% Mizar problem: t37_sfmastr3,sfmastr3,2154,39 fof(t37_sfmastr3,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] : ( ( ~ v1_sf_mastr(B) & m1_scmfsa_2(B) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( m2_scmfsa_2(E) => ( ( r1_xreal_0(1,k20_scmfsa_2(A,C)) & r1_xreal_0(k20_scmfsa_2(A,C),k20_scmfsa_2(A,D)) & r1_xreal_0(k20_scmfsa_2(A,D),k3_finseq_1(k21_scmfsa_2(A,E))) & k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 ) => ( C = B | D = B | k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),B) = k1_sfmastr3(k21_scmfsa_2(A,E),k1_int_2(k20_scmfsa_2(A,C)),k1_int_2(k20_scmfsa_2(A,D))) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_funct_2,cc1_int_1,cc1_membered,cc1_relset_1,cc1_scmfsa6b,cc1_scmfsa7b,cc1_scmfsa_4,cc1_setfam_1,cc1_sf_mastr,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_int_1,cc2_membered,cc2_scmfsa6b,cc2_xreal_0,cc3_arytm_3,cc3_int_1,cc3_membered,cc3_scmfsa6b,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_membered,cc8_xreal_0,cc9_membered,commutativity_k1_finsub_1,commutativity_k1_nat_1,commutativity_k2_sfmastr1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_setwiseo,commutativity_k4_subset_1,connectedness_r1_xreal_0,d1_absvalue,d1_enumset1,d2_tarski,d2_xboole_0,d4_finseq_4,d5_real_1,d5_sf_mastr,d6_sfmastr3,d8_sfmastr3,d9_sfmastr3,dt_g1_ami_1,dt_k10_scmfsa_2,dt_k11_ami_1,dt_k11_scmfsa_2,dt_k12_scmfsa_2,dt_k13_ami_1,dt_k13_finseq_1,dt_k16_complex1,dt_k16_scmfsa_2,dt_k1_card_1,dt_k1_enumset1,dt_k1_finsub_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_int_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_scmfsa6c,dt_k1_scmfsa_2,dt_k1_sf_mastr,dt_k1_sfmastr3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_scmfsa_2,dt_k21_scmfsa_2,dt_k2_ami_1,dt_k2_funct_7,dt_k2_scmfsa6a,dt_k2_scmfsa6b,dt_k2_scmfsa_2,dt_k2_scmfsa_9,dt_k2_sf_mastr,dt_k2_sfmastr1,dt_k2_sfmastr3,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_real_1,dt_k3_scmfsa6b,dt_k3_scmfsa_2,dt_k3_setwiseo,dt_k3_sfmastr1,dt_k3_sfmastr3,dt_k3_tarski,dt_k4_ami_1,dt_k4_card_1,dt_k4_card_3,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_numbers,dt_k4_scmfsa6a,dt_k4_scmfsa_2,dt_k4_sfmastr3,dt_k4_subset_1,dt_k4_xcmplx_0,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_scmfsa6a,dt_k5_scmfsa8b,dt_k5_scmfsa_2,dt_k5_scmfsa_4,dt_k5_scmfsa_9,dt_k6_ami_1,dt_k6_scmfsa6a,dt_k6_sfmastr1,dt_k6_xcmplx_0,dt_k7_ami_1,dt_k7_relat_1,dt_k7_scmfsa6a,dt_k7_scmfsa_2,dt_k8_scmfsa_2,dt_k9_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_struct_0,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_struct_0,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_membered,fc12_xreal_0,fc13_membered,fc13_scmfsa6c,fc13_sfmastr1,fc13_xreal_0,fc14_finset_1,fc14_membered,fc14_scmfsa6c,fc14_sfmastr1,fc14_xreal_0,fc15_membered,fc15_scmfsa6c,fc15_sfmastr1,fc15_xreal_0,fc16_finseq_1,fc16_membered,fc16_scmfsa6c,fc16_sfmastr1,fc16_xreal_0,fc17_finseq_1,fc17_membered,fc17_scmfsa6c,fc17_xreal_0,fc18_membered,fc18_scmfsa6c,fc18_xreal_0,fc19_membered,fc19_xreal_0,fc1_fraenkel,fc1_funct_2,fc1_int_1,fc1_ordinal2,fc1_scmfsa_2,fc1_scmfsa_4,fc1_sfmastr1,fc1_xreal_0,fc20_membered,fc20_scmfsa6c,fc20_sfmastr1,fc20_xreal_0,fc21_membered,fc21_scmfsa6c,fc22_membered,fc22_scmfsa6c,fc23_membered,fc23_scmfsa6c,fc24_membered,fc24_scmfsa6c,fc25_membered,fc25_scmfsa6c,fc26_membered,fc2_ami_1,fc2_finseq_1,fc2_finset_1,fc2_fraenkel,fc2_funct_2,fc2_membered,fc2_scmfsa6b,fc2_scmfsa6c,fc2_sf_mastr,fc2_sfmastr1,fc2_sfmastr3,fc2_wsierp_1,fc3_ami_1,fc3_finset_1,fc3_int_1,fc3_scmfsa6b,fc3_scmfsa6c,fc3_scmfsa_2,fc3_setfam_1,fc3_sf_mastr,fc3_sfmastr1,fc3_sfmastr3,fc3_xreal_0,fc4_ami_1,fc4_funct_1,fc4_int_1,fc4_membered,fc4_scmfsa6c,fc4_scmfsa8b,fc4_scmfsa_2,fc4_scmfsa_9,fc4_setfam_1,fc4_sf_mastr,fc4_sfmastr1,fc4_sfmastr3,fc5_int_1,fc5_membered,fc5_scmfsa6c,fc5_sfmastr1,fc5_xreal_0,fc6_int_1,fc6_membered,fc6_scmfsa6c,fc6_scmfsa7b,fc6_scmfsa8a,fc6_sf_mastr,fc7_scmfsa6c,fc7_xreal_0,fc8_int_1,fc8_scmfsa6c,fc8_xreal_0,fc9_finseq_1,fc9_finset_1,fc9_int_1,fc9_scmfsa6c,fc9_sfmastr1,fc9_xreal_0,free_g1_ami_1,idempotence_k1_finsub_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,involutiveness_k4_xcmplx_0,projectivity_k16_complex1,projectivity_k1_int_2,rc1_ami_1,rc1_arytm_3,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_funct_2,rc1_int_1,rc1_membered,rc1_partfun1,rc1_pre_circ,rc1_scmfsa6b,rc1_scmfsa6c,rc1_scmfsa_4,rc1_setfam_1,rc1_sf_mastr,rc1_sfmastr1,rc1_xreal_0,rc2_ami_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_partfun1,rc2_scmfsa6b,rc2_scmfsa7b,rc2_scmfsa_4,rc2_sfmastr1,rc2_xreal_0,rc3_ami_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_xreal_0,rc5_ami_1,rc6_ami_1,rc6_finseq_1,rc7_ami_1,rc7_finseq_1,rc8_ami_1,rc8_finseq_1,rc9_ami_1,redefinition_k11_ami_1,redefinition_k13_ami_1,redefinition_k1_finsub_1,redefinition_k1_int_2,redefinition_k1_nat_1,redefinition_k20_scmfsa_2,redefinition_k21_scmfsa_2,redefinition_k2_scmfsa6b,redefinition_k2_sfmastr1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_real_1,redefinition_k3_setwiseo,redefinition_k3_sfmastr1,redefinition_k4_card_1,redefinition_k4_finseq_1,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_m1_struct_0,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e43_51__sfmastr3,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc5_boole,spc5_numerals,t10_scmfsa6c,t10_sfmastr3,t11_sfmastr3,t11_xreal_1,t12_sfmastr1,t13_sfmastr1,t13_sfmastr3,t15_sfmastr1,t16_int_1,t16_sfmastr3,t17_sfmastr3,t18_sf_mastr,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t20_sfmastr3,t21_sfmastr1,t21_sfmastr3,t21_xreal_1,t22_sfmastr1,t23_sfmastr3,t25_sfmastr3,t27_finseq_3,t27_sfmastr3,t2_real,t2_subset,t2_xreal_1,t31_sf_mastr,t31_sfmastr3,t31_xreal_1,t32_sf_mastr,t32_sfmastr3,t35_scmfsa6b,t37_nat_1,t38_nat_1,t38_scmfsa6a,t3_real,t3_scmfsa6c,t3_sfmastr3,t3_subset,t43_scmfsa8b,t4_arithm,t4_real,t4_sfmastr3,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t6_scmfsa6c,t7_boole,t7_real,t7_sfmastr2,t80_scmfsa8c,t89_scmfsa_2,t8_boole,t8_real,t8_sfmastr1,t8_sfmastr3,t8_xreal_1,t90_scmfsa_2,t98_scmfsa_2,t9_scmfsa6c,t9_sfmastr1,t9_sfmastr3,t9_xreal_1]), [file(sfmastr3,t37_sfmastr3)]). 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(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [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), []). fof(cc13_membered,axiom,( ! [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), []). fof(cc14_membered,axiom,( ! [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), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [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), []). fof(cc19_membered,axiom,( ! [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), []). fof(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). 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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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_scmfsa6b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) ) ) ) ), file(scmfsa6b,cc1_scmfsa6b), []). fof(cc1_scmfsa7b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v1_scmfsa7b(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v3_scmfsa6b(A) ) ) ) ), file(scmfsa7b,cc1_scmfsa7b), []). fof(cc1_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) ) ) ), file(scmfsa_4,cc1_scmfsa_4), []). 