% Mizar problem: t17_scpisort,scpisort,1925,45 fof(t17_scpisort,conjecture,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(A,k1_scmp_gcd(6))),k2_scmpds_2(A,k1_scmp_gcd(4))) & k2_scmpds_2(A,k2_scmp_gcd) = 0 & E = k2_scmpds_2(A,k1_scmp_gcd(6)) & D = k6_xcmplx_0(k6_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(4)),k2_scmpds_2(A,k1_scmp_gcd(6))),1) & r1_scpisort(B,A,D) & r1_scpisort(C,k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),A),D) & k3_finseq_1(B) = k3_finseq_1(C) & r1_sfmastr3(B,1,E) ) => ( r1_xreal_0(k3_finseq_1(B),E) | ( r1_rfinseq(B,C) & r1_sfmastr3(C,1,k1_nat_1(E,1)) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r1_xreal_0(F,k3_finseq_1(B)) => ( r1_xreal_0(F,k1_nat_1(E,1)) | k1_funct_1(B,F) = k1_funct_1(C,F) ) ) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,F) & r1_xreal_0(F,k1_nat_1(E,1)) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,G) & r1_xreal_0(G,k1_nat_1(E,1)) & k1_funct_1(C,F) = k1_funct_1(B,G) ) ) ) ) ) ) ) ) ) ) ) ) ), 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_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_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_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,connectedness_r1_xreal_0,d1_scpisort,d4_scmpds_2,d4_sfmastr3,d5_real_1,dt_g1_ami_1,dt_k11_scmpds_2,dt_k12_scmpds_2,dt_k13_finseq_1,dt_k14_scmpds_2,dt_k16_complex1,dt_k17_scmpds_2,dt_k18_complex1,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_int_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_scmp_gcd,dt_k1_scmpds_2,dt_k1_scmpds_4,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_nat_1,dt_k2_scmp_gcd,dt_k2_scmpds_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_scmpds_2,dt_k3_scmpds_4,dt_k3_scmpds_6,dt_k3_scmpds_8,dt_k3_tarski,dt_k3_xcmplx_0,dt_k4_card_3,dt_k4_numbers,dt_k4_xcmplx_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_scmpds_4,dt_k6_scmpds_4,dt_k6_xcmplx_0,dt_k7_ami_1,dt_k9_scmpds_4,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_scmpds_2,dt_m1_subset_1,dt_m2_finseq_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_finseq_1,existence_m1_relset_1,existence_m1_scmpds_2,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc10_membered,fc10_scmpds_5,fc10_xreal_0,fc11_membered,fc11_scmpds_4,fc11_scmpds_6,fc11_xreal_0,fc12_membered,fc12_scmpds_4,fc12_scmpds_6,fc12_xreal_0,fc13_membered,fc13_scmpds_4,fc13_scmpds_5,fc13_xreal_0,fc14_membered,fc14_xreal_0,fc15_membered,fc15_scmpds_4,fc15_scmpds_5,fc15_xreal_0,fc16_membered,fc16_scmpds_4,fc16_xreal_0,fc17_scmpds_5,fc17_xreal_0,fc18_scmpds_5,fc18_xreal_0,fc19_xreal_0,fc1_fraenkel,fc1_int_1,fc1_scmpds_2,fc1_scmpds_4,fc1_struct_0,fc1_xreal_0,fc20_scmpds_5,fc20_xreal_0,fc21_xreal_0,fc22_membered,fc22_xreal_0,fc23_membered,fc23_scmpds_5,fc23_xreal_0,fc24_membered,fc24_scmpds_5,fc24_xreal_0,fc25_membered,fc25_scmpds_5,fc26_membered,fc27_scmpds_5,fc28_scmpds_5,fc29_scmpds_5,fc2_ami_1,fc2_fraenkel,fc2_int_1,fc2_membered,fc2_scmpds_2,fc2_setfam_1,fc2_wsierp_1,fc31_scmpds_5,fc32_scmpds_5,fc3_ami_1,fc3_int_1,fc3_scmpds_8,fc3_setfam_1,fc3_xreal_0,fc4_ami_1,fc4_int_1,fc4_membered,fc4_scmpds_2,fc4_scmpds_8,fc4_setfam_1,fc4_xreal_0,fc5_int_1,fc5_membered,fc5_scmpds_2,fc5_scmpds_4,fc5_xreal_0,fc6_int_1,fc6_membered,fc6_scmpds_4,fc7_int_1,fc7_membered,fc7_scmpds_5,fc7_xreal_0,fc8_int_1,fc8_membered,fc8_scmpds_4,fc8_scmpds_5,fc8_xreal_0,fc9_int_1,fc9_membered,fc9_xreal_0,free_g1_ami_1,idempotence_k2_xboole_0,involutiveness_k4_xcmplx_0,l23_scpisort,l32_scpisort,projectivity_k16_complex1,projectivity_k18_complex1,projectivity_k1_int_2,rc1_ami_1,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_membered,rc1_scmfsa_4,rc1_scmpds_4,rc1_scmpds_5,rc1_setfam_1,rc1_xreal_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_scmpds_4,rc2_scmpds_5,rc2_xreal_0,rc3_ami_1,rc3_funct_1,rc3_scmpds_4,rc3_struct_0,rc3_xreal_0,rc4_xreal_0,rc5_ami_1,rc5_struct_0,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,redefinition_k18_complex1,redefinition_k1_int_2,redefinition_k1_nat_1,redefinition_k2_nat_1,redefinition_k2_scmpds_2,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_rfinseq,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e6_36__scpisort,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,spc5_boole,spc5_numerals,spc6_boole,spc6_numerals,spc7_boole,spc7_numerals,symmetry_r1_rfinseq,t18_finseq_1,t1_arithm,t1_boole,t1_numerals,t1_real,t1_scpisort,t1_subset,t20_int_1,t23_scmpds_8,t26_nat_1,t29_nat_1,t2_arithm,t2_real,t2_rfinseq,t2_scpisort,t2_subset,t2_xreal_1,t31_xreal_1,t38_nat_1,t3_arithm,t3_real,t3_subset,t4_arithm,t4_real,t4_scpisort,t4_subset,t5_real,t5_scmp_gcd,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,t8_xreal_1]), [file(scpisort,t17_scpisort)]). 