% Mizar problem: t116_scmfsa8c,scmfsa8c,5179,50 fof(t116_scmfsa8c,conjecture,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( m1_scmfsa_2(C) => k1_funct_1(k1_scmfsa8b(C,k2_scmfsa8a(k5_scmfsa_2(2)),k6_scmfsa6a(A,k10_scmfsa_2(C,k4_scmfsa_2(0)))),k5_scmfsa_2(k1_nat_1(k4_card_1(k6_scmfsa6a(A,k10_scmfsa_2(C,k4_scmfsa_2(0)))),3))) = k13_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(k6_scmfsa6a(A,k10_scmfsa_2(C,k4_scmfsa_2(0)))),5))) ) ) ) ), 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_scmfsa6b,cc1_scmfsa7b,cc1_scmfsa_4,cc1_setfam_1,cc1_sf_mastr,cc1_xreal_0,cc20_membered,cc2_funct_1,cc2_int_1,cc2_membered,cc2_scmfsa6b,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_scmfsa6b,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,connectedness_r1_xreal_0,d1_scmfsa8b,d1_scmfsa_4,d5_scmfsa6a,dt_g1_ami_1,dt_k10_scmfsa_2,dt_k13_finseq_1,dt_k13_scmfsa_2,dt_k14_scmfsa_2,dt_k1_ami_5,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_scmfsa6a,dt_k1_scmfsa8b,dt_k1_scmfsa_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_scmfsa6a,dt_k2_scmfsa8a,dt_k2_scmfsa_4,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k3_tarski,dt_k4_card_1,dt_k4_card_3,dt_k4_numbers,dt_k4_scmfsa6a,dt_k4_scmfsa_2,dt_k4_scmfsa_4,dt_k5_ami_1,dt_k5_binarith,dt_k5_numbers,dt_k5_ordinal2,dt_k5_scmfsa6a,dt_k5_scmfsa_2,dt_k5_scmfsa_4,dt_k6_scmfsa6a,dt_k7_ami_1,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_scmfsa_2,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_finseq_2,existence_m1_relset_1,existence_m1_scmfsa_2,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc10_xreal_0,fc11_xreal_0,fc12_membered,fc12_xreal_0,fc13_membered,fc14_membered,fc15_membered,fc15_scmfsa6c,fc16_membered,fc1_fraenkel,fc1_int_1,fc1_scmfsa6a,fc1_scmfsa6c,fc1_scmfsa_2,fc1_scmfsa_4,fc20_scmfsa6c,fc21_scmfsa6c,fc22_membered,fc23_membered,fc23_scmfsa6c,fc24_membered,fc24_scmfsa6c,fc25_membered,fc26_membered,fc2_ami_1,fc2_fraenkel,fc2_membered,fc2_scmfsa6a,fc2_scmfsa6b,fc2_scmfsa6c,fc2_scmfsa8a,fc2_scmfsa_2,fc3_ami_1,fc3_scmfsa6b,fc3_scmfsa6c,fc3_scmfsa_2,fc3_setfam_1,fc3_xreal_0,fc4_ami_1,fc4_membered,fc4_scmfsa8a,fc4_scmfsa_2,fc4_setfam_1,fc5_membered,fc5_trees_2,fc6_ami_1,fc6_int_1,fc6_membered,fc6_scmfsa6c,fc6_scmfsa7b,fc6_scmfsa8a,fc6_sf_mastr,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,free_g1_ami_1,idempotence_k2_xboole_0,rc1_ami_1,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_membered,rc1_scmfsa6b,rc1_scmfsa6c,rc1_scmfsa7b,rc1_scmfsa_4,rc1_setfam_1,rc1_sf_mastr,rc1_xreal_0,rc2_ami_1,rc2_funct_1,rc2_int_1,rc2_scmfsa6b,rc2_scmfsa7b,rc2_scmfsa_4,rc2_xreal_0,rc3_ami_1,rc3_funct_1,rc3_xreal_0,rc4_ami_1,rc4_xreal_0,rc5_ami_1,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,rc9_trees_2,redefinition_k1_nat_1,redefinition_k3_finseq_2,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc5_boole,spc5_numerals,spc6_boole,spc6_numerals,t124_scmfsa_2,t13_scmfsa8c,t14_scmfsa_4,t15_scmfsa6a,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t28_scmfsa8a,t29_scmfsa8a,t2_real,t2_subset,t30_scmfsa8a,t38_nat_1,t3_real,t3_subset,t47_scmfsa8a,t47_scmfsa_2,t4_real,t4_subset,t51_binarith,t5_real,t5_subset,t61_scmfsa6a,t6_boole,t6_real,t6_scmfsa7b,t7_boole,t7_real,t8_boole,t8_real]), [file(scmfsa8c,t116_scmfsa8c)]). 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_scmfsa6b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) ) ) ) ), file(scmfsa6b,cc1_scmfsa6b), []). fof(cc1_scmfsa7b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v1_scmfsa7b(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v3_scmfsa6b(A) ) ) ) ), file(scmfsa7b,cc1_scmfsa7b), []). fof(cc1_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) ) ) ), file(scmfsa_4,cc1_scmfsa_4), []). fof(cc1_setfam_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(setfam_1,cc1_setfam_1), []). fof(cc1_sf_mastr,axiom,( ! [A,B] : ( v1_finset_1(A) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_finset_1(C) & v1_funct_2(C,