% Mizar problem: t59_amistd_2,amistd_2,3439,18 fof(t59_amistd_2,conjecture,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & v6_amistd_2(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & v10_amistd_1(C,A,B) & v11_amistd_1(C,A,B) & m1_ami_1(C,A,B) ) => k12_amistd_2(A,B,C,k7_amistd_2(A,B)) = C ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_amistd_2,cc10_membered,cc11_amistd_2,cc11_membered,cc12_amistd_2,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_amistd_1,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_7,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc1_scmfsa_4,cc1_setfam_1,cc1_tex_2,cc1_xreal_0,cc1_yellow13,cc20_membered,cc2_amistd_1,cc2_finset_1,cc2_funct_7,cc2_int_1,cc2_membered,cc2_nat_1,cc2_tex_2,cc2_xreal_0,cc3_amistd_2,cc3_int_1,cc3_membered,cc3_nat_1,cc3_tex_2,cc3_xreal_0,cc4_amistd_1,cc4_amistd_2,cc4_int_1,cc4_membered,cc4_tex_2,cc4_xreal_0,cc5_amistd_1,cc5_tex_2,cc5_xreal_0,cc6_amistd_1,cc6_amistd_2,cc6_membered,cc6_tex_2,cc6_xreal_0,cc7_amistd_2,cc7_tex_2,cc7_xreal_0,cc8_amistd_1,cc8_amistd_2,cc8_xreal_0,cc9_amistd_2,cc9_membered,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,d13_amistd_2,d16_amistd_2,d1_funct_4,d1_tarski,d21_amistd_2,d22_amistd_1,d22_amistd_2,d2_cqc_lang,d2_xboole_0,d3_xboole_0,d7_xboole_0,dt_k10_amistd_1,dt_k10_amistd_2,dt_k11_amistd_2,dt_k12_amistd_2,dt_k13_finseq_1,dt_k14_ami_3,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_scmfsa_4,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_cqc_lang,dt_k3_tarski,dt_k3_xboole_0,dt_k4_card_1,dt_k4_xboole_0,dt_k5_ami_1,dt_k5_amistd_1,dt_k5_binarith,dt_k5_numbers,dt_k5_ordinal2,dt_k6_amistd_2,dt_k7_ami_1,dt_k7_amistd_2,dt_k9_amistd_2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc10_finset_1,fc10_membered,fc10_xreal_0,fc11_finseq_1,fc11_finset_1,fc11_membered,fc11_xreal_0,fc12_finset_1,fc12_membered,fc12_relat_1,fc12_xreal_0,fc13_membered,fc14_finset_1,fc14_membered,fc15_amistd_2,fc15_membered,fc16_amistd_2,fc16_finseq_1,fc16_membered,fc17_finseq_1,fc18_amistd_2,fc1_amistd_1,fc1_amistd_2,fc1_card_4,fc1_finset_1,fc1_funct_7,fc1_int_1,fc1_nat_1,fc1_relat_1,fc1_struct_0,fc1_subset_1,fc1_tex_2,fc1_xboole_0,fc20_amistd_2,fc21_amistd_2,fc22_amistd_2,fc22_membered,fc23_amistd_2,fc23_membered,fc24_amistd_2,fc24_membered,fc25_amistd_2,fc25_membered,fc26_amistd_2,fc26_membered,fc27_membered,fc28_amistd_2,fc28_membered,fc29_amistd_2,fc29_membered,fc2_ami_1,fc2_amistd_1,fc2_amistd_2,fc2_finseq_1,fc2_finset_1,fc2_membered,fc2_relat_1,fc2_setfam_1,fc2_subset_1,fc2_xboole_0,fc30_amistd_2,fc30_membered,fc31_amistd_2,fc31_membered,fc32_amistd_2,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_amistd_2,fc3_funct_7,fc3_nat_1,fc3_relat_1,fc3_setfam_1,fc3_subset_1,fc3_xboole_0,fc3_xreal_0,fc40_membered,fc41_membered,fc4_amistd_2,fc4_nat_1,fc4_relat_1,fc4_setfam_1,fc4_subset_1,fc5_membered,fc5_relat_1,fc6_ami_1,fc6_int_1,fc6_membered,fc6_relat_1,fc7_membered,fc7_relat_1,fc7_xreal_0,fc8_membered,fc8_relat_1,fc8_xreal_0,fc9_amistd_2,fc9_finseq_1,fc9_finset_1,fc9_membered,fc9_xreal_0,fraenkel_a_3_8_amistd_2,fraenkel_a_4_1_amistd_2,idempotence_k1_funct_4,idempotence_k1_scmfsa_4,idempotence_k2_xboole_0,idempotence_k3_xboole_0,l41_amistd_2,l42_amistd_2,l74_amistd_2,rc11_amistd_1,rc1_amistd_1,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_int_1,rc1_membered,rc1_nat_1,rc1_pre_circ,rc1_relat_1,rc1_scmfsa_4,rc1_setfam_1,rc1_subset_1,rc1_tex_2,rc1_xboole_0,rc1_xreal_0,rc2_ami_1,rc2_amistd_1,rc2_amistd_2,rc2_finseq_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_relat_1,rc2_subset_1,rc2_tex_2,rc2_xboole_0,rc2_xreal_0,rc3_ami_1,rc3_amistd_1,rc3_amistd_2,