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(cc20_membered,axiom,( ! [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), []). fof(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_scmfsa6b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v3_scmfsa6b(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) ) ) ) ), file(scmfsa6b,cc2_scmfsa6b), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_scmfsa6b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) ) ) ) ), file(scmfsa6b,cc3_scmfsa6b), []). 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_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). 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_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). 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_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). 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_membered,axiom,( ! [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), []). 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(cc9_membered,axiom,( ! [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), []). 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_sfmastr1,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => k2_sfmastr1(A,B) = k2_sfmastr1(B,A) ) ), file(sfmastr1,k2_sfmastr1), []). 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_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(commutativity_k3_setwiseo,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k3_setwiseo(A,B,C) = k3_setwiseo(A,C,B) ) ), file(setwiseo,k3_setwiseo), []). 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(d1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xreal_0(0,A) => k16_complex1(A) = A ) & ( ~ r1_xreal_0(0,A) => k16_complex1(A) = k4_xcmplx_0(A) ) ) ) ), file(absvalue,d1_absvalue), []). fof(d1_enumset1,axiom,( ! [A,B,C,D] : ( D = k1_enumset1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ~ ( E != A & E != B & E != C ) ) ) ), file(enumset1,d1_enumset1), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d4_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). 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(d5_sf_mastr,axiom,( ! [A] : ( m1_scmfsa_2(A) => ( v1_sf_mastr(A) <=> A = k4_scmfsa_2(0) ) ) ), file(sf_mastr,d5_sf_mastr), []). fof(d6_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => k2_sfmastr3(A,B,C,D,E) = k5_scmfsa_9(k2_scmfsa6b(k2_scmfsa6b(E,k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(E,C),k20_scmfsa_2(E,B)),1)),A,k20_scmfsa_2(E,B)),k6_scmfsa6a(k6_scmfsa6a(D,k9_scmfsa_2(A,k4_scmfsa_2(0))),k10_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(0))),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D)))) ) ) ) ) ) ), file(sfmastr3,d6_sfmastr3), []). fof(d8_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k3_sfmastr3(A,B,C,D) = k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),C),k10_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),B)),k9_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(0))),k8_scmfsa_2(A,B)),k2_scmfsa_9(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k6_scmfsa6a(k6_scmfsa6a(D,k9_scmfsa_2(A,k4_scmfsa_2(0))),k10_scmfsa_2(k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(0))))) ) ) ) ) ), file(sfmastr3,d8_sfmastr3), []). fof(d9_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m2_scmfsa_2(D) => k4_sfmastr3(A,B,C,D) = k5_scmfsa6a(k8_scmfsa_2(C,A),k3_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(A,B,C)),A,B,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(A,B,C)),k6_sfmastr1(3,k3_sfmastr1(A,B,C)),D),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(A,B,C)),C,D)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(A,B,C)),k6_sfmastr1(1,k3_sfmastr1(A,B,C)),k2_scmfsa6a(k8_scmfsa_2(C,k6_sfmastr1(3,k3_sfmastr1(A,B,C)))),k5_scmfsa_4)))) ) ) ) ) ), file(sfmastr3,d9_sfmastr3), []). 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_k11_scmfsa_2,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m2_subset_1(k11_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,k11_scmfsa_2), []). fof(dt_k12_scmfsa_2,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m2_subset_1(k12_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,k12_scmfsa_2), []). fof(dt_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => m2_subset_1(k13_ami_1(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k13_ami_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). fof(dt_k16_scmfsa_2,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m2_scmfsa_2(C) ) => m2_subset_1(k16_scmfsa_2(A,B,C),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,k16_scmfsa_2), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_enumset1,axiom,( $true ), file(enumset1,k1_enumset1), []). 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_int_2,axiom,( ! [A] : ( v1_int_1(A) => m2_subset_1(k1_int_2(A),k1_numbers,k5_numbers) ) ), file(int_2,k1_int_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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). 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_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => m1_subset_1(k1_sf_mastr(A),k5_finsub_1(k2_scmfsa_2)) ) ), file(sf_mastr,k1_sf_mastr), []). fof(dt_k1_sfmastr3,axiom,( ! [A,B,C] : ( ( m1_finseq_1(A,k4_numbers) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,k5_numbers) ) => m2_subset_1(k1_sfmastr3(A,B,C),k1_numbers,k5_numbers) ) ), file(sfmastr3,k1_sfmastr3), []). 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_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => m1_subset_1(k2_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,k2_ami_1), []). fof(dt_k2_funct_7,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) ) ) ), file(funct_7,k2_funct_7), []). fof(dt_k2_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & m1_ami_1(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k2_scmfsa6a), []). fof(dt_k2_scmfsa6b,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_int_1(C) ) => m1_subset_1(k2_scmfsa6b(A,B,C),k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ), file(scmfsa6b,k2_scmfsa6b), []). 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_scmfsa_9,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & 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_ami_3(k2_scmfsa_9(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa_9(A,B)) & m1_ami_1(k2_scmfsa_9(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa_9,k2_scmfsa_9), []). 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_sfmastr1,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m1_subset_1(k2_sfmastr1(A,B),k1_zfmisc_1(k2_scmfsa_2)) ) ), file(sfmastr1,k2_sfmastr1), []). fof(dt_k2_sfmastr3,axiom,( ! [A,B,C,D,E] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m1_scmfsa_2(C) & v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) => ( v1_funct_1(k2_sfmastr3(A,B,C,D,E)) & v1_funct_2(k2_sfmastr3(A,B,C,D,E),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & m2_relset_1(k2_sfmastr3(A,B,C,D,E),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) ), file(sfmastr3,k2_sfmastr3), []). 