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_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_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_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) ), file(nat_1,k2_nat_1), []). 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(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_scpisort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [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_scpisort(A,B,C) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(A)) ) => k1_funct_1(A,D) = k2_scmpds_2(B,k1_scmp_gcd(k1_nat_1(C,D))) ) ) ) ) ) ) ), file(scpisort,d1_scpisort), []). fof(d4_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k3_scmpds_2(A,B) = k1_nat_1(k2_nat_1(2,k1_int_2(k2_xcmplx_0(A,B))),1) ) ) ), file(scmpds_2,d4_scmpds_2), []). fof(d4_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) => ( r1_sfmastr3(A,B,C) <=> ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(B,D) & r1_xreal_0(D,E) & r1_xreal_0(E,C) ) => r1_xreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) ) ) ) ) ) ) ), file(sfmastr3,d4_sfmastr3), []). fof(d5_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(dt_g1_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ), file(ami_1,g1_ami_1), []). fof(dt_k11_scmpds_2,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => m2_subset_1(k11_scmpds_2(A,B,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)) ) ), file(scmpds_2,k11_scmpds_2), []). fof(dt_k12_scmpds_2,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => m2_subset_1(k12_scmpds_2(A,B,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)) ) ), file(scmpds_2,k12_scmpds_2), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k14_scmpds_2,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => m2_subset_1(k14_scmpds_2(A,B,C,D),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)) ) ), file(scmpds_2,k14_scmpds_2), []). fof(dt_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k16_complex1(A)) ) ), file(complex1,k16_complex1), []). fof(dt_k17_scmpds_2,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => m2_subset_1(k17_scmpds_2(A,B,C,D),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)) ) ), file(scmpds_2,k17_scmpds_2), []). fof(dt_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k18_complex1(A),k1_numbers) ) ), file(complex1,k18_complex1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_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_scmp_gcd,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_scmpds_2(k1_scmp_gcd(A)) ) ), file(scmp_gcd,k1_scmp_gcd), []). 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_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k1_scmpds_4(A)) & m1_ami_1(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_4,k1_scmpds_4), []). 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_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k2_nat_1), []). fof(dt_k2_scmp_gcd,axiom,( m1_scmpds_2(k2_scmp_gcd) ), file(scmp_gcd,k2_scmp_gcd), []). fof(dt_k2_scmpds_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) & m1_scmpds_2(B) ) => v1_int_1(k2_scmpds_2(A,B)) ) ), file(scmpds_2,k2_scmpds_2), []). 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_scmpds_2,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => m1_scmpds_2(k3_scmpds_2(A,B)) ) ), file(scmpds_2,k3_scmpds_2), []). 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_scmpds_6,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(C) & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) & v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(D) & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_ami_3(k3_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_6(A,B,C,D)) & m1_ami_1(k3_scmpds_6(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_6,k3_scmpds_6), []). fof(dt_k3_scmpds_8,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(C) & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) ) => ( v1_ami_3(k3_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_8(A,B,C)) & m1_ami_1(k3_scmpds_8(A,B,C),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_8,k3_scmpds_8), []). 