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc3_relat_1,rc3_struct_0,rc3_tex_2,rc3_xreal_0,rc4_ami_1,rc4_finset_1,rc4_tex_2,rc4_xreal_0,rc5_amistd_2,rc5_struct_0,rc5_tex_2,rc6_amistd_1,rc6_finseq_1,rc6_tex_2,rc7_amistd_1,rc7_finseq_1,rc7_tex_2,rc8_amistd_1,rc8_finseq_1,rc9_amistd_1,redefinition_k14_ami_3,redefinition_k1_nat_1,redefinition_k1_scmfsa_4,redefinition_k1_struct_0,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_k7_amistd_2,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,t12_funct_4,t14_funct_4,t1_arithm,t1_boole,t1_numerals,t1_subset,t2_boole,t2_subset,t2_tarski,t3_boole,t3_subset,t48_amistd_2,t4_boole,t4_subset,t50_amistd_2,t55_amistd_1,t57_amistd_2,t58_amistd_2,t5_cqc_lang,t5_subset,t6_boole,t7_boole,t8_boole,t8_grfunc_1,t9_funct_1]), [file(amistd_2,t59_amistd_2)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v6_amistd_2(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v5_amistd_1(C,A,B) => ( ~ v1_xboole_0(C) & v4_amistd_2(C,A,B) & v10_amistd_2(C,A,B) ) ) ) ) ), file(amistd_2,cc10_amistd_2), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & v6_amistd_2(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v3_ami_1(C,A,B) => ( ~ v1_xboole_0(C) & v4_amistd_2(C,A,B) & v10_amistd_2(C,A,B) ) ) ) ) ), file(amistd_2,cc11_amistd_2), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_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) => ( ~ v1_xboole_0(C) & v12_amistd_2(C,A,B) ) ) ) ) ), file(amistd_2,cc12_amistd_2), []). 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_amistd_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(A) & v1_setfam_1(A) ) ) ), file(amistd_1,cc1_amistd_1), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_nat_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) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_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_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_tex_2(B,k1_zfmisc_1(A)) => ~ v1_xboole_0(B) ) ) ) ), file(tex_2,cc1_tex_2), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc1_yellow13,axiom,( ! [A] : ( v1_realset1(A) => v1_finset_1(A) ) ), file(yellow13,cc1_yellow13), []). 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_amistd_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_xboole_0(C) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) ) ) ) ) ), file(amistd_1,cc2_amistd_1), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_nat_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) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ), file(tex_2,cc2_tex_2), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( l1_ami_1(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) ) => ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v7_amistd_2(B,A) ) ) ) ) ), file(amistd_2,cc3_amistd_2), []). 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_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_tex_2(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc3_tex_2), []). 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_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( l1_ami_1(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) ) => ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v3_amistd_1(B,A) ) ) ) ) ), file(amistd_1,cc4_amistd_1), []). fof(cc4_amistd_2,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v8_amistd_2(B,A) => v2_amistd_2(B,A) ) ) ), file(amistd_2,cc4_amistd_2), []). 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_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_xboole_0(B) => ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc4_tex_2), []). 