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_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k3_scmfsa6b,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,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) => m1_subset_1(k3_scmfsa6b(A,B),k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ), file(scmfsa6b,k3_scmfsa6b), []). 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_setwiseo,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)) ) ), file(setwiseo,k3_setwiseo), []). fof(dt_k3_sfmastr1,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m1_scmfsa_2(C) ) => m1_subset_1(k3_sfmastr1(A,B,C),k1_zfmisc_1(k2_scmfsa_2)) ) ), file(sfmastr1,k3_sfmastr1), []). fof(dt_k3_sfmastr3,axiom,( ! [A,B,C,D] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m1_scmfsa_2(C) & v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k3_sfmastr3(A,B,C,D)) & m1_ami_1(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(sfmastr3,k3_sfmastr3), []). 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_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), []). fof(dt_k4_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) & 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_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & m1_ami_1(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k4_scmfsa6a), []). 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_sfmastr3,axiom,( ! [A,B,C,D] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m1_scmfsa_2(C) & m2_scmfsa_2(D) ) => ( v1_ami_3(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_sfmastr3(A,B,C,D)) & m1_ami_1(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(sfmastr3,k4_sfmastr3), []). 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_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_scmfsa6a,axiom,( ! [A,B] : ( ( 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) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & m1_ami_1(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k5_scmfsa6a), []). fof(dt_k5_scmfsa8b,axiom,( ! [A,B,C,D] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & 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) & v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k5_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa8b(A,B,C,D)) & m1_ami_1(k5_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa8b,k5_scmfsa8b), []). fof(dt_k5_scmfsa_2,axiom,( ! [A] : ( v4_ordinal2(A) => m1_struct_0(k5_scmfsa_2(A),k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k5_scmfsa_2), []). fof(dt_k5_scmfsa_4,axiom,( m1_ami_1(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ), file(scmfsa_4,k5_scmfsa_4), []). 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_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_struct_0(k6_ami_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(ami_1,k6_ami_1), []). 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_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). 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_k7_scmfsa6a,axiom,( ! [A,B] : ( ( m1_subset_1(A,u4_ami_1(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(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k7_scmfsa6a(A,B)) & m1_ami_1(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k7_scmfsa6a), []). fof(dt_k7_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => m1_struct_0(k7_scmfsa_2(A),k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k7_scmfsa_2), []). 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_k9_scmfsa_2,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m2_subset_1(k9_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,k9_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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). 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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). 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_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). 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_membered,axiom,( ! [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), []). 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(fc13_sfmastr1,axiom,( ! [A] : ( ( v1_sfmastr1(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_relat_1(k2_scmfsa6a(A)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & v1_scmfsa7b(k2_scmfsa6a(A)) ) ) ), file(sfmastr1,fc13_sfmastr1), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). 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(fc14_membered,axiom,( ! [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), []). fof(fc14_scmfsa6c,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k9_scmfsa_2(A,B)) & v2_scmfsa6c(k9_scmfsa_2(A,B)) ) ) ), file(scmfsa6c,fc14_scmfsa6c), []). fof(fc14_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_sfmastr1(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_relat_1(k7_scmfsa6a(A,B)) & v1_funct_1(k7_scmfsa6a(A,B)) & v1_finset_1(k7_scmfsa6a(A,B)) & v1_ami_3(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k7_scmfsa6a(A,B)) & v1_scmfsa7b(k7_scmfsa6a(A,B)) ) ) ), file(sfmastr1,fc14_sfmastr1), []). fof(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). fof(fc15_membered,axiom,( ! [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), []). 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(fc15_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(k5_scmfsa6a(A,B)) & v1_funct_1(k5_scmfsa6a(A,B)) & v1_finset_1(k5_scmfsa6a(A,B)) & v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & v1_scmfsa7b(k5_scmfsa6a(A,B)) ) ) ), file(sfmastr1,fc15_sfmastr1), []). fof(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc16_membered,axiom,( ! [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), []). fof(fc16_scmfsa6c,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k11_scmfsa_2(A,B)) & v2_scmfsa6c(k11_scmfsa_2(A,B)) ) ) ), file(scmfsa6c,fc16_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(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc17_membered,axiom,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_membered(k1_enumset1(A,B,C)) ) ), file(membered,fc17_membered), []). fof(fc17_scmfsa6c,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & ~ v1_sf_mastr(B) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k12_scmfsa_2(A,B)) & v2_scmfsa6c(k12_scmfsa_2(A,B)) ) ) ), file(scmfsa6c,fc17_scmfsa6c), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_membered,axiom,( ! [A,B,C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc18_membered), []). fof(fc18_scmfsa6c,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & m2_scmfsa_2(B) & ~ v1_sf_mastr(C) & m1_scmfsa_2(C) ) => ( v1_scmfsa6c(k16_scmfsa_2(C,A,B)) & v2_scmfsa6c(k16_scmfsa_2(C,A,B)) ) ) ), file(scmfsa6c,fc18_scmfsa6c), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_membered,axiom,( ! [A,B,C] : ( ( v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc19_membered), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_2), []). 