% Mizar problem: t84_scmpds_4,scmpds_4,2854,74 fof(t84_scmpds_4,conjecture,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [C] : ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(C) & v2_scmpds_4(C) & v3_scmpds_4(C) & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_tarski(k6_scmpds_3(k8_scmpds_4(C),D),B) & k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k2_scmpds_3(D) & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) ) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)),D) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E)) & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E)) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E),k2_ami_2) ) ) ) ) ) ) ) ) ), 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_fraenkel,cc1_funct_1,cc1_funct_7,cc1_int_1,cc1_membered,cc1_relset_1,cc1_scmfsa_4,cc1_scmpds_4,cc1_setfam_1,cc1_xreal_0,cc20_membered,cc2_funct_1,cc2_funct_7,cc2_int_1,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_membered,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,d12_ami_3,d12_scmpds_4,d15_ami_1,d17_ami_1,d18_ami_1,d19_ami_1,d1_ami_3,d20_ami_3,d2_scmpds_3,d2_scmpds_4,d3_scmpds_3,d3_scmpds_4,d5_ami_1,d6_scmpds_3,d7_ami_1,d7_scmpds_4,d9_scmpds_4,dt_g1_ami_1,dt_k10_ami_1,dt_k11_ami_1,dt_k12_ami_3,dt_k13_ami_1,dt_k13_finseq_1,dt_k14_ami_3,dt_k16_ami_3,dt_k17_ami_1,dt_k17_ami_2,dt_k1_ami_3,dt_k1_ami_5,dt_k1_card_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_funct_4,dt_k1_gr_cy_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_scmfsa_4,dt_k1_scmpds_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_1,dt_k2_ami_2,dt_k2_cat_3,dt_k2_scmpds_3,dt_k2_scmpds_4,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_ami_2,dt_k3_cqc_lang,dt_k3_scmpds_3,dt_k3_scmpds_4,dt_k3_tarski,dt_k3_xcmplx_0,dt_k4_ami_1,dt_k4_ami_2,dt_k4_card_1,dt_k4_card_3,dt_k4_numbers,dt_k5_ami_1,dt_k5_ami_2,dt_k5_numbers,dt_k5_ordinal2,dt_k5_scmpds_3,dt_k6_ami_1,dt_k6_scmpds_3,dt_k7_ami_1,dt_k7_relat_1,dt_k8_ami_1,dt_k8_funct_2,dt_k8_scmpds_4,dt_k9_ami_1,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_relset_1,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_fraenkel,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_membered,fc12_scmpds_4,fc12_xreal_0,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc17_scmpds_4,fc18_scmpds_4,fc1_fraenkel,fc1_funct_7,fc1_int_1,fc1_ordinal2,fc1_scmpds_2,fc1_scmpds_3,fc1_struct_0,fc1_xboole_0,fc21_xreal_0,fc22_membered,fc22_xreal_0,fc23_membered,fc23_xreal_0,fc24_membered,fc24_xreal_0,fc25_membered,fc26_membered,fc2_ami_1,fc2_fraenkel,fc2_int_1,fc2_membered,fc2_scmpds_2,fc2_setfam_1,fc2_xboole_0,fc3_ami_1,fc3_funct_7,fc3_scmpds_2,fc3_scmpds_4,fc3_setfam_1,fc3_xboole_0,fc3_xreal_0,fc4_ami_1,fc4_funct_1,fc4_membered,fc4_scmpds_2,fc4_setfam_1,fc4_xreal_0,fc5_membered,fc5_scmpds_2,fc5_trees_2,fc6_ami_1,fc6_int_1,fc6_membered,fc7_int_1,fc7_membered,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,free_g1_ami_1,idempotence_k17_ami_1,idempotence_k1_funct_4,idempotence_k1_scmfsa_4,idempotence_k2_xboole_0,rc1_ami_1,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_membered,rc1_scmfsa_4,rc1_scmpds_4,rc1_setfam_1,rc1_xboole_0,rc1_xreal_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_scmpds_3,rc2_scmpds_4,rc2_xboole_0,rc2_xreal_0,rc3_ami_1,rc3_funct_1,rc3_struct_0,rc3_xreal_0,rc4_ami_1,rc4_funct_1,rc4_xreal_0,rc5_ami_1,rc5_struct_0,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,rc9_trees_2,redefinition_k11_ami_1,redefinition_k13_ami_1,redefinition_k14_ami_3,redefinition_k17_ami_1,redefinition_k1_fraenkel,redefinition_k1_nat_1,redefinition_k1_scmfsa_4,redefinition_k2_cat_3,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_nat_1__e11_108__scmpds_4,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc9_boole,spc9_numerals,symmetry_r1_xboole_0,t1_arithm,t1_boole,t1_numerals,t1_subset,t29_scmpds_4,t2_arithm,t2_subset,t32_scmpds_3,t33_funct_4,t37_scmpds_3,t3_arithm,t3_subset,t4_subset,t54_ami_1,t54_scmpds_4,t5_subset,t6_boole,t75_scmpds_4,t76_scmpds_4,t7_boole,t7_scmpds_4,t83_scmpds_4,t8_boole,t8_grfunc_1]), [file(scmpds_4,t84_scmpds_4)]). 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_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_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). 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_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_scmpds_4,axiom,( ! [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) => ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v2_scmpds_4(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v1_scmpds_4(A) ) ) ) ), file(scmpds_4,cc1_scmpds_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_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_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_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(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) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). 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_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). 