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_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), []). 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_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_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) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k5_scmpds_4(A,B)) & m1_ami_1(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_4,k5_scmpds_4), []). fof(dt_k6_scmpds_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k6_scmpds_4(A,B)) & m1_ami_1(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) ), file(scmpds_4,k6_scmpds_4), []). 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_k9_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) & m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) => m1_subset_1(k9_scmpds_4(A,B),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ), file(scmpds_4,k9_scmpds_4), []). 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_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_scmpds_2,axiom,( ! [A] : ( m1_scmpds_2(A) => m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) ), file(scmpds_2,m1_scmpds_2), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_scmpds_2,axiom,( ? [A] : m1_scmpds_2(A) ), file(scmpds_2,m1_scmpds_2), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_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_scmpds_5,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => ( v4_scmpds_4(k14_scmpds_2(A,B,C,D)) & v1_scmpds_5(k14_scmpds_2(A,B,C,D)) ) ) ), file(scmpds_5,fc10_scmpds_5), []). 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_scmpds_4,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => v4_scmpds_4(k17_scmpds_2(A,B,C,D)) ) ), file(scmpds_4,fc11_scmpds_4), []). fof(fc11_scmpds_6,axiom,( ! [A,B,C,D] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v2_scmpds_4(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) & v2_scmpds_4(B) & v3_scmpds_4(B) & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) & m1_scmpds_2(C) & v1_int_1(D) ) => ( v1_relat_1(k3_scmpds_6(C,D,A,B)) & v1_funct_1(k3_scmpds_6(C,D,A,B)) & v1_finset_1(k3_scmpds_6(C,D,A,B)) & v1_ami_3(k3_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_6(C,D,A,B)) & v1_scmpds_4(k3_scmpds_6(C,D,A,B)) & v2_scmpds_4(k3_scmpds_6(C,D,A,B)) & v3_scmpds_4(k3_scmpds_6(C,D,A,B)) ) ) ), file(scmpds_6,fc11_scmpds_6), []). 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_scmpds_6,axiom,( ! [A,B,C,D] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v3_scmpds_5(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_5(B) & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) & m1_scmpds_2(C) & v1_int_1(D) ) => ( v1_relat_1(k3_scmpds_6(C,D,A,B)) & v1_funct_1(k3_scmpds_6(C,D,A,B)) & v1_finset_1(k3_scmpds_6(C,D,A,B)) & v1_ami_3(k3_scmpds_6(C,D,A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_6(C,D,A,B)) & v3_scmpds_5(k3_scmpds_6(C,D,A,B)) ) ) ), file(scmpds_6,fc12_scmpds_6), []). 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_scmpds_4,axiom,( ! [A] : ( ( v4_scmpds_4(A) & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( ~ v1_xboole_0(k1_scmpds_4(A)) & v1_relat_1(k1_scmpds_4(A)) & v1_funct_1(k1_scmpds_4(A)) & v1_finset_1(k1_scmpds_4(A)) & v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k1_scmpds_4(A)) & v3_scmpds_4(k1_scmpds_4(A)) ) ) ), file(scmpds_4,fc13_scmpds_4), []). fof(fc13_scmpds_5,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => ( v4_scmpds_4(k17_scmpds_2(A,B,C,D)) & v1_scmpds_5(k17_scmpds_2(A,B,C,D)) ) ) ), file(scmpds_5,fc13_scmpds_5), []). 