A,B) ) ) ) ) ), file(sf_mastr,cc1_sf_mastr), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_scmfsa6b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v3_scmfsa6b(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) ) ) ) ), file(scmfsa6b,cc2_scmfsa6b), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_scmfsa6b,axiom,( ! [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) ) ) ) ), file(scmfsa6b,cc3_scmfsa6b), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_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(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_scmfsa8b,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k1_scmfsa8b(A,B,C) = k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(k5_scmfsa6a(k14_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(C),3)),A),C),k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),1)))),B),k5_scmfsa_4) ) ) ) ), file(scmfsa8b,d1_scmfsa8b), []). fof(d1_scmfsa_4,axiom,( ! [A] : ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( C = k2_scmfsa_4(A,B) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k5_scmfsa_2(D) & C = k5_scmfsa_2(k1_nat_1(D,B)) ) ) ) ) ) ), file(scmfsa_4,d1_scmfsa_4), []). fof(d5_scmfsa6a,axiom,( ! [A] : ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k5_scmfsa6a(A,B) = k4_scmfsa6a(k2_scmfsa6a(A),B) ) ) ), file(scmfsa6a,d5_scmfsa6a), []). fof(dt_g1_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ), file(ami_1,g1_ami_1), []). fof(dt_k10_scmfsa_2,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => m2_subset_1(k10_scmfsa_2(A,B),k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k10_scmfsa_2), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => m2_subset_1(k13_scmfsa_2(A),k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k13_scmfsa_2), []). fof(dt_k14_scmfsa_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & m1_scmfsa_2(B) ) => m2_subset_1(k14_scmfsa_2(A,B),k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k14_scmfsa_2), []). 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_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_scmfsa6a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_ami_1(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k1_scmfsa6a), []). fof(dt_k1_scmfsa8b,axiom,( ! [A,B,C] : ( ( m1_scmfsa_2(A) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(C) & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k1_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k1_scmfsa8b(A,B,C)) & m1_ami_1(k1_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa8b,k1_scmfsa8b), []). fof(dt_k1_scmfsa_2,axiom, ( v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & l1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,k1_scmfsa_2), []). fof(dt_k1_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_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & m1_ami_1(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k2_scmfsa6a), []). fof(dt_k2_scmfsa8a,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( v1_ami_3(k2_scmfsa8a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa8a(A)) & v1_scmfsa7b(k2_scmfsa8a(A)) & v2_scmfsa7b(k2_scmfsa8a(A)) & m1_ami_1(k2_scmfsa8a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa8a,k2_scmfsa8a), []). fof(dt_k2_scmfsa_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & m1_subset_1(B,k5_numbers) ) => m1_struct_0(k2_scmfsa_4(A,B),k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_4,k2_scmfsa_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_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). 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_k4_scmfsa6a,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & m1_ami_1(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k4_scmfsa6a), []). fof(dt_k4_scmfsa_2,axiom,( ! [A] : ( v4_ordinal2(A) => m1_scmfsa_2(k4_scmfsa_2(A)) ) ), file(scmfsa_2,k4_scmfsa_2), []). fof(dt_k4_scmfsa_4,axiom,( ! [A,B] : ( ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k4_scmfsa_4(A,B),k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_4,k4_scmfsa_4), []). 