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_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_scmfsa_4,axiom, ( ~ v1_xboole_0(k5_scmfsa_4) & v1_relat_1(k5_scmfsa_4) & v1_funct_1(k5_scmfsa_4) & v1_finset_1(k5_scmfsa_4) & v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa_4) ), file(scmfsa_4,fc1_scmfsa_4), []). 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(fc1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). fof(fc20_membered,axiom,( ! [A,B,C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc20_membered), []). fof(fc20_scmfsa6c,axiom,( ! [A,B] : ( ( v1_scmfsa6c(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) & v2_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ~ v1_xboole_0(k5_scmfsa6a(A,B)) & v1_relat_1(k5_scmfsa6a(A,B)) & v1_funct_1(k5_scmfsa6a(A,B)) & v1_finset_1(k5_scmfsa6a(A,B)) & v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & v1_scmfsa6b(k5_scmfsa6a(A,B)) & v2_scmfsa6b(k5_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc20_scmfsa6c), []). 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(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(fc21_membered,axiom,( ! [A,B,C] : ( ( v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc21_membered), []). fof(fc21_scmfsa6c,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa6c(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k6_scmfsa6a(A,B)) & v1_relat_1(k6_scmfsa6a(A,B)) & v1_funct_1(k6_scmfsa6a(A,B)) & v1_finset_1(k6_scmfsa6a(A,B)) & 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)) & v1_scmfsa6b(k6_scmfsa6a(A,B)) & v2_scmfsa6b(k6_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc21_scmfsa6c), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc22_scmfsa6c,axiom,( ! [A,B] : ( ( v1_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_scmfsa6c(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k7_scmfsa6a(A,B)) & v1_relat_1(k7_scmfsa6a(A,B)) & v1_funct_1(k7_scmfsa6a(A,B)) & v1_finset_1(k7_scmfsa6a(A,B)) & v1_ami_3(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k7_scmfsa6a(A,B)) & v1_scmfsa6b(k7_scmfsa6a(A,B)) & v2_scmfsa6b(k7_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc22_scmfsa6c), []). fof(fc23_membered,axiom,( ! [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), []). fof(fc23_scmfsa6c,axiom,( ! [A,B] : ( ( v2_scmfsa6c(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) & v3_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k5_scmfsa6a(A,B)) & v1_funct_1(k5_scmfsa6a(A,B)) & v1_finset_1(k5_scmfsa6a(A,B)) & v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & v1_scmfsa6b(k5_scmfsa6a(A,B)) & v3_scmfsa6b(k5_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc23_scmfsa6c), []). fof(fc24_membered,axiom,( ! [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), []). fof(fc24_scmfsa6c,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v3_scmfsa6b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v2_scmfsa6c(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_relat_1(k6_scmfsa6a(A,B)) & v1_funct_1(k6_scmfsa6a(A,B)) & v1_finset_1(k6_scmfsa6a(A,B)) & 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)) & v1_scmfsa6b(k6_scmfsa6a(A,B)) & v3_scmfsa6b(k6_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc24_scmfsa6c), []). fof(fc25_membered,axiom,( ! [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), []). fof(fc25_scmfsa6c,axiom,( ! [A,B] : ( ( v2_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v2_scmfsa6c(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_relat_1(k7_scmfsa6a(A,B)) & v1_funct_1(k7_scmfsa6a(A,B)) & v1_finset_1(k7_scmfsa6a(A,B)) & v1_ami_3(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k7_scmfsa6a(A,B)) & v1_scmfsa6b(k7_scmfsa6a(A,B)) & v3_scmfsa6b(k7_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc25_scmfsa6c), []). fof(fc26_membered,axiom,( ! [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), []). 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_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). 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_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_scmfsa6b,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) & m1_ami_1(A,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) & v2_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ~ v1_xboole_0(k4_scmfsa6a(A,B)) & v1_relat_1(k4_scmfsa6a(A,B)) & v1_funct_1(k4_scmfsa6a(A,B)) & v1_finset_1(k4_scmfsa6a(A,B)) & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & v1_scmfsa6b(k4_scmfsa6a(A,B)) & v2_scmfsa6b(k4_scmfsa6a(A,B)) ) ) ), file(scmfsa6b,fc2_scmfsa6b), []). fof(fc2_scmfsa6c,axiom,( ! [A] : ( ( v1_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k2_scmfsa6a(A)) & v1_relat_1(k2_scmfsa6a(A)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & v1_scmfsa6b(k2_scmfsa6a(A)) & v2_scmfsa6b(k2_scmfsa6a(A)) ) ) ), file(scmfsa6c,fc2_scmfsa6c), []). fof(fc2_sf_mastr,axiom,( ~ v1_xboole_0(k2_scmfsa_2) ), file(sf_mastr,fc2_sf_mastr), []). fof(fc2_sfmastr1,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k9_scmfsa_2(A,B)) & v2_scmfsa6c(k9_scmfsa_2(A,B)) & v1_sfmastr1(k9_scmfsa_2(A,B)) ) ) ), file(sfmastr1,fc2_sfmastr1), []). fof(fc2_sfmastr3,axiom,( ! [A,B,C,D] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & 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) & v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & v1_scmfsa7b(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k5_scmfsa8b(A,B,C,D)) & v1_funct_1(k5_scmfsa8b(A,B,C,D)) & v1_finset_1(k5_scmfsa8b(A,B,C,D)) & v1_ami_3(k5_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa8b(A,B,C,D)) & v1_scmfsa7b(k5_scmfsa8b(A,B,C,D)) ) ) ), file(sfmastr3,fc2_sfmastr3), []). fof(fc2_wsierp_1,axiom,( ! [A,B] : ( m1_finseq_1(A,k4_numbers) => ( v1_xcmplx_0(k1_funct_1(A,B)) & v1_xreal_0(k1_funct_1(A,B)) & v1_int_1(k1_funct_1(A,B)) & v1_rat_1(k1_funct_1(A,B)) ) ) ), file(wsierp_1,fc2_wsierp_1), []). 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_finset_1,axiom,( ! [A,B,C] : v1_finset_1(k1_enumset1(A,B,C)) ), file(finset_1,fc3_finset_1), []). fof(fc3_int_1,axiom,( ! [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), []). fof(fc3_scmfsa6b,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v3_scmfsa6b(A) & m1_ami_1(A,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) & v3_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k4_scmfsa6a(A,B)) & v1_funct_1(k4_scmfsa6a(A,B)) & v1_finset_1(k4_scmfsa6a(A,B)) & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & v1_scmfsa6b(k4_scmfsa6a(A,B)) & v3_scmfsa6b(k4_scmfsa6a(A,B)) ) ) ), file(scmfsa6b,fc3_scmfsa6b), []). fof(fc3_scmfsa6c,axiom,( ! [A] : ( ( v2_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k2_scmfsa6a(A)) & v1_relat_1(k2_scmfsa6a(A)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & v1_scmfsa6b(k2_scmfsa6a(A)) & v3_scmfsa6b(k2_scmfsa6a(A)) ) ) ), file(scmfsa6c,fc3_scmfsa6c), []). 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_sfmastr3,axiom,( ! [A,B,C,D] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) & m1_scmfsa_2(C) & v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & v1_scmfsa7b(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k3_sfmastr3(A,B,C,D)) & v1_funct_1(k3_sfmastr3(A,B,C,D)) & v1_finset_1(k3_sfmastr3(A,B,C,D)) & v1_ami_3(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k3_sfmastr3(A,B,C,D)) & v1_scmfsa7b(k3_sfmastr3(A,B,C,D)) ) ) ), file(sfmastr3,fc3_sfmastr3), []). 