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_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_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_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) & v4_scmpds_4(B) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_relat_1(k5_scmpds_4(A,B)) & v1_funct_1(k5_scmpds_4(A,B)) & v1_finset_1(k5_scmpds_4(A,B)) & v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k5_scmpds_4(A,B)) & v3_scmpds_4(k5_scmpds_4(A,B)) ) ) ), file(scmpds_4,fc15_scmpds_4), []). fof(fc15_scmpds_5,axiom,( ! [A] : ( ( v2_scmpds_5(A) & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( ~ v1_xboole_0(k1_scmpds_4(A)) & v1_relat_1(k1_scmpds_4(A)) & v1_funct_1(k1_scmpds_4(A)) & v1_finset_1(k1_scmpds_4(A)) & v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k1_scmpds_4(A)) & v1_scmpds_4(k1_scmpds_4(A)) & v2_scmpds_4(k1_scmpds_4(A)) ) ) ), file(scmpds_5,fc15_scmpds_5), []). 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_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_scmpds_4,axiom,( ! [A,B] : ( ( v4_scmpds_4(A) & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & v4_scmpds_4(B) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_relat_1(k6_scmpds_4(A,B)) & v1_funct_1(k6_scmpds_4(A,B)) & v1_finset_1(k6_scmpds_4(A,B)) & v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k6_scmpds_4(A,B)) & v3_scmpds_4(k6_scmpds_4(A,B)) ) ) ), file(scmpds_4,fc16_scmpds_4), []). 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_scmpds_5,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => ( v4_scmpds_4(k11_scmpds_2(A,B,C)) & v1_scmpds_5(k11_scmpds_2(A,B,C)) & v2_scmpds_5(k11_scmpds_2(A,B,C)) ) ) ), file(scmpds_5,fc17_scmpds_5), []). 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_scmpds_5,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => ( v4_scmpds_4(k12_scmpds_2(A,B,C)) & v1_scmpds_5(k12_scmpds_2(A,B,C)) & v2_scmpds_5(k12_scmpds_2(A,B,C)) ) ) ), file(scmpds_5,fc18_scmpds_5), []). 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_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_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_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_4,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ( ~ v1_xboole_0(k1_scmpds_4(A)) & v1_relat_1(k1_scmpds_4(A)) & v1_funct_1(k1_scmpds_4(A)) & v1_finset_1(k1_scmpds_4(A)) & v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k1_scmpds_4(A)) ) ) ), file(scmpds_4,fc1_scmpds_4), []). 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_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_scmpds_5,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => ( v4_scmpds_4(k14_scmpds_2(A,B,C,D)) & v1_scmpds_5(k14_scmpds_2(A,B,C,D)) & v2_scmpds_5(k14_scmpds_2(A,B,C,D)) ) ) ), file(scmpds_5,fc20_scmpds_5), []). 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_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_scmpds_5,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => ( v4_scmpds_4(k17_scmpds_2(A,B,C,D)) & v1_scmpds_5(k17_scmpds_2(A,B,C,D)) & v2_scmpds_5(k17_scmpds_2(A,B,C,D)) ) ) ), file(scmpds_5,fc23_scmpds_5), []). 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_scmpds_5,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v3_scmpds_5(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_5(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_5(k3_scmpds_4(A,B)) ) ) ), file(scmpds_5,fc24_scmpds_5), []). 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(fc25_scmpds_5,axiom,( ! [A] : ( ( v1_scmpds_5(A) & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( ~ v1_xboole_0(k1_scmpds_4(A)) & v1_relat_1(k1_scmpds_4(A)) & v1_funct_1(k1_scmpds_4(A)) & v1_finset_1(k1_scmpds_4(A)) & v1_ami_3(k1_scmpds_4(A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k1_scmpds_4(A)) & v3_scmpds_5(k1_scmpds_4(A)) ) ) ), file(scmpds_5,fc25_scmpds_5), []). 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(fc27_scmpds_5,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v3_scmpds_5(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_5(B) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_relat_1(k5_scmpds_4(A,B)) & v1_funct_1(k5_scmpds_4(A,B)) & v1_finset_1(k5_scmpds_4(A,B)) & v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k5_scmpds_4(A,B)) & v3_scmpds_5(k5_scmpds_4(A,B)) ) ) ), file(scmpds_5,fc27_scmpds_5), []). fof(fc28_scmpds_5,axiom,( ! [A,B] : ( ( v1_scmpds_5(A) & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & v1_scmpds_5(B) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_relat_1(k6_scmpds_4(A,B)) & v1_funct_1(k6_scmpds_4(A,B)) & v1_finset_1(k6_scmpds_4(A,B)) & v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k6_scmpds_4(A,B)) & v3_scmpds_5(k6_scmpds_4(A,B)) ) ) ), file(scmpds_5,fc28_scmpds_5), []). fof(fc29_scmpds_5,axiom,( ! [A,B] : ( ( 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_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(B) & v2_scmpds_4(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)) & v1_scmpds_4(k3_scmpds_4(A,B)) & v2_scmpds_4(k3_scmpds_4(A,B)) ) ) ), file(scmpds_5,fc29_scmpds_5), []). 