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_binarith,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k5_binarith(A,B),k1_numbers,k5_numbers) ) ), file(binarith,k5_binarith), []). 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_scmfsa6a,axiom,( ! [A,B] : ( ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & m1_ami_1(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k5_scmfsa6a), []). fof(dt_k5_scmfsa_2,axiom,( ! [A] : ( v4_ordinal2(A) => m1_struct_0(k5_scmfsa_2(A),k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ), file(scmfsa_2,k5_scmfsa_2), []). fof(dt_k5_scmfsa_4,axiom,( m1_ami_1(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ), file(scmfsa_4,k5_scmfsa_4), []). fof(dt_k6_scmfsa6a,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_ami_3(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k6_scmfsa6a(A,B)) & m1_ami_1(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ), file(scmfsa6a,k6_scmfsa6a), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_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_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) ), file(scmfsa_2,m1_scmfsa_2), []). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_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_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_scmfsa_2,axiom,( ? [A] : m1_scmfsa_2(A) ), file(scmfsa_2,m1_scmfsa_2), []). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(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(fc15_scmfsa6c,axiom,( ! [A,B] : ( ( ~ v1_sf_mastr(A) & m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => ( v1_scmfsa6c(k10_scmfsa_2(A,B)) & v2_scmfsa6c(k10_scmfsa_2(A,B)) ) ) ), file(scmfsa6c,fc15_scmfsa6c), []). fof(fc16_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(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_scmfsa6a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k1_scmfsa6a(A)) & v1_funct_1(k1_scmfsa6a(A)) & v1_finset_1(k1_scmfsa6a(A)) & v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k1_scmfsa6a(A)) ) ) ), file(scmfsa6a,fc1_scmfsa6a), []). fof(fc1_scmfsa6c,axiom, ( v3_ami_1(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa6c(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v2_scmfsa6c(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ), file(scmfsa6c,fc1_scmfsa6c), []). fof(fc1_scmfsa_2,axiom, ( ~ v3_struct_0(k1_scmfsa_2) & v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & ~ v2_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,fc1_scmfsa_2), []). fof(fc1_scmfsa_4,axiom, ( ~ v1_xboole_0(k5_scmfsa_4) & v1_relat_1(k5_scmfsa_4) & v1_funct_1(k5_scmfsa_4) & v1_finset_1(k5_scmfsa_4) & v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa_4) ), file(scmfsa_4,fc1_scmfsa_4), []). fof(fc20_scmfsa6c,axiom,( ! [A,B] : ( ( v1_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & v2_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ~ v1_xboole_0(k5_scmfsa6a(A,B)) & v1_relat_1(k5_scmfsa6a(A,B)) & v1_funct_1(k5_scmfsa6a(A,B)) & v1_finset_1(k5_scmfsa6a(A,B)) & v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & v1_scmfsa6b(k5_scmfsa6a(A,B)) & v2_scmfsa6b(k5_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc20_scmfsa6c), []). fof(fc21_scmfsa6c,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa6c(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k6_scmfsa6a(A,B)) & v1_relat_1(k6_scmfsa6a(A,B)) & v1_funct_1(k6_scmfsa6a(A,B)) & v1_finset_1(k6_scmfsa6a(A,B)) & v1_ami_3(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k6_scmfsa6a(A,B)) & v1_scmfsa6b(k6_scmfsa6a(A,B)) & v2_scmfsa6b(k6_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc21_scmfsa6c), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc23_scmfsa6c,axiom,( ! [A,B] : ( ( v2_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & v3_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