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_int_1,axiom,( ! [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), []). fof(fc4_membered,axiom, ( ~ 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), []). 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_scmfsa8b,axiom,( ! [A,B,C,D] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) & m1_ami_1(A,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) & v2_scmfsa6b(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_sf_mastr(D) & m1_scmfsa_2(D) ) => ( ~ v1_xboole_0(k5_scmfsa8b(C,D,A,B)) & v1_relat_1(k5_scmfsa8b(C,D,A,B)) & v1_funct_1(k5_scmfsa8b(C,D,A,B)) & v1_finset_1(k5_scmfsa8b(C,D,A,B)) & v1_ami_3(k5_scmfsa8b(C,D,A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa8b(C,D,A,B)) & v1_scmfsa6b(k5_scmfsa8b(C,D,A,B)) & v2_scmfsa6b(k5_scmfsa8b(C,D,A,B)) ) ) ), file(scmfsa8b,fc4_scmfsa8b), []). 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_scmfsa_9,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa7b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_scmfsa_2(B) ) => ( v1_relat_1(k2_scmfsa_9(B,A)) & v1_funct_1(k2_scmfsa_9(B,A)) & v1_finset_1(k2_scmfsa_9(B,A)) & v1_ami_3(k2_scmfsa_9(B,A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa_9(B,A)) & v1_scmfsa7b(k2_scmfsa_9(B,A)) ) ) ), file(scmfsa_9,fc4_scmfsa_9), []). 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(fc4_sfmastr1,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k11_scmfsa_2(A,B)) & v2_scmfsa6c(k11_scmfsa_2(A,B)) & v1_sfmastr1(k11_scmfsa_2(A,B)) ) ) ), file(sfmastr1,fc4_sfmastr1), []). fof(fc4_sfmastr3,axiom,( ! [A,B,C,D] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & ~ v1_sf_mastr(C) & m1_scmfsa_2(C) & m2_scmfsa_2(D) ) => ( v1_relat_1(k4_sfmastr3(A,B,C,D)) & v1_funct_1(k4_sfmastr3(A,B,C,D)) & v1_finset_1(k4_sfmastr3(A,B,C,D)) & v1_ami_3(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_sfmastr3(A,B,C,D)) & v1_scmfsa7b(k4_sfmastr3(A,B,C,D)) ) ) ), file(sfmastr3,fc4_sfmastr3), []). fof(fc5_int_1,axiom,( ! [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), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_scmfsa6c,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => v1_scmfsa6c(k9_scmfsa_2(A,B)) ) ), file(scmfsa6c,fc5_scmfsa6c), []). fof(fc5_sfmastr1,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & ~ v1_sf_mastr(B) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k12_scmfsa_2(A,B)) & v2_scmfsa6c(k12_scmfsa_2(A,B)) & v1_sfmastr1(k12_scmfsa_2(A,B)) ) ) ), file(sfmastr1,fc5_sfmastr1), []). fof(fc5_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). 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_membered,axiom, ( 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), []). 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_scmfsa7b,axiom, ( v1_relat_1(k5_scmfsa_4) & v1_funct_1(k5_scmfsa_4) & ~ v1_xboole_0(k5_scmfsa_4) & v1_finset_1(k5_scmfsa_4) & v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa_4) & v1_scmfsa6b(k5_scmfsa_4) & v2_scmfsa6b(k5_scmfsa_4) & v1_scmfsa7b(k5_scmfsa_4) ), file(scmfsa7b,fc6_scmfsa7b), []). fof(fc6_scmfsa8a,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa7b(A) & m1_ami_1(A,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(k4_scmfsa6a(A,B)) & v1_funct_1(k4_scmfsa6a(A,B)) & v1_finset_1(k4_scmfsa6a(A,B)) & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & v1_scmfsa7b(k4_scmfsa6a(A,B)) ) ) ), file(scmfsa8a,fc6_scmfsa8a), []). fof(fc6_sf_mastr,axiom,( v1_sf_mastr(k4_scmfsa_2(0)) ), file(sf_mastr,fc6_sf_mastr), []). fof(fc7_scmfsa6c,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => v1_scmfsa6c(k11_scmfsa_2(A,B)) ) ), file(scmfsa6c,fc7_scmfsa6c), []). 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_int_1,axiom,( ! [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), []). fof(fc8_scmfsa6c,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => v1_scmfsa6c(k12_scmfsa_2(A,B)) ) ), file(scmfsa6c,fc8_scmfsa6c), []). 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_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). 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_int_1,axiom,( ! [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), []). fof(fc9_scmfsa6c,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m2_scmfsa_2(C) ) => v1_scmfsa6c(k16_scmfsa_2(B,A,C)) ) ), file(scmfsa6c,fc9_scmfsa6c), []). fof(fc9_sfmastr1,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & m2_scmfsa_2(B) & ~ v1_sf_mastr(C) & m1_scmfsa_2(C) ) => ( v1_scmfsa6c(k16_scmfsa_2(C,A,B)) & v2_scmfsa6c(k16_scmfsa_2(C,A,B)) & v1_sfmastr1(k16_scmfsa_2(C,A,B)) ) ) ), file(sfmastr1,fc9_sfmastr1), []). 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(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k1_int_2,axiom,( ! [A] : ( v1_int_1(A) => k1_int_2(k1_int_2(A)) = k1_int_2(A) ) ), file(int_2,k1_int_2), []). 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_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_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_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). 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_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_scmfsa6b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) ) ), file(scmfsa6b,rc1_scmfsa6b), []). 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_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_ami_3(C,A,B) ) ) ), file(scmfsa_4,rc1_scmfsa_4), []). 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_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). 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_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_scmfsa6b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v2_scmfsa6b(A) & v3_scmfsa6b(A) ) ), file(scmfsa6b,rc2_scmfsa6b), []). fof(rc2_scmfsa7b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v2_scmfsa6b(A) & v1_scmfsa7b(A) ) ), file(scmfsa7b,rc2_scmfsa7b), []). fof(rc2_scmfsa_4,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) ) ), file(scmfsa_4,rc2_scmfsa_4), []). 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_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). 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_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_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(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). 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(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_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(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). 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_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => k13_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k13_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_int_2,axiom,( ! [A] : ( v1_int_1(A) => k1_int_2(A) = k16_complex1(A) ) ), file(int_2,k1_int_2), []). 