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_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_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_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(d12_ami_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => k12_ami_3(A,B,C) = k2_cat_3(u2_ami_1(A,B),k2_ami_1(A,B),C) ) ) ) ), file(ami_3,d12_ami_3), []). fof(d12_scmpds_4,axiom,( ! [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) => ( v3_scmpds_4(A) <=> ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( ( r2_hidden(k2_scmpds_3(B),k1_relat_1(A)) & C = k1_funct_1(A,k2_scmpds_3(B)) ) => ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C) != 1 & k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C) != 3 & r1_scmpds_4(C,B) ) ) ) ) ) ) ), file(scmpds_4,d12_scmpds_4), []). fof(d15_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k6_ami_1(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ), file(ami_1,d15_ami_1), []). fof(d17_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k8_ami_1(A,B,C) = k1_funct_1(C,k6_ami_1(A,B,C)) ) ) ) ), file(ami_1,d17_ami_1), []). fof(d18_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k9_ami_1(A,B,C) = k4_ami_1(A,B,k8_ami_1(A,B,C),C) ) ) ) ), file(ami_1,d18_ami_1), []). fof(d19_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m2_relset_1(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) ) => ( D = k10_ami_1(A,B,C) <=> ( k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,0) = C & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,k1_nat_1(E,1)) = k9_ami_1(A,B,k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,E)) ) ) ) ) ) ) ) ), file(ami_1,d19_ami_1), []). fof(d1_ami_3,axiom,( k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,0,k3_ami_2,k1_gr_cy_1(9),k4_ami_2,k5_ami_2,k17_ami_2) ), file(ami_3,d1_ami_3), []). fof(d20_ami_3,axiom,( ! [A] : ( v4_ordinal2(A) => k16_ami_3(A) = k2_xcmplx_0(k3_xcmplx_0(2,A),2) ) ), file(ami_3,d20_ami_3), []). fof(d2_scmpds_3,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k2_scmpds_3(A) = k16_ami_3(A) ) ), file(scmpds_3,d2_scmpds_3), []). fof(d2_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => k2_scmpds_4(A) = k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(0))) ) ), file(scmpds_4,d2_scmpds_4), []). fof(d3_scmpds_3,axiom,( ! [A] : ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( C = k3_scmpds_3(A,B) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k2_scmpds_3(D) & C = k2_scmpds_3(k1_nat_1(D,B)) ) ) ) ) ) ), file(scmpds_3,d3_scmpds_3), []). fof(d3_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => ! [B] : ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(B) & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) ) => k3_scmpds_4(A,B) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,k6_scmpds_3(B,k4_card_1(A))) ) ) ), file(scmpds_4,d3_scmpds_4), []). fof(d5_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => k2_ami_1(A,B) = u1_ami_1(A,B) ) ), file(ami_1,d5_ami_1), []). fof(d6_scmpds_3,axiom,( k5_scmpds_3 = k14_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(0),k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ), file(scmpds_3,d6_scmpds_3), []). fof(d7_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m2_subset_1(C,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)) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => k4_ami_1(A,B,C,D) = k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D) ) ) ) ) ), file(ami_1,d7_ami_1), []). fof(d7_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => k8_scmpds_4(A) = k3_scmpds_4(A,k5_scmpds_3) ) ), file(scmpds_4,d7_scmpds_4), []). fof(d9_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_scmpds_4(A) <=> ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_tarski(k2_scmpds_4(k8_scmpds_4(A)),B) => r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),C)),k1_relat_1(k8_scmpds_4(A))) ) ) ) ) ) ), file(scmpds_4,d9_scmpds_4), []). 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_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_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))) ) => ( v1_funct_1(k10_ami_1(A,B,C)) & v1_funct_2(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) & m2_relset_1(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) ) ) ), file(ami_1,k10_ami_1), []). 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_k12_ami_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) ) => m1_ami_1(k12_ami_3(A,B,C),A,B) ) ), file(ami_3,k12_ami_3), []). 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_k14_ami_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => ( v1_ami_3(k14_ami_3(A,B,C,D),A,B) & m1_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) ), file(ami_3,k14_ami_3), []). fof(dt_k16_ami_3,axiom,( ! [A] : ( v4_ordinal2(A) => m1_struct_0(k16_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k16_ami_3), []). fof(dt_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => m1_ami_1(k17_ami_1(A,B,C,D),A,B) ) ), file(ami_1,k17_ami_1), []). fof(dt_k17_ami_2,axiom, ( v1_funct_1(k17_ami_2) & v1_funct_2(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) & m2_relset_1(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) ), file(ami_2,k17_ami_2), []). fof(dt_k1_ami_3,axiom, ( v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & l1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,k1_ami_3), []). fof(dt_k1_ami_5,axiom,( ! [A,B,C] : ( ( l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) ) => m1_subset_1(k1_ami_5(A,B,C),u3_ami_1(A,B)) ) ), file(ami_5,k1_ami_5), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), []). 