k5_scmfsa6a(A,B)) & v1_funct_1(k5_scmfsa6a(A,B)) & v1_finset_1(k5_scmfsa6a(A,B)) & v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa6a(A,B)) & v1_scmfsa6b(k5_scmfsa6a(A,B)) & v3_scmfsa6b(k5_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc23_scmfsa6c), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc24_scmfsa6c,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v3_scmfsa6b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v2_scmfsa6c(B) & m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( v1_relat_1(k6_scmfsa6a(A,B)) & v1_funct_1(k6_scmfsa6a(A,B)) & v1_finset_1(k6_scmfsa6a(A,B)) & v1_ami_3(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k6_scmfsa6a(A,B)) & v1_scmfsa6b(k6_scmfsa6a(A,B)) & v3_scmfsa6b(k6_scmfsa6a(A,B)) ) ) ), file(scmfsa6c,fc24_scmfsa6c), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(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_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( ~ v1_xboole_0(k2_scmfsa6a(A)) & v1_relat_1(k2_scmfsa6a(A)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) ) ) ), file(scmfsa6a,fc2_scmfsa6a), []). fof(fc2_scmfsa6b,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & v2_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( ~ v1_xboole_0(k4_scmfsa6a(A,B)) & v1_relat_1(k4_scmfsa6a(A,B)) & v1_funct_1(k4_scmfsa6a(A,B)) & v1_finset_1(k4_scmfsa6a(A,B)) & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & v1_scmfsa6b(k4_scmfsa6a(A,B)) & v2_scmfsa6b(k4_scmfsa6a(A,B)) ) ) ), file(scmfsa6b,fc2_scmfsa6b), []). fof(fc2_scmfsa6c,axiom,( ! [A] : ( ( v1_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k2_scmfsa6a(A)) & v1_relat_1(k2_scmfsa6a(A)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & v1_scmfsa6b(k2_scmfsa6a(A)) & v2_scmfsa6b(k2_scmfsa6a(A)) ) ) ), file(scmfsa6c,fc2_scmfsa6c), []). fof(fc2_scmfsa8a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k1_scmfsa6a(A)) & v1_funct_1(k1_scmfsa6a(A)) & v1_finset_1(k1_scmfsa6a(A)) & v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v2_scmfsa7b(k1_scmfsa6a(A)) ) ) ), file(scmfsa8a,fc2_scmfsa8a), []). fof(fc2_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( v4_ordinal2(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A)) & v1_xreal_0(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A)) & ~ v3_xreal_0(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A)) & v1_int_1(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A)) & v1_xcmplx_0(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A)) ) ) ), file(scmfsa_2,fc2_scmfsa_2), []). 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_scmfsa6b,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v3_scmfsa6b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & v3_scmfsa6b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k4_scmfsa6a(A,B)) & v1_funct_1(k4_scmfsa6a(A,B)) & v1_finset_1(k4_scmfsa6a(A,B)) & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & v1_scmfsa6b(k4_scmfsa6a(A,B)) & v3_scmfsa6b(k4_scmfsa6a(A,B)) ) ) ), file(scmfsa6b,fc3_scmfsa6b), []). fof(fc3_scmfsa6c,axiom,( ! [A] : ( ( v2_scmfsa6c(A) & m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) => ( ~ v1_xboole_0(k2_scmfsa6a(A)) & v1_relat_1(k2_scmfsa6a(A)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) & v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k2_scmfsa6a(A)) & v1_scmfsa6b(k2_scmfsa6a(A)) & v3_scmfsa6b(k2_scmfsa6a(A)) ) ) ), file(scmfsa6c,fc3_scmfsa6c), []). fof(fc3_scmfsa_2,axiom, ( ~ v3_struct_0(k1_scmfsa_2) & v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & ~ v2_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v5_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v6_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v7_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v8_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v10_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,fc3_scmfsa_2), []). fof(fc3_setfam_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)) ) ) ), file(setfam_1,fc3_setfam_1), []). fof(fc3_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_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_scmfsa8a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa7b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k1_scmfsa6a(A)) & v1_funct_1(k1_scmfsa6a(A)) & v1_finset_1(k1_scmfsa6a(A)) & v1_ami_3(k1_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k1_scmfsa6a(A)) & v1_scmfsa7b(k1_scmfsa6a(A)) & v2_scmfsa7b(k1_scmfsa6a(A)) ) ) ), file(scmfsa8a,fc4_scmfsa8a), []). fof(fc4_scmfsa_2,axiom, ( ~ v3_struct_0(k1_scmfsa_2) & v1_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & ~ v2_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v4_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v5_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v6_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v7_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v8_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) & v10_ami_1(k1_scmfsa_2,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))) ), file(scmfsa_2,fc4_scmfsa_2), []). fof(fc4_setfam_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_1), []). fof(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_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(fc6_scmfsa6c,axiom,( ! [A,B] : ( ( m1_scmfsa_2(A) & m1_scmfsa_2(B) ) => v1_scmfsa6c(k10_scmfsa_2(A,B)) ) ), file(scmfsa6c,fc6_scmfsa6c), []). fof(fc6_scmfsa7b,axiom, ( v1_relat_1(k5_scmfsa_4) & v1_funct_1(k5_scmfsa_4) & ~ v1_xboole_0(k5_scmfsa_4) & v1_finset_1(k5_scmfsa_4) & v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k5_scmfsa_4) & v1_scmfsa6b(k5_scmfsa_4) & v2_scmfsa6b(k5_scmfsa_4) & v1_scmfsa7b(k5_scmfsa_4) ), file(scmfsa7b,fc6_scmfsa7b), []). fof(fc6_scmfsa8a,axiom,( ! [A,B] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa7b(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & v1_scmfsa7b(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ( v1_relat_1(k4_scmfsa6a(A,B)) & v1_funct_1(k4_scmfsa6a(A,B)) & v1_finset_1(k4_scmfsa6a(A,B)) & v1_ami_3(k4_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(k4_scmfsa6a(A,B)) & v1_scmfsa7b(k4_scmfsa6a(A,B)) ) ) ), file(scmfsa8a,fc6_scmfsa8a), []). fof(fc6_sf_mastr,axiom,( v1_sf_mastr(k4_scmfsa_2(0)) ), file(sf_mastr,fc6_sf_mastr), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_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(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_scmfsa6b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v2_scmfsa6b(A) ) ), file(scmfsa6b,rc1_scmfsa6b), []). fof(rc1_scmfsa6c,axiom,( ? [A] : ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) & v1_scmfsa6c(A) & v2_scmfsa6c(A) ) ), file(scmfsa6c,rc1_scmfsa6c), []). fof(rc1_scmfsa7b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa7b(A) & v2_scmfsa7b(A) ) ), file(scmfsa7b,rc1_scmfsa7b), []). fof(rc1_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_ami_3(C,A,B) ) ) ), file(scmfsa_4,rc1_scmfsa_4), []). fof(rc1_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_1), []). fof(rc1_sf_mastr,axiom,( ? [A] : ( m1_scmfsa_2(A) & ~ v1_sf_mastr(A) ) ), file(sf_mastr,rc1_sf_mastr), []). fof(rc1_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_scmfsa6b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v2_scmfsa6b(A) & v3_scmfsa6b(A) ) ), file(scmfsa6b,rc2_scmfsa6b), []). fof(rc2_scmfsa7b,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & v1_scmfsa6b(A) & v2_scmfsa6b(A) & v1_scmfsa7b(A) ) ), file(scmfsa7b,rc2_scmfsa7b), []). fof(rc2_scmfsa_4,axiom,( ? [A] : ( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) ) ), file(scmfsa_4,rc2_scmfsa_4), []). fof(rc2_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_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_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) ) ), file(ami_1,rc5_ami_1), []). fof(rc6_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) ) ), file(ami_1,rc6_ami_1), []). fof(rc7_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) ) ), file(ami_1,rc7_ami_1), []). fof(rc8_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc8_ami_1), []). fof(rc9_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc9_ami_1), []). fof(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_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_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). 