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_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_k2_scmfsa6b,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_int_1(C) ) => k2_scmfsa6b(A,B,C) = k2_funct_7(A,B,C) ) ), file(scmfsa6b,k2_scmfsa6b), []). fof(redefinition_k2_sfmastr1,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => k2_sfmastr1(A,B) = k2_tarski(A,B) ) ), file(sfmastr1,k2_sfmastr1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). fof(redefinition_k3_setwiseo,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k3_setwiseo(A,B,C) = k2_tarski(B,C) ) ), file(setwiseo,k3_setwiseo), []). fof(redefinition_k3_sfmastr1,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) & m1_scmfsa_2(C) ) => k3_sfmastr1(A,B,C) = k1_enumset1(A,B,C) ) ), file(sfmastr1,k3_sfmastr1), []). fof(redefinition_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). 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_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). 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__e43_51__sfmastr3,axiom,( ! [A,B,C,D,E,F,G] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) & ~ v1_sf_mastr(B) & m1_scmfsa_2(B) & m1_scmfsa_2(C) & m1_scmfsa_2(D) & m2_scmfsa_2(E) & m2_subset_1(F,k1_numbers,k5_numbers) & m2_subset_1(G,k1_numbers,k5_numbers) ) => ( ( ( r1_xreal_0(0,k1_nat_1(G,1)) => ( r1_xreal_0(0,0) | ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),0),k4_scmfsa_2(0)) = 1 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),0),k6_sfmastr1(3,k3_sfmastr1(C,D,B))) = k2_xcmplx_0(0,k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),C)) & k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),0),E) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),E) & ? [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) & H = k5_real_1(k1_nat_1(0,F),1) & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),0),B) = k1_sfmastr3(k21_scmfsa_2(A,E),F,H) ) ) ) ) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ( ( r1_xreal_0(I,k1_nat_1(G,1)) => ( r1_xreal_0(I,0) | ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),k4_scmfsa_2(0)) = 1 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),k6_sfmastr1(3,k3_sfmastr1(C,D,B))) = k2_xcmplx_0(I,k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),C)) & k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),E) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),E) & ? [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) & J = k5_real_1(k1_nat_1(I,F),1) & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),B) = k1_sfmastr3(k21_scmfsa_2(A,E),F,J) ) ) ) ) => ( r1_xreal_0(k1_nat_1(I,1),k1_nat_1(G,1)) => ( r1_xreal_0(k1_nat_1(I,1),0) | ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),k1_nat_1(I,1)),k4_scmfsa_2(0)) = 1 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),k1_nat_1(I,1)),k6_sfmastr1(3,k3_sfmastr1(C,D,B))) = k2_xcmplx_0(k1_nat_1(I,1),k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),C)) & k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),k1_nat_1(I,1)),E) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),E) & ? [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) & K = k5_real_1(k1_nat_1(k1_nat_1(I,1),F),1) & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),k1_nat_1(I,1)),B) = k1_sfmastr3(k21_scmfsa_2(A,E),F,K) ) ) ) ) ) ) ) => ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ( r1_xreal_0(I,k1_nat_1(G,1)) => ( r1_xreal_0(I,0) | ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),k4_scmfsa_2(0)) = 1 & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),k6_sfmastr1(3,k3_sfmastr1(C,D,B))) = k2_xcmplx_0(I,k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),C)) & k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),E) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A)),E) & ? [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) & L = k5_real_1(k1_nat_1(I,F),1) & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(k6_sfmastr1(3,k3_sfmastr1(C,D,B)),C,D,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k6_sfmastr1(3,k3_sfmastr1(C,D,B)),E),k16_scmfsa_2(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),B,E)),k5_scmfsa8b(k6_sfmastr1(2,k3_sfmastr1(C,D,B)),k6_sfmastr1(1,k3_sfmastr1(C,D,B)),k2_scmfsa6a(k8_scmfsa_2(B,k6_sfmastr1(3,k3_sfmastr1(C,D,B)))),k5_scmfsa_4)),k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(B,C),k1_scmfsa6c(A))),I),B) = k1_sfmastr3(k21_scmfsa_2(A,E),F,L) ) ) ) ) ) ) ) ), file(sfmastr3,s1_nat_1__e43_51__sfmastr3), []). 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(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc5_boole,axiom,( ~ v1_xboole_0(5) ), file(boole,spc5_boole), []). fof(spc5_numerals,axiom, ( v2_xreal_0(5) & m1_subset_1(5,k5_numbers) ), file(numerals,spc5_numerals), []). fof(t10_scmfsa6c,axiom,( ! [A] : ( m2_scmfsa_2(A) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [C] : ( ( v1_scmfsa6c(C) & v2_scmfsa6c(C) & m2_subset_1(C,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)) ) => ! [D] : ( ( v1_scmfsa6c(D) & m2_subset_1(D,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)) ) => k21_scmfsa_2(k3_scmfsa6b(k7_scmfsa6a(C,D),B),A) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(B))),A) ) ) ) ) ), file(scmfsa6c,t10_scmfsa6c), []). fof(t10_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_scmfsa_2(C) => ( A != B => r1_scmfsa7b(k8_scmfsa_2(C,B),A) ) ) ) ) ), file(sfmastr3,t10_sfmastr3), []). fof(t11_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m2_scmfsa_2(D) => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,D),A),B) = k4_finseq_4(k5_numbers,k4_numbers,k21_scmfsa_2(A,D),k1_int_2(k20_scmfsa_2(A,C))) ) ) ) ) ), file(sfmastr3,t11_sfmastr3), []). fof(t11_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,B) <=> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t11_xreal_1), []). fof(t12_sfmastr1,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) & v1_scmfsa7b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( ( v1_scmfsa6c(C) & m2_subset_1(C,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)) ) => ! [D] : ( m1_scmfsa_2(D) => ( ( v2_scmfsa6b(B) | ( r6_scmfsa7b(B,k1_scmfsa6c(A)) & r5_scmfsa7b(B,k1_scmfsa6c(A)) ) ) => k20_scmfsa_2(k3_scmfsa6b(k6_scmfsa6a(B,C),A),D) = k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6b(B,A)),D) ) ) ) ) ) ), file(sfmastr1,t12_sfmastr1), []). fof(t13_sfmastr1,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) & v1_scmfsa7b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( ( v1_scmfsa6c(C) & m2_subset_1(C,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)) ) => ! [D] : ( m2_scmfsa_2(D) => ( ( v2_scmfsa6b(B) | ( r6_scmfsa7b(B,k1_scmfsa6c(A)) & r5_scmfsa7b(B,k1_scmfsa6c(A)) ) ) => k21_scmfsa_2(k3_scmfsa6b(k6_scmfsa6a(B,C),A),D) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6b(B,A)),D) ) ) ) ) ) ), file(sfmastr1,t13_sfmastr1), []). fof(t13_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [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] : ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(D) & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k2_sf_mastr(k5_scmfsa8b(A,B,C,D)) = k4_subset_1(k2_scmfsa_2,k4_subset_1(k2_scmfsa_2,k2_sfmastr1(A,B),k2_sf_mastr(C)),k2_sf_mastr(D)) ) ) ) ) ), file(sfmastr3,t13_sfmastr3), []). fof(t15_sfmastr1,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] : ( ( v1_scmfsa6c(C) & v1_sfmastr1(C) & m2_subset_1(C,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)) ) => ! [D] : ( m1_scmfsa_2(D) => ( ( v2_scmfsa6b(B) | ( r6_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))) & r5_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))) ) ) => k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa6a(C,B),A),D) = k20_scmfsa_2(k3_scmfsa6b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))),D) ) ) ) ) ) ), file(sfmastr1,t15_sfmastr1), []). 