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_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_gr_cy_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( ~ v1_xboole_0(k1_gr_cy_1(A)) & m1_subset_1(k1_gr_cy_1(A),k1_zfmisc_1(k5_numbers)) ) ) ), file(gr_cy_1,k1_gr_cy_1), []). 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_scmfsa_4,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => ( v1_ami_3(k1_scmfsa_4(A,B,C,D),A,B) & m1_ami_1(k1_scmfsa_4(A,B,C,D),A,B) ) ) ), file(scmfsa_4,k1_scmfsa_4), []). fof(dt_k1_scmpds_2,axiom, ( v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & l1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,k1_scmpds_2), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_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_ami_2,axiom,( m1_subset_1(k2_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k2_ami_2), []). fof(dt_k2_cat_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => ( v1_funct_1(k2_cat_3(A,B,C)) & v1_funct_2(k2_cat_3(A,B,C),k1_tarski(B),A) & m2_relset_1(k2_cat_3(A,B,C),k1_tarski(B),A) ) ) ), file(cat_3,k2_cat_3), []). fof(dt_k2_scmpds_3,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_struct_0(k2_scmpds_3(A),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ), file(scmpds_3,k2_scmpds_3), []). fof(dt_k2_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => m1_ami_1(k2_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ), file(scmpds_4,k2_scmpds_4), []). 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_ami_2,axiom,( m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k3_ami_2), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). fof(dt_k3_scmpds_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & m1_subset_1(B,k5_numbers) ) => m1_struct_0(k3_scmpds_3(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ), file(scmpds_3,k3_scmpds_3), []). fof(dt_k3_scmpds_4,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(B) & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_4(A,B)) & m1_ami_1(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_4,k3_scmpds_4), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). 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_ami_2,axiom,( m1_subset_1(k4_ami_2,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ), file(ami_2,k4_ami_2), []). 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_numbers,axiom,( $true ), file(numbers,k4_numbers), []). fof(dt_k5_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => m2_subset_1(k5_ami_1(A,B),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,k5_ami_1), []). fof(dt_k5_ami_2,axiom, ( v1_funct_1(k5_ami_2) & v1_funct_2(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) & m2_relset_1(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) ), file(ami_2,k5_ami_2), []). 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_scmpds_3,axiom,( m1_ami_1(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2) ), file(scmpds_3,k5_scmpds_3), []). 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_scmpds_3,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & m1_subset_1(B,k5_numbers) ) => ( v1_ami_3(k6_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & m1_ami_1(k6_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_3,k6_scmpds_3), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k8_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_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))) ) => m2_subset_1(k8_ami_1(A,B,C),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,k8_ami_1), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_ami_3(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k8_scmpds_4(A)) & m1_ami_1(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_4,k8_scmpds_4), []). fof(dt_k9_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_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(k9_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k9_ami_1), []). 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_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). 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_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_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_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). 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_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). 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_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). 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_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). 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_scmpds_4,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v3_scmpds_4(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(B) & v3_scmpds_4(B) & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_relat_1(k3_scmpds_4(A,B)) & v1_funct_1(k3_scmpds_4(A,B)) & v1_finset_1(k3_scmpds_4(A,B)) & v1_ami_3(k3_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_4(A,B)) & v3_scmpds_4(k3_scmpds_4(A,B)) ) ) ), file(scmpds_4,fc12_scmpds_4), []). 