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_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(fc31_scmpds_5,axiom,( ! [A,B] : ( ( 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) & v4_scmpds_4(B) & v2_scmpds_5(B) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_relat_1(k5_scmpds_4(A,B)) & v1_funct_1(k5_scmpds_4(A,B)) & v1_finset_1(k5_scmpds_4(A,B)) & v1_ami_3(k5_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k5_scmpds_4(A,B)) & v1_scmpds_4(k5_scmpds_4(A,B)) & v2_scmpds_4(k5_scmpds_4(A,B)) ) ) ), file(scmpds_5,fc31_scmpds_5), []). fof(fc32_scmpds_5,axiom,( ! [A,B] : ( ( v2_scmpds_5(A) & m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & v4_scmpds_4(B) & v2_scmpds_5(B) & m1_subset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) => ( v1_relat_1(k6_scmpds_4(A,B)) & v1_funct_1(k6_scmpds_4(A,B)) & v1_finset_1(k6_scmpds_4(A,B)) & v1_ami_3(k6_scmpds_4(A,B),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k6_scmpds_4(A,B)) & v1_scmpds_4(k6_scmpds_4(A,B)) & v2_scmpds_4(k6_scmpds_4(A,B)) ) ) ), file(scmpds_5,fc32_scmpds_5), []). 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_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_scmpds_8,axiom,( ! [A,B,C] : ( ( 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) & m1_scmpds_2(B) & v1_int_1(C) ) => ( v1_relat_1(k3_scmpds_8(B,C,A)) & v1_funct_1(k3_scmpds_8(B,C,A)) & v1_finset_1(k3_scmpds_8(B,C,A)) & v1_ami_3(k3_scmpds_8(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_8(B,C,A)) & v3_scmpds_4(k3_scmpds_8(B,C,A)) ) ) ), file(scmpds_8,fc3_scmpds_8), []). 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_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_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_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_scmpds_8,axiom,( ! [A,B,C] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(A) & v3_scmpds_5(A) & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) & m1_scmpds_2(B) & v1_int_1(C) ) => ( v1_relat_1(k3_scmpds_8(B,C,A)) & v1_funct_1(k3_scmpds_8(B,C,A)) & v1_finset_1(k3_scmpds_8(B,C,A)) & v1_ami_3(k3_scmpds_8(B,C,A),k1_tarski(k4_numbers),k1_scmpds_2) & v1_scmpds_3(k3_scmpds_8(B,C,A)) & v3_scmpds_5(k3_scmpds_8(B,C,A)) ) ) ), file(scmpds_8,fc4_scmpds_8), []). 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_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_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_scmpds_4,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => v4_scmpds_4(k11_scmpds_2(A,B,C)) ) ), file(scmpds_4,fc5_scmpds_4), []). 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_scmpds_4,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => v4_scmpds_4(k12_scmpds_2(A,B,C)) ) ), file(scmpds_4,fc6_scmpds_4), []). 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_scmpds_5,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => ( v4_scmpds_4(k11_scmpds_2(A,B,C)) & v1_scmpds_5(k11_scmpds_2(A,B,C)) ) ) ), file(scmpds_5,fc7_scmpds_5), []). 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_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_scmpds_4,axiom,( ! [A,B,C,D] : ( ( m1_scmpds_2(A) & m1_scmpds_2(B) & v1_int_1(C) & v1_int_1(D) ) => v4_scmpds_4(k14_scmpds_2(A,B,C,D)) ) ), file(scmpds_4,fc8_scmpds_4), []). fof(fc8_scmpds_5,axiom,( ! [A,B,C] : ( ( m1_scmpds_2(A) & v1_int_1(B) & v1_int_1(C) ) => ( v4_scmpds_4(k12_scmpds_2(A,B,C)) & v1_scmpds_5(k12_scmpds_2(A,B,C)) ) ) ), file(scmpds_5,fc8_scmpds_5), []). 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_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_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_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). 