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_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),0),k4_scmfsa_2(0)) = 1 ) ) ) ) ) ) ), file(sfmastr3,t16_sfmastr3), []). fof(t17_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),0),B) = k20_scmfsa_2(A,C) ) ) ) ) ) ), file(sfmastr3,t17_sfmastr3), []). fof(t18_sf_mastr,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m2_subset_1(C,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)) => ( ~ ( C != k8_scmfsa_2(A,B) & C != k9_scmfsa_2(A,B) & C != k10_scmfsa_2(A,B) & C != k11_scmfsa_2(A,B) & C != k12_scmfsa_2(A,B) ) => k1_sf_mastr(C) = k3_setwiseo(u1_struct_0(k1_scmfsa_2),A,B) ) ) ) ) ), file(sf_mastr,t18_sf_mastr), []). 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(t20_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( m1_scmfsa_2(E) => ! [F] : ( ( v1_ami_3(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(F) & m1_ami_1(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( r2_hidden(C,k2_sf_mastr(F)) => ( B = C | k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,D,E,F,A),0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) ) ) ), file(sfmastr3,t20_sfmastr3), []). fof(t21_sfmastr1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ r2_hidden(k6_sfmastr1(B,A),A) ) ) ), file(sfmastr1,t21_sfmastr1), []). fof(t21_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( m2_scmfsa_2(E) => ! [F] : ( ( v1_ami_3(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(F) & m1_ami_1(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,F,A),0),E) = k21_scmfsa_2(A,E) ) ) ) ) ) ) ), file(sfmastr3,t21_sfmastr3), []). fof(t21_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(k2_xcmplx_0(A,B),C) <=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ), file(xreal_1,t21_xreal_1), []). fof(t22_sfmastr1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( B != C & k6_sfmastr1(B,A) = k6_sfmastr1(C,A) ) ) ) ) ), file(sfmastr1,t22_sfmastr1), []). fof(t23_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & v2_scmfsa6b(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => r3_sfmastr3(B,C,D,E,A) ) ) ) ) ) ), file(sfmastr3,t23_sfmastr3), []). fof(t25_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & v1_scmfsa7b(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ( k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 & r3_sfmastr3(B,C,D,E,A) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r1_xreal_0(F,k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),1)) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k4_scmfsa_2(0)) = 1 & ( r4_scmfsa7b(E,B) => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),B) = k2_xcmplx_0(F,k20_scmfsa_2(A,C)) & r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),B),k2_xcmplx_0(k20_scmfsa_2(A,D),1)) ) ) & k2_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),F) = k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),1) ) ) ) ) ) ) ) ) ) ), file(sfmastr3,t25_sfmastr3), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t27_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & v1_scmfsa7b(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ( k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 & r3_sfmastr3(B,C,D,E,A) ) => ( r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),1),F) | k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),k1_nat_1(F,1)),k2_xboole_0(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)),k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(k6_scmfsa6a(E,k9_scmfsa_2(B,k4_scmfsa_2(0))),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F)),k2_xboole_0(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)),k3_scmfsa_2)) ) ) ) ) ) ) ) ) ), file(sfmastr3,t27_sfmastr3), []). 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(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t31_sf_mastr,axiom,( ! [A] : ( ( 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) ) => ! [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) ) => k2_sf_mastr(k4_scmfsa6a(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B)) ) ) ), file(sf_mastr,t31_sf_mastr), []). fof(t31_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & v1_scmfsa7b(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( ( k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 & F = k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,C),k20_scmfsa_2(A,D)),1) ) => ( ( ~ r3_sfmastr3(B,D,C,E,A) & ~ v2_scmfsa6b(E) ) | k7_relat_1(k3_scmfsa6b(k3_sfmastr3(B,D,C,E),A),k4_subset_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,k2_sfmastr3(B,D,C,E,A),F),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ), file(sfmastr3,t31_sfmastr3), []). fof(t31_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,0) & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ), file(xreal_1,t31_xreal_1), []). fof(t32_sf_mastr,axiom,( ! [A] : ( m2_subset_1(A,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)) => k2_sf_mastr(k2_scmfsa6a(A)) = k1_sf_mastr(A) ) ), file(sf_mastr,t32_sf_mastr), []). fof(t32_sfmastr3,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] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(E) & v1_scmfsa7b(E) & m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 => ( ( ~ r3_sfmastr3(B,C,D,E,A) & ~ v2_scmfsa6b(E) ) | ( r5_scmfsa7b(k3_sfmastr3(B,C,D,E),A) & r6_scmfsa7b(k3_sfmastr3(B,C,D,E),A) ) ) ) ) ) ) ) ) ), file(sfmastr3,t32_sfmastr3), []). fof(t35_scmfsa6b,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) & v2_scmfsa6b(B) & v3_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k20_scmfsa_2(k3_scmfsa6b(B,A),k4_scmfsa_2(0)) = 1 ) ) ), file(scmfsa6b,t35_scmfsa6b), []). fof(t37_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( r1_xreal_0(A,B) => r1_xreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ), file(nat_1,t37_nat_1), []). 