(rqRealDiff__k6_xcmplx_0__rm8_rm1_rm7,theorem,( k6_xcmplx_0(k4_xcmplx_0(8),k4_xcmplx_0(1)) = k4_xcmplx_0(7) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm1_rm7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm1_rm7)]). fof(rqRealDiff__k6_xcmplx_0__rm8_rm7_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(8),k4_xcmplx_0(7)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm7_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm7_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm8_rm8_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(8),k4_xcmplx_0(8)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm8_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm8_r0)]). fof(rqRealDiff__k6_xcmplx_0__rm8_rm9_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(8),k4_xcmplx_0(9)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm9_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm8_rm9_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm9_rm1_rm8,theorem,( k6_xcmplx_0(k4_xcmplx_0(9),k4_xcmplx_0(1)) = k4_xcmplx_0(8) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm1_rm8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm1_rm8)]). fof(rqRealDiff__k6_xcmplx_0__rm9_rm7_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(9),k4_xcmplx_0(7)) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm7_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm7_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm9_rm8_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(9),k4_xcmplx_0(8)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm8_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm8_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm9_rm9_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(9),k4_xcmplx_0(9)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm9_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm9_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,( k3_xcmplx_0(0,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,( k3_xcmplx_0(0,1) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r2_r0,theorem,( k3_xcmplx_0(0,2) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r8_r0,theorem,( k3_xcmplx_0(0,8) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r8_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r8_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0,theorem,( k3_xcmplx_0(0,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,( k3_xcmplx_0(1,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r7_r7,theorem,( k3_xcmplx_0(1,7) = 7 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r7_r7), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r7_r7)]). fof(rqRealMult__k3_xcmplx_0__r1_r8_r8,theorem,( k3_xcmplx_0(1,8) = 8 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r8_r8), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r8_r8)]). fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2,theorem,( k3_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]). fof(rqRealMult__k3_xcmplx_0__r1_rm8_rm8,theorem,( k3_xcmplx_0(1,k4_xcmplx_0(8)) = k4_xcmplx_0(8) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rm8_rm8), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm8_rm8)]). fof(rqRealMult__k3_xcmplx_0__r2_r0_r0,theorem,( k3_xcmplx_0(2,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r7_r1_r7,theorem,( k3_xcmplx_0(7,1) = 7 ), file(arithm,rqRealMult__k3_xcmplx_0__r7_r1_r7), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r7_r1_r7)]). fof(rqRealMult__k3_xcmplx_0__r8_r0_r0,theorem,( k3_xcmplx_0(8,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r8_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r8_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r8_r1_r8,theorem,( k3_xcmplx_0(8,1) = 8 ), file(arithm,rqRealMult__k3_xcmplx_0__r8_r1_r8), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r8_r1_r8)]). fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]). fof(rqRealMult__k3_xcmplx_0__rm7_r1_rm7,theorem,( k3_xcmplx_0(k4_xcmplx_0(7),1) = k4_xcmplx_0(7) ), file(arithm,rqRealMult__k3_xcmplx_0__rm7_r1_rm7), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm7_r1_rm7)]). fof(rqRealMult__k3_xcmplx_0__rm8_r1_rm8,theorem,( k3_xcmplx_0(k4_xcmplx_0(8),1) = k4_xcmplx_0(8) ), file(arithm,rqRealMult__k3_xcmplx_0__rm8_r1_rm8), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm8_r1_rm8)]). fof(rqRealMult__k3_xcmplx_0__rm9_r1_rm9,theorem,( k3_xcmplx_0(k4_xcmplx_0(9),1) = k4_xcmplx_0(9) ), file(arithm,rqRealMult__k3_xcmplx_0__rm9_r1_rm9), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm9_r1_rm9)]). fof(rqRealNeg__k4_xcmplx_0__r7_rm7,theorem,( k4_xcmplx_0(7) = k4_xcmplx_0(7) ), file(arithm,rqRealNeg__k4_xcmplx_0__r7_rm7), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r7_rm7)]). fof(rqRealNeg__k4_xcmplx_0__r8_rm8,theorem,( k4_xcmplx_0(8) = k4_xcmplx_0(8) ), file(arithm,rqRealNeg__k4_xcmplx_0__r8_rm8), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r8_rm8)]). 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(rqRealNeg__k4_xcmplx_0__rm7_r7,theorem,( k4_xcmplx_0(k4_xcmplx_0(7)) = 7 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm7_r7), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm7_r7)]). fof(rqRealNeg__k4_xcmplx_0__rm8_r8,theorem,( k4_xcmplx_0(k4_xcmplx_0(8)) = 8 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm8_r8), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm8_r8)]). fof(rqRealNeg__k4_xcmplx_0__rm9_r9,theorem,( k4_xcmplx_0(k4_xcmplx_0(9)) = 9 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm9_r9), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm9_r9)]). fof(t2_tarski,theorem,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), [interesting(0.9),axiom,file(tarski,t2_tarski)]). fof(fraenkel_a_0_1_ami_2,definition,( ! [A] : ( r2_hidden(A,a_0_1_ami_2) <=> ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & A = k2_nat_1(2,B) & ~ r1_xreal_0(B,0) ) ) ), file(ami_2,a_0_1_ami_2), [interesting(0.9),axiom,file(ami_2,a_0_1_ami_2)]). fof(spc7_numerals,theorem, ( v2_xreal_0(7) & m2_subset_1(7,k1_numbers,k5_numbers) & m1_subset_1(7,k5_numbers) & m1_subset_1(7,k1_numbers) ), file(numerals,spc7_numerals), [interesting(0.9),axiom,file(numerals,spc7_numerals)]). fof(spc8_numerals,theorem, ( v2_xreal_0(8) & m2_subset_1(8,k1_numbers,k5_numbers) & m1_subset_1(8,k5_numbers) & m1_subset_1(8,k1_numbers) ), file(numerals,spc8_numerals), [interesting(0.9),axiom,file(numerals,spc8_numerals)]). fof(spc7_boole,theorem,( ~ v1_xboole_0(7) ), file(boole,spc7_boole), [interesting(0.9),axiom,file(boole,spc7_boole)]). fof(spc8_boole,theorem,( ~ v1_xboole_0(8) ), file(boole,spc8_boole), [interesting(0.9),axiom,file(boole,spc8_boole)]). fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,( ~ r1_xreal_0(1,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]). fof(rqLessOrEqual__r1_xreal_0__r2_r0,theorem,( ~ r1_xreal_0(2,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r0)]). fof(rqLessOrEqual__r1_xreal_0__r2_r1,theorem,( ~ r1_xreal_0(2,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1)]). fof(e6_3__ami_3,plain,( c3_3__ami_3 = k1_nat_1(k2_nat_1(2,c4_3__ami_3),k2_nat_1(2,1)) ), inference(consider,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[dh_c4_3__ami_3,e5_3__ami_3]), [interesting(0.8),file(ami_3,e6_3__ami_3),[file(ami_3,e6_3__ami_3)]]). fof(t19_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ~ ( 0 != A & r1_xreal_0(A,0) ) ) ), file(nat_1,t19_nat_1), [interesting(0.9),axiom,file(nat_1,t19_nat_1)]). 