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(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(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(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(fc17_scmpds_4,axiom, ( ~ v1_xboole_0(k5_scmpds_3) & v1_relat_1(k5_scmpds_3) & v1_funct_1(k5_scmpds_3) & v1_finset_1(k5_scmpds_3) & v1_ami_3(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k5_scmpds_3) & v1_scmpds_4(k5_scmpds_3) & v2_scmpds_4(k5_scmpds_3) & v3_scmpds_4(k5_scmpds_3) ), file(scmpds_4,fc17_scmpds_4), []). fof(fc18_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v3_scmpds_4(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_relat_1(k8_scmpds_4(A)) & v1_funct_1(k8_scmpds_4(A)) & v1_finset_1(k8_scmpds_4(A)) & v1_ami_3(k8_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k8_scmpds_4(A)) & v3_scmpds_4(k8_scmpds_4(A)) ) ) ), file(scmpds_4,fc18_scmpds_4), []). fof(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_funct_7,axiom,( ! [A,B] : ( ~ v1_xboole_0(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) ) ), file(funct_7,fc1_funct_7), []). 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_scmpds_2,axiom, ( ~ v3_struct_0(k1_scmpds_2) & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,fc1_scmpds_2), []). fof(fc1_scmpds_3,axiom, ( ~ v1_xboole_0(k5_scmpds_3) & v1_relat_1(k5_scmpds_3) & v1_funct_1(k5_scmpds_3) & v1_finset_1(k5_scmpds_3) & v1_ami_3(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k5_scmpds_3) ), file(scmpds_3,fc1_scmpds_3), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). 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(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_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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_scmpds_2,axiom, ( ~ v3_struct_0(k1_scmpds_2) & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,fc2_scmpds_2), []). fof(fc2_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)) ) ) ), file(setfam_1,fc2_setfam_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). 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_funct_7,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) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). fof(fc3_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( v4_ordinal2(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) & v1_xcmplx_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) & v1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) & ~ v3_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) & v1_int_1(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) ), file(scmpds_2,fc3_scmpds_2), []). fof(fc3_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v2_scmpds_4(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_relat_1(k2_scmpds_4(k8_scmpds_4(A))) & v1_funct_1(k2_scmpds_4(k8_scmpds_4(A))) & v1_finset_1(k2_scmpds_4(k8_scmpds_4(A))) & v12_ami_1(k2_scmpds_4(k8_scmpds_4(A)),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_4,fc3_scmpds_4), []). 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_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). 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_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_scmpds_2,axiom, ( ~ v3_struct_0(k1_scmpds_2) & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,fc4_scmpds_2), []). fof(fc4_setfam_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_1), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). 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_scmpds_2,axiom, ( ~ v3_struct_0(k1_scmpds_2) & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,fc5_scmpds_2), []). fof(fc5_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(trees_2,fc5_trees_2), []). fof(fc6_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => v3_ami_1(k5_ami_1(A,B),A,B) ) ), file(ami_1,fc6_ami_1), []). 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(fc7_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). 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_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). 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_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => k17_ami_1(A,B,C,C) = C ) ), file(ami_1,k17_ami_1), []). fof(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(idempotence_k1_scmfsa_4,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => k1_scmfsa_4(A,B,C,C) = C ) ), file(scmfsa_4,k1_scmfsa_4), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). 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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_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_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_scmpds_4,axiom,( ? [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v2_scmpds_4(A) ) ), file(scmpds_4,rc1_scmpds_4), []). fof(rc1_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). 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_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_scmpds_3,axiom,( ? [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) ) ), file(scmpds_3,rc2_scmpds_3), []). fof(rc2_scmpds_4,axiom,( ? [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v1_scmpds_4(A) & v2_scmpds_4(A) & v3_scmpds_4(A) ) ), file(scmpds_4,rc2_scmpds_4), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_subset_1(C,u4_ami_1(A,B)) & v3_ami_1(C,A,B) ) ) ), file(ami_1,rc4_ami_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(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) ) ), file(ami_1,rc6_ami_1), []). fof(rc7_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) ) ), file(ami_1,rc7_ami_1), []). fof(rc8_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc8_ami_1), []). fof(rc9_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc9_ami_1), []). fof(rc9_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), []). 