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_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))) => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A)) = k5_scmfsa_2(0) & k20_scmfsa_2(k1_scmfsa6c(A),k4_scmfsa_2(0)) = 1 & ! [B] : ( ( ~ v1_sf_mastr(B) & m1_scmfsa_2(B) ) => k20_scmfsa_2(k1_scmfsa6c(A),B) = k20_scmfsa_2(A,B) ) & ! [B] : ( m2_scmfsa_2(B) => k21_scmfsa_2(k1_scmfsa6c(A),B) = k21_scmfsa_2(A,B) ) & ! [B] : ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => k13_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),B) = k13_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B) ) ) ) ), file(scmfsa6c,t3_scmfsa6c), []). fof(t3_sfmastr3,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,C) & r1_xreal_0(C,k3_finseq_1(A)) ) => ( D = k1_sfmastr3(A,B,C) <=> ( r1_xreal_0(B,D) & r1_xreal_0(D,C) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(B,E) & r1_xreal_0(E,C) ) => r1_xreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) ) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(B,E) & ~ r1_xreal_0(D,E) & r1_xreal_0(k1_funct_1(A,E),k1_funct_1(A,D)) ) ) ) ) ) ) ) ) ) ), file(sfmastr3,t3_sfmastr3), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t43_scmfsa8b,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) & v2_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & v2_scmfsa6b(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [D] : ( ( ~ v1_sf_mastr(D) & m1_scmfsa_2(D) ) => ! [E] : ( ( ~ v1_sf_mastr(E) & m1_scmfsa_2(E) ) => ( ( r2_scmfsa7b(B,D) & r2_scmfsa7b(C,D) ) => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),5)) & ( ~ r1_xreal_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,E)) => ( ! [F] : ( m1_scmfsa_2(F) => ( D != F => k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k20_scmfsa_2(k3_scmfsa6b(B,A),F) ) ) & ! [F] : ( m2_scmfsa_2(F) => k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k21_scmfsa_2(k3_scmfsa6b(B,A),F) ) ) ) & ( r1_xreal_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,E)) => ( ! [F] : ( m1_scmfsa_2(F) => ( D != F => k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k20_scmfsa_2(k3_scmfsa6b(C,A),F) ) ) & ! [F] : ( m2_scmfsa_2(F) => k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k21_scmfsa_2(k3_scmfsa6b(C,A),F) ) ) ) ) ) ) ) ) ) ) ), file(scmfsa8b,t43_scmfsa8b), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). 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_sfmastr3,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) => k1_sfmastr3(A,B,B) = B ) ) ) ), file(sfmastr3,t4_sfmastr3), []). 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(t6_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))) => ! [B] : ( ( v1_scmfsa6c(B) & m2_subset_1(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)) ) => k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k1_scmfsa6c(A)) = k3_scmfsa6b(k2_scmfsa6a(B),A) ) ) ), file(scmfsa6c,t6_scmfsa6c), []). 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(t7_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_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2)) => ( k7_relat_1(A,k2_xboole_0(C,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(C,k3_scmfsa_2)) <=> ( ! [D] : ( m1_scmfsa_2(D) => ( r2_hidden(D,C) => k20_scmfsa_2(A,D) = k20_scmfsa_2(B,D) ) ) & ! [D] : ( m2_scmfsa_2(D) => k21_scmfsa_2(A,D) = k21_scmfsa_2(B,D) ) ) ) ) ) ) ), file(sfmastr2,t7_sfmastr2), []). fof(t80_scmfsa8c,axiom,( ! [A] : ( m2_subset_1(A,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)) => ! [B] : ( m1_scmfsa_2(B) => ( r1_scmfsa7b(A,B) => r2_scmfsa7b(k2_scmfsa6a(A),B) ) ) ) ), file(scmfsa8c,t80_scmfsa8c), []). fof(t89_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ( k1_funct_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(A,B),C),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k7_scmfsa_2(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C)) & k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(A,B),C),A) = k20_scmfsa_2(C,B) & ! [D] : ( m1_scmfsa_2(D) => ( D != A => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(A,B),C),D) = k20_scmfsa_2(C,D) ) ) & ! [D] : ( m2_scmfsa_2(D) => k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(A,B),C),D) = k21_scmfsa_2(C,D) ) ) ) ) ) ), file(scmfsa_2,t89_scmfsa_2), []). 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), []). fof(t8_sfmastr1,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] : ( ( 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) ) => ! [D] : ( m1_scmfsa_2(D) => ~ ( ( v2_scmfsa6b(C) | ( r6_scmfsa7b(C,k1_scmfsa6c(A)) & r5_scmfsa7b(C,k1_scmfsa6c(A)) ) ) & ( v2_scmfsa6b(B) | ( r6_scmfsa7b(B,k3_scmfsa6b(C,A)) & r5_scmfsa7b(B,k3_scmfsa6b(C,A)) ) ) & k20_scmfsa_2(k3_scmfsa6b(k4_scmfsa6a(C,B),A),D) != k20_scmfsa_2(k3_scmfsa6b(B,k3_scmfsa6b(C,A)),D) ) ) ) ) ) ), file(sfmastr1,t8_sfmastr1), []). fof(t8_sfmastr3,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ( k20_scmfsa_2(A,k4_scmfsa_2(0)) = 1 => k7_relat_1(k3_scmfsa6b(k5_scmfsa_4,A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ), file(sfmastr3,t8_sfmastr3), []). fof(t8_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,B) <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t8_xreal_1), []). fof(t90_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ( k1_funct_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k9_scmfsa_2(A,B),C),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k7_scmfsa_2(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C)) & k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k9_scmfsa_2(A,B),C),A) = k2_xcmplx_0(k20_scmfsa_2(C,A),k20_scmfsa_2(C,B)) & ! [D] : ( m1_scmfsa_2(D) => ( D != A => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k9_scmfsa_2(A,B),C),D) = k20_scmfsa_2(C,D) ) ) & ! [D] : ( m2_scmfsa_2(D) => k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k9_scmfsa_2(A,B),C),D) = k21_scmfsa_2(C,D) ) ) ) ) ) ), file(scmfsa_2,t90_scmfsa_2), []). fof(t98_scmfsa_2,axiom,( ! [A] : ( m2_scmfsa_2(A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ( k1_funct_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,A),D),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k7_scmfsa_2(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D)) & ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & E = k1_int_2(k20_scmfsa_2(D,C)) & k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,A),D),B) = k4_finseq_4(k5_numbers,k4_numbers,k21_scmfsa_2(D,A),E) ) & ! [E] : ( m1_scmfsa_2(E) => ( E != B => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,A),D),E) = k20_scmfsa_2(D,E) ) ) & ! [E] : ( m2_scmfsa_2(E) => k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,A),D),E) = k21_scmfsa_2(D,E) ) ) ) ) ) ) ), file(scmfsa_2,t98_scmfsa_2), []). fof(t9_scmfsa6c,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) => ! [C] : ( ( v1_scmfsa6c(C) & v2_scmfsa6c(C) & m2_subset_1(C,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)) ) => ! [D] : ( ( v1_scmfsa6c(D) & m2_subset_1(D,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)) ) => k20_scmfsa_2(k3_scmfsa6b(k7_scmfsa6a(C,D),B),A) = k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(B))),A) ) ) ) ) ), file(scmfsa6c,t9_scmfsa6c), []). fof(t9_sfmastr1,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] : ( ( 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) ) => ! [D] : ( m2_scmfsa_2(D) => ~ ( ( v2_scmfsa6b(C) | ( r6_scmfsa7b(C,k1_scmfsa6c(A)) & r5_scmfsa7b(C,k1_scmfsa6c(A)) ) ) & ( v2_scmfsa6b(B) | ( r6_scmfsa7b(B,k3_scmfsa6b(C,A)) & r5_scmfsa7b(B,k3_scmfsa6b(C,A)) ) ) & k21_scmfsa_2(k3_scmfsa6b(k4_scmfsa6a(C,B),A),D) != k21_scmfsa_2(k3_scmfsa6b(B,k3_scmfsa6b(C,A)),D) ) ) ) ) ) ), file(sfmastr1,t9_sfmastr1), []). fof(t9_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => r2_scmfsa7b(k5_scmfsa_4,A) ) ), file(sfmastr3,t9_sfmastr3), []). fof(t9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ), file(xreal_1,t9_xreal_1), []).