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(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(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__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__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(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(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__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_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(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__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_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__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(e7_3__ami_3,plain, ( c3_3__ami_3 = k2_nat_1(2,k1_nat_1(c4_3__ami_3,1)) & ~ r1_xreal_0(k1_nat_1(c4_3__ami_3,1),0) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc1_xboole_0,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_xcmplx_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_xcmplx_0,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_3__ami_3,cc15_membered,cc1_finset_1,cc1_nat_1,cc2_int_1,cc2_nat_1,cc4_int_1,fc1_int_1,fc1_nat_1,fc2_int_1,fc2_membered,fc3_int_1,fc3_nat_1,fc4_int_1,fc4_nat_1,fc5_int_1,fc6_int_1,fc7_int_1,fc8_int_1,fc9_int_1,rc1_int_1,rc1_nat_1,rc1_xboole_0,rc2_int_1,rc2_xboole_0,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__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__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__rm2_r0_rm2,rqRealAdd__k2_xcmplx_0__rm2_r1_rm1,rqRealAdd__k2_xcmplx_0__rm2_r2_r0,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_real,t2_subset,t3_arithm,t3_real,t4_arithm,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_nat_1,redefinition_k2_nat_1,dt_k1_nat_1,dt_k2_nat_1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_c3_3__ami_3,dt_c4_3__ami_3,de_c3_3__ami_3,cc3_int_1,cc3_nat_1,fc2_nat_1,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealNeg__k4_xcmplx_0__rm1_r1,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e6_3__ami_3,t19_nat_1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2]), [interesting(0.8),file(ami_3,e7_3__ami_3),[file(ami_3,e7_3__ami_3)]]). fof(d3_ami_2,definition,( k3_ami_2 = a_0_1_ami_2 ), file(ami_2,d3_ami_2), [interesting(0.9),axiom,file(ami_2,d3_ami_2)]). fof(rqRealNeg__k4_xcmplx_0__r9_rm9,theorem,( k4_xcmplx_0(9) = k4_xcmplx_0(9) ), file(arithm,rqRealNeg__k4_xcmplx_0__r9_rm9), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r9_rm9)]). fof(rqRealDiff__k6_xcmplx_0__rm9_rm2_rm7,theorem,( k6_xcmplx_0(k4_xcmplx_0(9),k4_xcmplx_0(2)) = k4_xcmplx_0(7) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm2_rm7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm9_rm2_rm7)]). fof(rqRealDiff__k6_xcmplx_0__r2_r9_rm7,theorem,( k6_xcmplx_0(2,9) = k4_xcmplx_0(7) ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r9_rm7), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r9_rm7)]). fof(rqRealDiff__k6_xcmplx_0__r1_r9_rm8,theorem,( k6_xcmplx_0(1,9) = k4_xcmplx_0(8) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r9_rm8), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r9_rm8)]). fof(rqRealDiff__k6_xcmplx_0__r0_r9_rm9,theorem,( k6_xcmplx_0(0,9) = k4_xcmplx_0(9) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r9_rm9), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r9_rm9)]). fof(rqLessOrEqual__r1_xreal_0__r9_r0,theorem,( ~ r1_xreal_0(9,0) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_r0), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_r0)]). fof(rqLessOrEqual__r1_xreal_0__r9_r2,theorem,( ~ r1_xreal_0(9,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_r2)]). fof(rqLessOrEqual__r1_xreal_0__r9_r1,theorem,( ~ r1_xreal_0(9,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r9_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r9_r1)]). fof(e8_3__ami_3,plain,( r2_hidden(c2_3__ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[existence_m1_fraenkel,dt_m1_fraenkel,cc1_fraenkel,rc1_fraenkel,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_k1_fraenkel,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_fraenkel,dt_k1_funct_2,dt_k1_xboole_0,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_tarski,dt_k4_card_3,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u1_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,cc1_relset_1,cc1_setfam_1,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc1_fraenkel,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finset_1,fc2_fraenkel,fc2_int_1,fc2_nat_1,fc2_xboole_0,fc3_ami_1,fc3_int_1,fc3_nat_1,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc4_int_1,fc4_nat_1,fc4_setfam_1,fc5_membered,fc6_int_1,fc6_membered,fc7_int_1,fc8_int_1,fc9_finset_1,fc9_membered,rc1_int_1,rc1_nat_1,rc1_setfam_1,rc2_int_1,rc2_nat_1,rc3_nat_1,t1_boole,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,free_g1_ami_1,commutativity_k2_xcmplx_0,abstractness_v1_ami_1,existence_l1_ami_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_g1_ami_1,dt_k17_ami_2,dt_k1_gr_cy_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k4_ami_2,dt_k5_ami_2,dt_k5_numbers,dt_l1_ami_1,dt_m1_subset_1,dt_m2_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_finset_1,cc1_int_1,cc1_membered,cc1_nat_1,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_membered,cc4_membered,cc6_membered,cc8_membered,cc9_membered,fc2_ami_1,fc2_membered,fc2_setfam_1,fc3_ami_2,fc5_int_1,fc7_membered,fc8_membered,fc9_int_1,rc1_ami_1,rc1_finset_1,rc1_membered,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,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_r7_r7,rqRealAdd__k2_xcmplx_0__r0_r8_r8,rqRealAdd__k2_xcmplx_0__r0_r9_r9,rqRealAdd__k2_xcmplx_0__r0_rm1_rm1,rqRealAdd__k2_xcmplx_0__r0_rm2_rm2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealAdd__k2_xcmplx_0__r1_r7_r8,rqRealAdd__k2_xcmplx_0__r1_r8_r9,rqRealAdd__k2_xcmplx_0__r1_rm1_r0,rqRealAdd__k2_xcmplx_0__r1_rm2_rm1,rqRealAdd__k2_xcmplx_0__r1_rm9_rm8,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealAdd__k2_xcmplx_0__r2_r7_r9,rqRealAdd__k2_xcmplx_0__r2_rm1_r1,rqRealAdd__k2_xcmplx_0__r2_rm2_r0,rqRealAdd__k2_xcmplx_0__r2_rm9_rm7,rqRealAdd__k2_xcmplx_0__r7_r0_r7,rqRealAdd__k2_xcmplx_0__r7_r1_r8,rqRealAdd__k2_xcmplx_0__r7_r2_r9,rqRealAdd__k2_xcmplx_0__r8_r0_r8,rqRealAdd__k2_xcmplx_0__r8_r1_r9,rqRealAdd__k2_xcmplx_0__r8_rm1_r7,rqRealAdd__k2_xcmplx_0__r8_rm8_r0,rqRealAdd__k2_xcmplx_0__r9_r0_r9,rqRealAdd__k2_xcmplx_0__r9_rm1_r8,rqRealAdd__k2_xcmplx_0__r9_rm2_r7,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_r8_r7,rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2,rqRealAdd__k2_xcmplx_0__rm1_rm7_rm8,rqRealAdd__k2_xcmplx_0__rm1_rm8_rm9,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__rm2_r9_r7,rqRealAdd__k2_xcmplx_0__rm7_rm1_rm8,rqRealAdd__k2_xcmplx_0__rm8_r8_r0,rqRealAdd__k2_xcmplx_0__rm9_r1_rm8,rqRealAdd__k2_xcmplx_0__rm9_r2_rm7,spc1_arithm,spc2_arithm,spc5_arithm,spc6_arithm,spc7_arithm,spc8_arithm,spc9_arithm,t1_arithm,t1_numerals,t1_real,t2_arithm,t2_subset,t3_arithm,t3_subset,t4_arithm,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_nat_1,redefinition_k2_nat_1,dt_k1_ami_3,dt_k1_nat_1,dt_k1_tarski,dt_k2_nat_1,dt_k3_ami_2,dt_k3_xcmplx_0,dt_k4_numbers,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_u2_ami_1,dt_c2_3__ami_3,dt_c3_3__ami_3,dt_c4_3__ami_3,de_c3_3__ami_3,fc1_ami_3,fc1_finset_1,fc2_ami_2,fc4_membered,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r2,rqLessOrEqual__r1_xreal_0__r0_r7,rqLessOrEqual__r1_xreal_0__r0_r8,rqLessOrEqual__r1_xreal_0__r0_r9,rqLessOrEqual__r1_xreal_0__r0_rm1,rqLessOrEqual__r1_xreal_0__r0_rm2,rqLessOrEqual__r1_xreal_0__r0_rm7,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r7,rqLessOrEqual__r1_xreal_0__r1_r8,rqLessOrEqual__r1_xreal_0__r1_r9,rqLessOrEqual__r1_xreal_0__r1_rm1,rqLessOrEqual__r1_xreal_0__r1_rm2,rqLessOrEqual__r1_xreal_0__r1_rm7,rqLessOrEqual__r1_xreal_0__r1_rm8,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r2_r7,rqLessOrEqual__r1_xreal_0__r2_r8,rqLessOrEqual__r1_xreal_0__r2_r9,rqLessOrEqual__r1_xreal_0__r2_rm1,rqLessOrEqual__r1_xreal_0__r2_rm2,rqLessOrEqual__r1_xreal_0__r2_rm7,rqLessOrEqual__r1_xreal_0__r2_rm8,rqLessOrEqual__r1_xreal_0__r7_r0,rqLessOrEqual__r1_xreal_0__r7_r1,rqLessOrEqual__r1_xreal_0__r7_r2,rqLessOrEqual__r1_xreal_0__r7_r7,rqLessOrEqual__r1_xreal_0__r7_r8,rqLessOrEqual__r1_xreal_0__r7_r9,rqLessOrEqual__r1_xreal_0__r7_rm1,rqLessOrEqual__r1_xreal_0__r7_rm2,rqLessOrEqual__r1_xreal_0__r7_rm7,rqLessOrEqual__r1_xreal_0__r8_r0,rqLessOrEqual__r1_xreal_0__r8_r1,rqLessOrEqual__r1_xreal_0__r8_r2,rqLessOrEqual__r1_xreal_0__r8_r7,rqLessOrEqual__r1_xreal_0__r8_r8,rqLessOrEqual__r1_xreal_0__r8_r9,rqLessOrEqual__r1_xreal_0__r8_rm1,rqLessOrEqual__r1_xreal_0__r8_rm2,rqLessOrEqual__r1_xreal_0__r8_rm8,rqLessOrEqual__r1_xreal_0__r9_r7,rqLessOrEqual__r1_xreal_0__r9_r8,rqLessOrEqual__r1_xreal_0__r9_r9,rqLessOrEqual__r1_xreal_0__r9_rm1,rqLessOrEqual__r1_xreal_0__r9_rm7,rqLessOrEqual__r1_xreal_0__rm1_r0,rqLessOrEqual__r1_xreal_0__rm1_r1,rqLessOrEqual__r1_xreal_0__rm1_r2,rqLessOrEqual__r1_xreal_0__rm1_r7,rqLessOrEqual__r1_xreal_0__rm1_r8,rqLessOrEqual__r1_xreal_0__rm1_r9,rqLessOrEqual__r1_xreal_0__rm1_rm1,rqLessOrEqual__r1_xreal_0__rm1_rm2,rqLessOrEqual__r1_xreal_0__rm2_r0,rqLessOrEqual__r1_xreal_0__rm2_r1,rqLessOrEqual__r1_xreal_0__rm2_r2,rqLessOrEqual__r1_xreal_0__rm2_r7,rqLessOrEqual__r1_xreal_0__rm2_r8,rqLessOrEqual__r1_xreal_0__rm2_rm1,rqLessOrEqual__r1_xreal_0__rm2_rm2,rqLessOrEqual__r1_xreal_0__rm7_r0,rqLessOrEqual__r1_xreal_0__rm7_r1,rqLessOrEqual__r1_xreal_0__rm7_r2,rqLessOrEqual__r1_xreal_0__rm7_r7,rqLessOrEqual__r1_xreal_0__rm7_r9,rqLessOrEqual__r1_xreal_0__rm7_rm7,rqLessOrEqual__r1_xreal_0__rm8_r0,rqLessOrEqual__r1_xreal_0__rm8_r1,rqLessOrEqual__r1_xreal_0__rm8_r2,rqLessOrEqual__r1_xreal_0__rm8_r8,rqLessOrEqual__r1_xreal_0__rm8_rm2,rqLessOrEqual__r1_xreal_0__rm8_rm8,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r7_rm7,rqRealDiff__k6_xcmplx_0__r0_r8_rm8,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rm7_r7,rqRealDiff__k6_xcmplx_0__r1_r8_rm7,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rm7_r8,rqRealDiff__k6_xcmplx_0__r1_rm8_r9,rqRealDiff__k6_xcmplx_0__r7_r0_r7,rqRealDiff__k6_xcmplx_0__r7_r7_r0,rqRealDiff__k6_xcmplx_0__r7_r8_rm1,rqRealDiff__k6_xcmplx_0__r7_r9_rm2,rqRealDiff__k6_xcmplx_0__r7_rm1_r8,rqRealDiff__k6_xcmplx_0__r7_rm2_r9,rqRealDiff__k6_xcmplx_0__r8_r0_r8,rqRealDiff__k6_xcmplx_0__r8_r1_r7,rqRealDiff__k6_xcmplx_0__r8_r7_r1,rqRealDiff__k6_xcmplx_0__r8_r8_r0,rqRealDiff__k6_xcmplx_0__r8_r9_rm1,rqRealDiff__k6_xcmplx_0__r8_rm1_r9,rqRealDiff__k6_xcmplx_0__r9_r0_r9,rqRealDiff__k6_xcmplx_0__r9_r1_r8,rqRealDiff__k6_xcmplx_0__r9_r2_r7,rqRealDiff__k6_xcmplx_0__r9_r7_r2,rqRealDiff__k6_xcmplx_0__r9_r8_r1,rqRealDiff__k6_xcmplx_0__r9_r9_r0,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_r7_rm8,rqRealDiff__k6_xcmplx_0__rm1_r8_rm9,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm8_r7,rqRealDiff__k6_xcmplx_0__rm1_rm9_r8,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_r7_rm9,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm9_r7,rqRealDiff__k6_xcmplx_0__rm7_r1_rm8,rqRealDiff__k6_xcmplx_0__rm7_r2_rm9,rqRealDiff__k6_xcmplx_0__rm7_rm7_r0,rqRealDiff__k6_xcmplx_0__rm7_rm8_r1,rqRealDiff__k6_xcmplx_0__rm7_rm9_r2,rqRealDiff__k6_xcmplx_0__rm8_r0_rm8,rqRealDiff__k6_xcmplx_0__rm8_r1_rm9,rqRealDiff__k6_xcmplx_0__rm8_rm1_rm7,rqRealDiff__k6_xcmplx_0__rm8_rm7_rm1,rqRealDiff__k6_xcmplx_0__rm8_rm8_r0,rqRealDiff__k6_xcmplx_0__rm8_rm9_r1,rqRealDiff__k6_xcmplx_0__rm9_rm1_rm8,rqRealDiff__k6_xcmplx_0__rm9_rm7_rm2,rqRealDiff__k6_xcmplx_0__rm9_rm8_rm1,rqRealDiff__k6_xcmplx_0__rm9_rm9_r0,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r0_r8_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_r7_r7,rqRealMult__k3_xcmplx_0__r1_r8_r8,rqRealMult__k3_xcmplx_0__r1_r9_r9,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rm8_rm8,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r7_r1_r7,rqRealMult__k3_xcmplx_0__r8_r0_r0,rqRealMult__k3_xcmplx_0__r8_r1_r8,rqRealMult__k3_xcmplx_0__r9_r1_r9,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm7_r1_rm7,rqRealMult__k3_xcmplx_0__rm8_r1_rm8,rqRealMult__k3_xcmplx_0__rm9_r1_rm9,rqRealNeg__k4_xcmplx_0__r7_rm7,rqRealNeg__k4_xcmplx_0__r8_rm8,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__rm7_r7,rqRealNeg__k4_xcmplx_0__rm8_r8,rqRealNeg__k4_xcmplx_0__rm9_r9,t1_subset,t7_boole,t2_tarski,fraenkel_a_0_1_ami_2,d1_ami_3,spc0_numerals,spc1_numerals,spc2_numerals,spc7_numerals,spc8_numerals,spc9_numerals,spc0_boole,spc1_boole,spc2_boole,spc7_boole,spc8_boole,spc9_boole,e7_3__ami_3,d3_ami_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealNeg__k4_xcmplx_0__r9_rm9,rqRealDiff__k6_xcmplx_0__rm9_rm2_rm7,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealDiff__k6_xcmplx_0__r2_r9_rm7,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_r9_rm8,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_r9_rm9,rqLessOrEqual__r1_xreal_0__r2_r0,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r9_r0,rqLessOrEqual__r1_xreal_0__r9_r2,rqLessOrEqual__r1_xreal_0__r9_r1]), [interesting(0.8),file(ami_3,e8_3__ami_3),[file(ami_3,e8_3__ami_3)]]). fof(i3_3__ami_3,theorem,( $true ), introduced(tautology,[file(ami_3,i3_3__ami_3)]), [interesting(0.8),trivial,file(ami_3,i3_3__ami_3)]). fof(i2_3__ami_3,plain,( r2_hidden(c2_3__ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), inference(conclusion,[status(thm),assumptions([dt_c2_3__ami_3,e1_3__ami_3])],[e8_3__ami_3,i3_3__ami_3]), [interesting(0.8),file(ami_3,i2_3__ami_3),[file(ami_3,i2_3__ami_3)]]). fof(i2_3_tmp__ami_3,plain, ( r2_hidden(c2_3__ami_3,k10_relat_1(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) => r2_hidden(c2_3__ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_3__ami_3]),discharge_asm(discharge,[e1_3__ami_3])],[e1_3__ami_3,i2_3__ami_3]), [interesting(0.8),i1_3__ami_3]). fof(i1_3__ami_3,plain,( ~ ( r2_hidden(c2_3__ami_3,k3_funct_2(u1_struct_0(k1_ami_3),k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),u5_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) & ~ r2_hidden(c2_3__ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c2_3__ami_3])],[i2_3_tmp__ami_3,cc1_fraenkel,rc1_fraenkel,dt_k1_funct_2,dt_k4_card_3,cc3_int_1,cc3_nat_1,fc11_membered,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc3_ami_1,fc4_ami_1,rc1_nat_1,free_g1_ami_1,dt_g1_ami_1,dt_u1_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc20_membered,cc4_int_1,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc26_membered,fc4_setfam_1,fc7_membered,fc8_membered,fc9_membered,rc1_membered,rc1_setfam_1,rc2_int_1,abstractness_v1_ami_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_l1_ami_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_int_1,cc1_relset_1,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc8_membered,fc14_finset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc2_ami_1,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc9_finset_1,rc1_ami_1,rc1_finset_1,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,redefinition_k3_funct_2,dt_k10_relat_1,dt_k1_ami_3,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k3_funct_2,dt_k4_numbers,dt_u1_struct_0,dt_u2_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_c2_3__ami_3,fc1_ami_3,fc1_finset_1,fc2_finset_1,fc4_membered]), [interesting(0.8),file(ami_3,i1_3__ami_3),[file(ami_3,i1_3__ami_3)]]). fof(i1_3_tmp__ami_3,plain,( ~ ( r2_hidden(c2_3__ami_3,k3_funct_2(u1_struct_0(k1_ami_3),k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))),u5_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_tarski(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) & ~ r2_hidden(c2_3__ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c2_3__ami_3])],[dt_c2_3__ami_3,i1_3__ami_3]), [interesting(1),t1_ami_3]). fof(t1_ami_3,theorem,( v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), inference(let,[status(thm),assumptions([])],[i1_3_tmp__ami_3,cc1_fraenkel,rc1_fraenkel,dt_k1_funct_2,dt_k4_card_3,cc3_int_1,cc3_nat_1,fc11_membered,fc16_membered,fc1_fraenkel,fc2_fraenkel,fc3_ami_1,fc4_ami_1,rc1_nat_1,free_g1_ami_1,dt_g1_ami_1,dt_u1_ami_1,dt_u6_ami_1,cc14_membered,cc1_membered,cc1_setfam_1,cc20_membered,cc4_int_1,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc26_membered,fc4_setfam_1,fc7_membered,fc8_membered,fc9_membered,rc1_membered,rc1_setfam_1,rc2_int_1,abstractness_v1_ami_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u3_ami_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_int_1,cc1_relset_1,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,cc8_membered,fc14_finset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc2_ami_1,fc2_setfam_1,fc2_xboole_0,fc3_setfam_1,fc3_xboole_0,fc9_finset_1,rc1_ami_1,rc1_finset_1,rc1_xboole_0,rc2_ami_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,rc5_ami_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k3_funct_2,dt_k1_ami_3,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k3_funct_2,dt_k4_numbers,dt_l1_ami_1,dt_u1_struct_0,dt_u2_ami_1,dt_u4_ami_1,dt_u5_ami_1,fc1_ami_3,fc1_finset_1,fc2_finset_1,fc4_membered,d12_ami_1,d3_tarski,dh_c2_3__ami_3]), [interesting(1),file(ami_3,t1_ami_3),[file(ami_3,t1_ami_3)]]).