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(l23_scpisort,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(A,k1_scmp_gcd(6))),k2_scmpds_2(A,k1_scmp_gcd(4))) & k2_scmpds_2(A,k2_scmp_gcd) = 0 ) => ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(6)),0) | ( k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k2_scmp_gcd) = 0 & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(1)) = k2_scmpds_2(A,k1_scmp_gcd(1)) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(2)) = k2_scmpds_2(A,k1_scmp_gcd(2)) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(3)) = k2_scmpds_2(A,k1_scmp_gcd(3)) & ~ r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(6)),k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(6))) & r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(6))),k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(4))) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r1_xreal_0(7,B) => ( B = k6_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(4)),1) | B = k2_scmpds_2(A,k1_scmp_gcd(4)) | k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(B)) = k2_scmpds_2(A,k1_scmp_gcd(B)) ) ) ) & ( ~ r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),k4_xcmplx_0(1))),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),0))) => ( k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),k4_xcmplx_0(1))) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),0)) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),0)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),k4_xcmplx_0(1))) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(6)) = k6_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(6)),1) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(4)) = k6_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(4)),1) ) ) & ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),k4_xcmplx_0(1))),k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),0))) => ( k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),k4_xcmplx_0(1))) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),k4_xcmplx_0(1))) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),0)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(4)),0)) & k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A),k1_scmp_gcd(6)) = 0 ) ) ) ) ) ) ), file(scpisort,l23_scpisort), []). fof(l32_scpisort,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(A,k1_scmp_gcd(6))),k2_scmpds_2(A,k1_scmp_gcd(4))) & k2_scmpds_2(A,k2_scmp_gcd) = 0 ) => ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(6)),0) | k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),A) = k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),k9_scmpds_4(k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0)))),A)) ) ) ) ), file(scpisort,l32_scpisort), []). fof(projectivity_k16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ), file(complex1,k16_complex1), []). fof(projectivity_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ), file(complex1,k18_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_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_scmpds_5,axiom,( ? [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & v4_scmpds_4(A) & v1_scmpds_5(A) & v2_scmpds_5(A) ) ), file(scmpds_5,rc1_scmpds_5), []). fof(rc1_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), []). 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_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_scmpds_5,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) & v3_scmpds_5(A) ) ), file(scmpds_5,rc2_scmpds_5), []). 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_scmpds_4,axiom,( ? [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) & v4_scmpds_4(A) ) ), file(scmpds_4,rc3_scmpds_4), []). 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_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(redefinition_k18_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k18_complex1(A) = k16_complex1(A) ) ), file(complex1,k18_complex1), []). 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_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ), file(nat_1,k2_nat_1), []). fof(redefinition_k2_scmpds_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) & m1_scmpds_2(B) ) => k2_scmpds_2(A,B) = k1_funct_1(A,B) ) ), file(scmpds_2,k2_scmpds_2), []). 