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_k14_ami_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => k14_ami_3(A,B,C,D) = k3_cqc_lang(C,D) ) ), file(ami_3,k14_ami_3), []). fof(redefinition_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => k17_ami_1(A,B,C,D) = k1_funct_4(C,D) ) ), file(ami_1,k17_ami_1), []). fof(redefinition_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_scmfsa_4,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => k1_scmfsa_4(A,B,C,D) = k1_funct_4(C,D) ) ), file(scmfsa_4,k1_scmfsa_4), []). fof(redefinition_k2_cat_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k2_cat_3(A,B,C) = k3_cqc_lang(B,C) ) ), file(cat_3,k2_cat_3), []). 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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). 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_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(s1_nat_1__e11_108__scmpds_4,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) & m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),0)),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),0)) & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),0)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),0)) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),0),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),0),k2_ami_2) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D)),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k2_ami_2) ) => ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_nat_1(D,1))),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),k1_nat_1(D,1))) & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_nat_1(D,1))) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),k1_nat_1(D,1))) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_nat_1(D,1)),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),k1_nat_1(D,1)),k2_ami_2) ) ) ) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D)),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k2_ami_2) ) ) ) ) ), file(scmpds_4,s1_nat_1__e11_108__scmpds_4), []). 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(spc9_boole,axiom,( ~ v1_xboole_0(9) ), file(boole,spc9_boole), []). fof(spc9_numerals,axiom, ( v2_xreal_0(9) & m1_subset_1(9,k5_numbers) ), file(numerals,spc9_numerals), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). 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_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t29_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => k1_funct_1(k2_scmpds_4(A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k2_scmpds_3(0) ) ), file(scmpds_4,t29_scmpds_4), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t32_scmpds_3,axiom,( ! [A] : ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & A = k2_scmpds_3(B) ) ) ), file(scmpds_3,t32_scmpds_3), []). fof(t33_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) => r1_tarski(A,k1_funct_4(A,B)) ) ) ) ), file(funct_4,t33_funct_4), []). fof(t37_scmpds_3,axiom,( ! [A] : ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2) & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( r2_hidden(A,k1_relat_1(C)) => k1_funct_1(k6_scmpds_3(C,B),k3_scmpds_3(A,B)) = k1_funct_1(C,A) ) ) ) ) ), file(scmpds_3,t37_scmpds_3), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). 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(t54_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => ! [D] : ( m1_struct_0(D,B,u2_ami_1(A,B)) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k13_ami_1(A,B,C,D) = k13_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ), file(ami_1,t54_ami_1), []). fof(t54_scmpds_4,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(B) & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) ) => r1_xboole_0(k1_relat_1(B),k1_relat_1(k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(A)))) ) ) ), file(scmpds_4,t54_scmpds_4), []). 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(t75_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => r2_hidden(k2_scmpds_3(0),k1_relat_1(k8_scmpds_4(A))) ) ), file(scmpds_4,t75_scmpds_4), []). fof(t76_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( r2_hidden(C,k1_relat_1(A)) => r2_hidden(k3_scmpds_3(C,B),k1_relat_1(k6_scmpds_3(A,B))) ) ) ) ) ), file(scmpds_4,t76_scmpds_4), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_scmpds_4,axiom,( ! [A] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) ) => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(k2_scmpds_4(A))) ) ), file(scmpds_4,t7_scmpds_4), []). fof(t83_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(D) & r1_scmpds_4(E,D) & k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) ) => ( k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,E) = 1 | k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,E) = 3 | ( k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,A)),C) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,B)) & k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,A),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,E,B),k2_ami_2) ) ) ) ) ) ) ) ) ), file(scmpds_4,t83_scmpds_4), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ), file(grfunc_1,t8_grfunc_1), []).