% Mizar problem: t18_sfmastr2,sfmastr2,507,41 fof(t18_sfmastr2,conjecture,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & v1_scmfsa7b(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ( r1_sfmastr2(A,B,C) & r1_xreal_0(0,k20_scmfsa_2(A,B)) ) => ( ( k20_scmfsa_2(A,k4_scmfsa_2(0)) != 1 & v1_sf_mastr(B) ) | ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_xreal_0(k20_scmfsa_2(A,B),D) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = 0 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(0)) = 1 ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_int_1,cc1_relset_1,cc1_setfam_1,cc1_sf_mastr,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_xreal_0,cc3_int_1,cc3_xreal_0,cc4_int_1,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_finsub_1,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k4_subset_1,connectedness_r1_xreal_0,d2_sfmastr2,d5_real_1,dt_g1_ami_1,dt_k10_scmfsa_2,dt_k11_ami_1,dt_k13_finseq_1,dt_k1_finsub_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_scmfsa6c,dt_k1_scmfsa_2,dt_k1_sfmastr1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_scmfsa_2,dt_k21_scmfsa_2,dt_k2_scmfsa_2,dt_k2_sf_mastr,dt_k2_sfmastr2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k3_scmfsa_2,dt_k3_tarski,dt_k4_ami_1,dt_k4_card_3,dt_k4_numbers,dt_k4_scmfsa_2,dt_k4_subset_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_scmfsa_9,dt_k6_scmfsa6a,dt_k6_sfmastr1,dt_k7_ami_1,dt_k7_relat_1,dt_k8_scmfsa_2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_scmfsa_2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_scmfsa_2,dt_m2_subset_1,dt_u1_ami_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_scmfsa_2,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_scmfsa_2,existence_m2_subset_1,fc10_ami_1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc13_scmfsa6c,fc14_finset_1,fc15_scmfsa6c,fc16_sfmastr1,fc1_finset_1,fc1_fraenkel,fc1_int_1,fc1_numbers,fc1_ordinal2,fc1_scmfsa_2,fc1_sfmastr1,fc20_sfmastr1,fc2_ami_1,fc2_finset_1,fc2_fraenkel,fc2_setfam_1,fc2_sf_mastr,fc3_ami_1,fc3_scmfsa_2,fc3_setfam_1,fc3_sf_mastr,fc3_sfmastr1,fc3_xreal_0,fc4_ami_1,fc4_funct_1,fc4_numbers,fc4_scmfsa6c,fc4_scmfsa_2,fc4_setfam_1,fc4_sf_mastr,fc6_int_1,fc6_scmfsa6c,fc6_sf_mastr,fc7_xreal_0,fc8_xreal_0,fc9_finset_1,fc9_xreal_0,free_g1_ami_1,idempotence_k1_finsub_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc1_ami_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_scmfsa6c,rc1_setfam_1,rc1_sf_mastr,rc1_sfmastr1,rc1_xreal_0,rc2_ami_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_sfmastr1,rc2_xreal_0,rc3_ami_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc5_ami_1,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,redefinition_k11_ami_1,redefinition_k1_finsub_1,redefinition_k1_nat_1,redefinition_k1_sfmastr1,redefinition_k20_scmfsa_2,redefinition_k21_scmfsa_2,redefinition_k3_finseq_2,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e6_23__sfmastr2,spc0_boole,spc1_boole,spc1_numerals,t16_int_1,t16_sfmastr2,t17_sfmastr2,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t2_real,t2_subset,t37_scmfsa9a,t38_nat_1,t38_scmfsa6a,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]), [file(sfmastr2,t18_sfmastr2)]). fof(abstractness_v1_ami_1,axiom,( ! [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), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_1), []). fof(cc1_relset_1,axiom,( ! [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), []). fof(cc1_setfam_1,axiom,( ! [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), []). fof(cc1_sf_mastr,axiom,( ! [A,B] : ( v1_finset_1(A) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_finset_1(C) & v1_funct_2(C,A,B) ) ) ) ) ), file(sf_mastr,cc1_sf_mastr), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_int_1,axiom,( ! [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), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(commutativity_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B) ) ), file(finsub_1,k1_finsub_1), []). fof(commutativity_k1_nat_1,axiom,( ! [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), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [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), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(connectedness_r1_xreal_0,axiom,( ! [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), []). fof(d2_sfmastr2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( m1_scmfsa_2(C) => k2_sfmastr2(A,B,C) = k5_scmfsa_9(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B))),C),k1_scmfsa6c(A)),k6_scmfsa6a(B,k10_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B))),k4_scmfsa_2(0))),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B)))) ) ) ) ), file(sfmastr2,d2_sfmastr2), []). fof(d5_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_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), []). fof(dt_k10_scmfsa_2,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m2_subset_1(k10_scmfsa_2(A,B),k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k10_scmfsa_2), []). fof(dt_k11_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,k5_numbers) ) => m1_subset_1(k11_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k11_ami_