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_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(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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc5_boole,axiom,( ~ v1_xboole_0(5) ), file(boole,spc5_boole), []). fof(spc5_numerals,axiom, ( v2_xreal_0(5) & m1_subset_1(5,k5_numbers) ), file(numerals,spc5_numerals), []). fof(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(t124_scmfsa_2,axiom,( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = 0 ), file(scmfsa_2,t124_scmfsa_2), []). fof(t13_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(k4_card_1(A),C) => ( r1_xreal_0(k1_nat_1(k4_card_1(A),k4_card_1(B)),C) | ! [D] : ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( D = k1_funct_1(B,k5_scmfsa_2(k5_binarith(C,k4_card_1(A)))) => k1_funct_1(k4_scmfsa6a(A,B),k5_scmfsa_2(C)) = k4_scmfsa_4(D,k4_card_1(A)) ) ) ) ) ) ) ) ), file(scmfsa8c,t13_scmfsa8c), []). fof(t14_scmfsa_4,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => k4_scmfsa_4(k13_scmfsa_2(B),A) = k13_scmfsa_2(k2_scmfsa_4(B,A)) ) ) ), file(scmfsa_4,t14_scmfsa_4), []). fof(t15_scmfsa6a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k4_card_1(A),B) <=> r2_hidden(k5_scmfsa_2(B),k1_relat_1(A)) ) ) ) ), file(scmfsa6a,t15_scmfsa6a), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t28_scmfsa8a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(k4_scmfsa6a(A,B),C) = k1_funct_1(k1_scmfsa6a(A),C) ) ) ) ), file(scmfsa8a,t28_scmfsa8a), []). fof(t29_scmfsa8a,axiom,( ! [A] : ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => k4_card_1(k2_scmfsa8a(A)) = 1 ) ), file(scmfsa8a,t29_scmfsa8a), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t30_scmfsa8a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [B] : ( r2_hidden(B,k1_relat_1(A)) => ( ( k1_funct_1(A,B) = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => k1_funct_1(k1_scmfsa6a(A),B) = k13_scmfsa_2(k5_scmfsa_2(k4_card_1(A))) ) & ( k1_funct_1(A,B) != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) => k1_funct_1(k1_scmfsa6a(A),B) = k1_funct_1(A,B) ) ) ) ) ), file(scmfsa8a,t30_scmfsa8a), []). 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_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(t47_scmfsa8a,axiom,( ! [A] : ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => ( r2_hidden(k5_scmfsa_2(0),k1_relat_1(k2_scmfsa8a(A))) & k1_funct_1(k2_scmfsa8a(A),k5_scmfsa_2(0)) = k13_scmfsa_2(A) ) ) ), file(scmfsa8a,t47_scmfsa8a), []). fof(t47_scmfsa_2,axiom,( ! [A] : ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k13_scmfsa_2(A)) = 6 ) ), file(scmfsa_2,t47_scmfsa_2), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_binarith,axiom,( ! [A] : ( v4_ordinal2(A) => k5_binarith(A,A) = 0 ) ), file(binarith,t51_binarith), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t61_scmfsa6a,axiom,( ! [A] : ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(A) & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => ! [B] : ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) & v1_scmfsa_4(B) & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) => k4_card_1(k4_scmfsa6a(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ), file(scmfsa6a,t61_scmfsa6a), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t6_scmfsa7b,axiom,( ! [A] : ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) => k4_card_1(k2_scmfsa6a(A)) = 2 ) ), file(scmfsa7b,t6_scmfsa7b), []). 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), []).