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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_rfinseq,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => r1_rfinseq(A,A) ) ), file(rfinseq,r1_rfinseq), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s1_nat_1__e6_36__scpisort,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ( ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(B,k1_scmp_gcd(6))),k2_scmpds_2(B,k1_scmp_gcd(4))) & k2_scmpds_2(B,k2_scmp_gcd) = 0 & 0 = k2_scmpds_2(B,k1_scmp_gcd(6)) & A = k6_xcmplx_0(k6_xcmplx_0(k2_scmpds_2(B,k1_scmp_gcd(4)),k2_scmpds_2(B,k1_scmp_gcd(6))),1) & r1_scpisort(C,B,A) & r1_scpisort(D,k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),B),A) & k3_finseq_1(C) = k3_finseq_1(D) & r1_sfmastr3(C,1,0) ) => ( r1_xreal_0(k3_finseq_1(C),0) | ( r1_rfinseq(C,D) & r1_sfmastr3(D,1,k1_nat_1(0,1)) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r1_xreal_0(E,k3_finseq_1(C)) => ( r1_xreal_0(E,k1_nat_1(0,1)) | k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,E) & r1_xreal_0(E,k1_nat_1(0,1)) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,F) & r1_xreal_0(F,k1_nat_1(0,1)) & k1_funct_1(D,E) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ! [H] : ( m1_subset_1(H,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [I] : ( m2_finseq_1(I,k4_numbers) => ! [J] : ( m2_finseq_1(J,k4_numbers) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(H,k1_scmp_gcd(6))),k2_scmpds_2(H,k1_scmp_gcd(4))) & k2_scmpds_2(H,k2_scmp_gcd) = 0 & G = k2_scmpds_2(H,k1_scmp_gcd(6)) & A = k6_xcmplx_0(k6_xcmplx_0(k2_scmpds_2(H,k1_scmp_gcd(4)),k2_scmpds_2(H,k1_scmp_gcd(6))),1) & r1_scpisort(I,H,A) & r1_scpisort(J,k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),H),A) & k3_finseq_1(I) = k3_finseq_1(J) & r1_sfmastr3(I,1,G) ) => ( r1_xreal_0(k3_finseq_1(I),G) | ( r1_rfinseq(I,J) & r1_sfmastr3(J,1,k1_nat_1(G,1)) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ( r1_xreal_0(K,k3_finseq_1(I)) => ( r1_xreal_0(K,k1_nat_1(G,1)) | k1_funct_1(I,K) = k1_funct_1(J,K) ) ) ) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,K) & r1_xreal_0(K,k1_nat_1(G,1)) & ! [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,L) & r1_xreal_0(L,k1_nat_1(G,1)) & k1_funct_1(J,K) = k1_funct_1(I,L) ) ) ) ) ) ) ) ) ) ) => ! [M] : ( m1_subset_1(M,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [N] : ( m2_finseq_1(N,k4_numbers) => ! [O] : ( m2_finseq_1(O,k4_numbers) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(M,k1_scmp_gcd(6))),k2_scmpds_2(M,k1_scmp_gcd(4))) & k2_scmpds_2(M,k2_scmp_gcd) = 0 & k1_nat_1(G,1) = k2_scmpds_2(M,k1_scmp_gcd(6)) & A = k6_xcmplx_0(k6_xcmplx_0(k2_scmpds_2(M,k1_scmp_gcd(4)),k2_scmpds_2(M,k1_scmp_gcd(6))),1) & r1_scpisort(N,M,A) & r1_scpisort(O,k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),M),A) & k3_finseq_1(N) = k3_finseq_1(O) & r1_sfmastr3(N,1,k1_nat_1(G,1)) ) => ( r1_xreal_0(k3_finseq_1(N),k1_nat_1(G,1)) | ( r1_rfinseq(N,O) & r1_sfmastr3(O,1,k1_nat_1(k1_nat_1(G,1),1)) & ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ( r1_xreal_0(P,k3_finseq_1(N)) => ( r1_xreal_0(P,k1_nat_1(k1_nat_1(G,1),1)) | k1_funct_1(N,P) = k1_funct_1(O,P) ) ) ) & ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,P) & r1_xreal_0(P,k1_nat_1(k1_nat_1(G,1),1)) & ! [Q] : ( m2_subset_1(Q,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,Q) & r1_xreal_0(Q,k1_nat_1(k1_nat_1(G,1),1)) & k1_funct_1(O,P) = k1_funct_1(N,Q) ) ) ) ) ) ) ) ) ) ) ) ) ) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [R] : ( m1_subset_1(R,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [S] : ( m2_finseq_1(S,k4_numbers) => ! [T] : ( m2_finseq_1(T,k4_numbers) => ( ( r1_xreal_0(k2_xcmplx_0(7,k2_scmpds_2(R,k1_scmp_gcd(6))),k2_scmpds_2(R,k1_scmp_gcd(4))) & k2_scmpds_2(R,k2_scmp_gcd) = 0 & G = k2_scmpds_2(R,k1_scmp_gcd(6)) & A = k6_xcmplx_0(k6_xcmplx_0(k2_scmpds_2(R,k1_scmp_gcd(4)),k2_scmpds_2(R,k1_scmp_gcd(6))),1) & r1_scpisort(S,R,A) & r1_scpisort(T,k9_scmpds_4(k3_scmpds_8(k2_scmp_gcd,6,k3_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k14_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,0)),k3_scmpds_6(k2_scmp_gcd,5,k5_scmpds_4(k5_scmpds_4(k5_scmpds_4(k6_scmpds_4(k17_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(4),5,k4_xcmplx_0(1)),k17_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(4),k4_xcmplx_0(1),0)),k17_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,0,5)),k12_scmpds_2(k2_scmp_gcd,4,k4_xcmplx_0(1))),k12_scmpds_2(k2_scmp_gcd,6,k4_xcmplx_0(1))),k1_scmpds_4(k11_scmpds_2(k2_scmp_gcd,6,0))))),R),A) & k3_finseq_1(S) = k3_finseq_1(T) & r1_sfmastr3(S,1,G) ) => ( r1_xreal_0(k3_finseq_1(S),G) | ( r1_rfinseq(S,T) & r1_sfmastr3(T,1,k1_nat_1(G,1)) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ( r1_xreal_0(U,k3_finseq_1(S)) => ( r1_xreal_0(U,k1_nat_1(G,1)) | k1_funct_1(S,U) = k1_funct_1(T,U) ) ) ) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,U) & r1_xreal_0(U,k1_nat_1(G,1)) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,V) & r1_xreal_0(V,k1_nat_1(G,1)) & k1_funct_1(T,U) = k1_funct_1(S,V) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(scpisort,s1_nat_1__e6_36__scpisort), []). 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(spc4_boole,axiom,( ~ v1_xboole_0(4) ), file(boole,spc4_boole), []). fof(spc4_numerals,axiom, ( v2_xreal_0(4) & m1_subset_1(4,k5_numbers) ), file(numerals,spc4_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(spc6_boole,axiom,( ~ v1_xboole_0(6) ), file(boole,spc6_boole), []). fof(spc6_numerals,axiom, ( v2_xreal_0(6) & m1_subset_1(6,k5_numbers) ), file(numerals,spc6_numerals), []). fof(spc7_boole,axiom,( ~ v1_xboole_0(7) ), file(boole,spc7_boole), []). fof(spc7_numerals,axiom, ( v2_xreal_0(7) & m1_subset_1(7,k5_numbers) ), file(numerals,spc7_numerals), []). fof(symmetry_r1_rfinseq,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( r1_rfinseq(A,B) => r1_rfinseq(B,A) ) ) ), file(rfinseq,r1_rfinseq), []). fof(t18_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(A)) ) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) ), file(finseq_1,t18_finseq_1), []). 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_scpisort,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) => ( r1_xreal_0(C,B) => r1_sfmastr3(A,B,C) ) ) ) ) ), file(scpisort,t1_scpisort), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xreal_0(B,A) => r1_xreal_0(k2_xcmplx_0(A,1),B) ) ) ) ), file(int_1,t20_int_1), []). fof(t23_scmpds_8,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(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) ) => ! [C] : ( m1_scmpds_2(C) => ! [D] : ( m1_scmpds_2(D) => ! [E] : ( v1_int_1(E) => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),0) => k2_scmpds_2(k9_scmpds_4(k3_scmpds_8(C,E,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ), file(scmpds_8,t23_scmpds_8), []). fof(t26_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( r1_xreal_0(A,k2_xcmplx_0(B,1)) & ~ r1_xreal_0(A,B) & A != k2_xcmplx_0(B,1) ) ) ) ), file(nat_1,t26_nat_1), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). 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_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_rfinseq(A,B) & r1_rfinseq(A,C) ) => r1_rfinseq(B,C) ) ) ) ) ), file(rfinseq,t2_rfinseq), []). fof(t2_scpisort,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ? [D] : ( m2_finseq_1(D,k4_numbers) & k3_finseq_1(D) = B & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,E) & r1_xreal_0(E,k3_finseq_1(D)) ) => k1_funct_1(D,E) = k2_scmpds_2(A,k1_scmp_gcd(k1_nat_1(C,E))) ) ) ) ) ) ) ), file(scpisort,t2_scpisort), []). 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_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(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(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_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_scpisort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,D) & r1_xreal_0(D,k3_finseq_1(A)) & r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(A)) & k3_finseq_1(A) = k3_finseq_1(B) & k1_funct_1(A,C) = k1_funct_1(B,D) & k1_funct_1(A,D) = k1_funct_1(B,C) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,E) & r1_xreal_0(E,k3_finseq_1(A)) ) => ( E = C | E = D | k1_funct_1(A,E) = k1_funct_1(B,E) ) ) ) ) => r1_rfinseq(A,B) ) ) ) ) ) ), file(scpisort,t4_scpisort), []). 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_scmp_gcd,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k3_scmpds_2(A,B) = k1_scmp_gcd(k1_nat_1(A,B)) ) ) ), file(scmp_gcd,t5_scmp_gcd), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). 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), []).