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m1_subset_1(k1_finsub_1(A,B,C),A) ) ), file(finsub_1,k1_finsub_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_scmfsa6c,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => m1_subset_1(k1_scmfsa6c(A),k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ), file(scmfsa6c,k1_scmfsa6c), []). fof(dt_k1_scmfsa_2,axiom, ( v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & l1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,k1_scmfsa_2), []). fof(dt_k1_sfmastr1,axiom,( ! [A] : ( m1_scmfsa_2(A) => m1_subset_1(k1_sfmastr1(A),k1_zfmisc_1(k2_scmfsa_2)) ) ), file(sfmastr1,k1_sfmastr1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k20_scmfsa_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m1_scmfsa_2(B) ) => v1_int_1(k20_scmfsa_2(A,B)) ) ), file(scmfsa_2,k20_scmfsa_2), []). fof(dt_k21_scmfsa_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m2_scmfsa_2(B) ) => m2_finseq_1(k21_scmfsa_2(A,B),k4_numbers) ) ), file(scmfsa_2,k21_scmfsa_2), []). fof(dt_k2_scmfsa_2,axiom,( m1_subset_1(k2_scmfsa_2,k1_zfmisc_1(u1_struct_0(k1_scmfsa_2))) ), file(scmfsa_2,k2_scmfsa_2), []). fof(dt_k2_sf_mastr,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => m1_subset_1(k2_sf_mastr(A),k1_zfmisc_1(k2_scmfsa_2)) ) ), file(sf_mastr,k2_sf_mastr), []). fof(dt_k2_sfmastr2,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_scmfsa_2(C) ) => ( v1_funct_1(k2_sfmastr2(A,B,C)) & v1_funct_2(k2_sfmastr2(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m2_relset_1(k2_sfmastr2(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) ), file(sfmastr2,k2_sfmastr2), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_scmfsa_2,axiom,( m1_subset_1(k3_scmfsa_2,k1_zfmisc_1(u1_struct_0(k1_scmfsa_2))) ), file(scmfsa_2,k3_scmfsa_2), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k4_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k4_ami_1), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), []). fof(dt_k4_scmfsa_2,axiom,( ! [A] : ( v4_ordinal2(A) => m1_scmfsa_2(k4_scmfsa_2(A)) ) ), file(scmfsa_2,k4_scmfsa_2), []). fof(dt_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_scmfsa_9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & ~ v1_sf_mastr(C) & m1_scmfsa_2(C) ) => ( v1_funct_1(k5_scmfsa_9(A,B,C)) & v1_funct_2(k5_scmfsa_9(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m2_relset_1(k5_scmfsa_9(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) ), file(scmfsa_9,k5_scmfsa_9), []). fof(dt_k6_scmfsa6a,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_ami_3(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k6_scmfsa6a(A,B)) & m1_ami_1(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k6_scmfsa6a), []). fof(dt_k6_sfmastr1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) ) => m1_scmfsa_2(k6_sfmastr1(A,B)) ) ), file(sfmastr1,k6_sfmastr1), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k8_scmfsa_2,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m2_subset_1(k8_scmfsa_2(A,B),k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k8_scmfsa_2), []). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ), file(ami_1,m1_ami_1), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) ), file(scmfsa_2,m1_scmfsa_2), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). 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), []). fof(dt_m2_scmfsa_2,axiom,( ! [A] : ( m2_scmfsa_2(A) => m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) ), file(scmfsa_2,m2_scmfsa_2), []). 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), []). 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), []). fof(dt_u1_struct_0,axiom,( $true ), 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), []). 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), []). 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), []). 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), []). 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), []). fof(existence_l1_ami_1,axiom,( ! [A] : ? [B] : l1_ami_1(B,A) ), file(ami_1,l1_ami_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : m1_ami_1(C,A,B) ) ), file(ami_1,m1_ami_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_scmfsa_2,axiom,( ? [A] : m1_scmfsa_2(A) ), file(scmfsa_2,m1_scmfsa_2), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_scmfsa_2,axiom,( ? [A] : m2_scmfsa_2(A) ), file(scmfsa_2,m2_scmfsa_2), []). 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), []). fof(fc10_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k7_ami_1(A)) & v1_fraenkel(k7_ami_1(A)) ) ) ), file(ami_1,fc10_ami_1), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_scmfsa6c,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k8_scmfsa_2(A,B)) & v2_scmfsa6c(k8_scmfsa_2(A,B)) ) ) ), file(scmfsa6c,fc13_scmfsa6c), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc15_scmfsa6c,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k10_scmfsa_2(A,B)) & v2_scmfsa6c(k10_scmfsa_2(A,B)) ) ) ), file(scmfsa6c,fc15_scmfsa6c), []). fof(fc16_sfmastr1,axiom,( ! [A,B] : ( ( v1_sfmastr1(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & v1_scmfsa7b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k6_scmfsa6a(B,A)) & v1_funct_1(k6_scmfsa6a(B,A)) & v1_finset_1(k6_scmfsa6a(B,A)) & v1_ami_3(k6_scmfsa6a(B,A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k6_scmfsa6a(B,A)) & v1_scmfsa7b(k6_scmfsa6a(B,A)) ) ) ), file(sfmastr1,fc16_sfmastr1), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_int_1,axiom,( ! [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), []). fof(fc1_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_scmfsa_2,axiom, ( ~ v3_struct_0(k1_scmfsa_2) & v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & ~ v2_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,fc1_scmfsa_2), []). fof(fc1_sfmastr1,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k8_scmfsa_2(A,B)) & v2_scmfsa6c(k8_scmfsa_2(A,B)) & v1_sfmastr1(k8_scmfsa_2(A,B)) ) ) ), file(sfmastr1,fc1_sfmastr1), []). fof(fc20_sfmastr1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) ) => ~ v1_sf_mastr(k6_sfmastr1(A,B)) ) ), file(sfmastr1,fc20_sfmastr1), []). fof(fc2_ami_1,axiom,( ! [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), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_fraenkel,axiom,( ! [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), []). fof(fc2_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)) ) ) ), file(setfam_1,fc2_setfam_1), []). fof(fc2_sf_mastr,axiom,( ~ v1_xboole_0(k2_scmfsa_2) ), file(sf_mastr,fc2_sf_mastr), []). fof(fc3_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(ami_1,fc3_ami_1), []). fof(fc3_scmfsa_2,axiom, ( ~ v3_struct_0(k1_scmfsa_2) & v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & ~ v2_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v5_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v6_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v7_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v8_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v10_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,fc3_scmfsa_2), []). fof(fc3_setfam_1,axiom,( ! [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), []). fof(fc3_sf_mastr,axiom,( ~ v1_xboole_0(k3_scmfsa_2) ), file(sf_mastr,fc3_sf_mastr), []). fof(fc3_sfmastr1,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k10_scmfsa_2(A,B)) & v2_scmfsa6c(k10_scmfsa_2(A,B)) & v1_sfmastr1(k10_scmfsa_2(A,B)) ) ) ), file(sfmastr1,fc3_sfmastr1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_ami_1,axiom,( ! [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), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_numbers,axiom,( ~ v1_xboole_0(k4_numbers) ), file(numbers,fc4_numbers), []). fof(fc4_scmfsa6c,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => v1_scmfsa6c(k8_scmfsa_2(A,B)) ) ), file(scmfsa6c,fc4_scmfsa6c), []). fof(fc4_scmfsa_2,axiom, ( ~ v3_struct_0(k1_scmfsa_2) & v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & ~ v2_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v4_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v5_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v6_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v7_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v8_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v10_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,fc4_scmfsa_2), []). fof(fc4_setfam_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_1), []). fof(fc4_sf_mastr,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => v1_finset_1(k2_sf_mastr(A)) ) ), file(sf_mastr,fc4_sf_mastr), []). fof(fc6_int_1,axiom,( ! [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), []). fof(fc6_scmfsa6c,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => v1_scmfsa6c(k10_scmfsa_2(A,B)) ) ), file(scmfsa6c,fc6_scmfsa6c), []). fof(fc6_sf_mastr,axiom,( v1_sf_mastr(k4_scmfsa_2(0)) ), file(sf_mastr,fc6_sf_mastr), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(free_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))) ) => ! [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), []). fof(idempotence_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k1_finsub_1(A,B,B) = B ) ), file(finsub_1,k1_finsub_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), []). fof(rc1_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) ) ), file(ami_1,rc1_ami_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_int_1,axiom,( ? [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), []). fof(rc1_scmfsa6c,axiom,( ? [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_scmfsa6c(A) & v2_scmfsa6c(A) ) ), file(scmfsa6c,rc1_scmfsa6c), []). fof(rc1_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), []). fof(rc1_sf_mastr,axiom,( ? [A] : ( m1_scmfsa_2(A) & ~ v1_sf_mastr(A) ) ), file(sf_mastr,rc1_sf_mastr), []). fof(rc1_sfmastr1,axiom,( ? [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_scmfsa6c(A) & v1_sfmastr1(A) ) ), file(sfmastr1,rc1_sfmastr1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_sfmastr1,axiom,( ? [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_sfmastr1(A) ) ), file(sfmastr1,rc2_sfmastr1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) ) ) ), file(ami_1,rc3_ami_1), []). fof(rc3_finset_1,axiom,( ! [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), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finset_1,axiom,( ! [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), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) ) ), file(ami_1,rc5_ami_1), []). fof(rc6_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) ) ), file(ami_1,rc6_ami_1), []). fof(rc7_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) ) ), file(ami_1,rc7_ami_1), []). fof(rc8_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc8_ami_1), []). fof(rc9_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc9_ami_1), []). fof(redefinition_k11_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,k5_numbers) ) => k11_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k11_ami_1), []). fof(redefinition_k1_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k1_finsub_1(A,B,C) = k2_xboole_0(B,C) ) ), file(finsub_1,k1_finsub_1), []). fof(redefinition_k1_nat_1,axiom,( ! [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), []). fof(redefinition_k1_sfmastr1,axiom,( ! [A] : ( m1_scmfsa_2(A) => k1_sfmastr1(A) = k1_tarski(A) ) ), file(sfmastr1,k1_sfmastr1), []). fof(redefinition_k20_scmfsa_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m1_scmfsa_2(B) ) => k20_scmfsa_2(A,B) = k1_funct_1(A,B) ) ), file(scmfsa_2,k20_scmfsa_2), []). fof(redefinition_k21_scmfsa_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m2_scmfsa_2(B) ) => k21_scmfsa_2(A,B) = k1_funct_1(A,B) ) ), file(scmfsa_2,k21_scmfsa_2), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_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,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s1_nat_1__e6_23__sfmastr2,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m1_scmfsa_2(B) & v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & v1_scmfsa7b(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ( ( r1_xreal_0(k20_scmfsa_2(A,B),0) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),0),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = 0 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),0),k4_scmfsa_2(0)) = 1 ) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(k20_scmfsa_2(A,B),D) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = 0 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(0)) = 1 ) ) => ( r1_xreal_0(k20_scmfsa_2(A,B),k1_nat_1(D,1)) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,1)),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = 0 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,1)),k4_scmfsa_2(0)) = 1 ) ) ) ) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_xreal_0(k20_scmfsa_2(A,B),D) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = 0 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(0)) = 1 ) ) ) ) ) ), file(sfmastr2,s1_nat_1__e6_23__sfmastr2), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(t16_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( r1_xreal_0(0,A) => r2_hidden(A,k5_numbers) ) ) ), file(int_1,t16_int_1), []). fof(t16_sfmastr2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & v1_scmfsa7b(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( r1_sfmastr2(A,B,C) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_xreal_0(D,k20_scmfsa_2(A,B)) => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(0)) = 1 ) ) ) ) ) ) ), file(sfmastr2,t16_sfmastr2), []). fof(t17_sfmastr2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & v1_scmfsa7b(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( r1_sfmastr2(A,B,C) => ( ( k20_scmfsa_2(A,k4_scmfsa_2(0)) != 1 & v1_sf_mastr(B) ) | ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_xreal_0(D,k20_scmfsa_2(A,B)) => k2_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),D) = k20_scmfsa_2(A,B) ) ) ) ) ) ) ) ), file(sfmastr2,t17_sfmastr2), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [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), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t2_real,axiom,( ! [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), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t37_scmfsa9a,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [B] : ( ( ~ v1_sf_mastr(B) & m1_scmfsa_2(B) ) => ! [C] : ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),0) => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(D,1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ), file(scmfsa9a,t37_scmfsa9a), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t38_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ( ( ! [C] : ( m1_scmfsa_2(C) => k20_scmfsa_2(A,C) = k20_scmfsa_2(B,C) ) & ! [C] : ( m2_scmfsa_2(C) => k21_scmfsa_2(A,C) = k21_scmfsa_2(B,C) ) ) <=> k7_relat_1(A,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ), file(scmfsa6a,t38_scmfsa6a), []). fof(t3_real,axiom,( ! [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), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_real,axiom,( ! [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), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_real,axiom,( ! [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), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [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), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [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), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [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), []).