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_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v5_amistd_1(C,A,B) => ( ~ v1_xboole_0(C) & ~ v3_ami_1(C,A,B) ) ) ) ) ), file(amistd_1,cc5_amistd_1), []). fof(cc5_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc5_tex_2), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v3_ami_1(C,A,B) => ( ~ v1_xboole_0(C) & ~ v5_amistd_1(C,A,B) ) ) ) ) ), file(amistd_1,cc6_amistd_1), []). fof(cc6_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v6_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( ~ v1_xboole_0(C) & v4_amistd_2(C,A,B) ) ) ) ), file(amistd_2,cc6_amistd_2), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & v1_realset1(B) ) => ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ), file(tex_2,cc6_tex_2), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v1_realset1(C) ) => ( v1_relat_1(C) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v11_amistd_1(C,A,B) ) ) ) ) ), file(amistd_2,cc7_amistd_2), []). fof(cc7_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) => ( ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ) ) ), file(tex_2,cc7_tex_2), []). 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_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_xboole_0(C) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v9_amistd_1(C,A,B) ) ) ) ) ), file(amistd_1,cc8_amistd_1), []). fof(cc8_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v6_amistd_2(B,A) & v7_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v3_ami_1(C,A,B) => ( ~ v1_xboole_0(C) & v4_amistd_2(C,A,B) & v9_amistd_2(C,A,B) ) ) ) ) ), file(amistd_2,cc8_amistd_2), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v6_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v5_amistd_1(C,A,B) => ( ~ v1_xboole_0(C) & v4_amistd_2(C,A,B) & v9_amistd_2(C,A,B) ) ) ) ) ), file(amistd_2,cc9_amistd_2), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(d13_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => k6_amistd_2(A,B) = k14_ami_3(A,B,k5_amistd_1(A,B,0),k5_ami_1(A,B)) ) ) ), file(amistd_2,d13_amistd_2), []). fof(d16_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ! [D] : ( v4_ordinal2(D) => ! [E] : ( m1_ami_1(E,A,B) => ( E = k10_amistd_2(A,B,C,D) <=> ( k1_relat_1(E) = a_4_1_amistd_2(A,B,C,D) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r2_hidden(k5_amistd_1(A,B,F),k1_relat_1(C)) => k1_funct_1(E,k5_amistd_1(A,B,k2_xcmplx_0(F,D))) = k1_funct_1(C,k5_amistd_1(A,B,F)) ) ) ) ) ) ) ) ) ) ), file(amistd_2,d16_amistd_2), []). fof(d1_funct_4,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) ) => ( C = k1_funct_4(A,B) <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) => ( ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(C,D) = k1_funct_1(B,D) ) & ( ~ r2_hidden(D,k1_relat_1(B)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ), file(funct_4,d1_funct_4), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d21_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => k11_amistd_2(A,B,C) = k4_xboole_0(C,k3_cqc_lang(k10_amistd_1(A,B,C),k1_funct_1(C,k10_amistd_1(A,B,C)))) ) ) ) ), file(amistd_2,d21_amistd_2), []). fof(d22_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => ( v10_amistd_1(C,A,B) <=> k1_funct_1(C,k10_amistd_1(A,B,C)) = k5_ami_1(A,B) ) ) ) ) ), file(amistd_1,d22_amistd_1), []). fof(d22_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => k12_amistd_2(A,B,C,D) = k1_scmfsa_4(A,B,k11_amistd_2(A,B,C),k10_amistd_2(A,B,k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),1)),k5_binarith(k4_card_1(C),1))) ) ) ) ) ), file(amistd_2,d22_amistd_2), []). fof(d2_cqc_lang,axiom,( ! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ), file(cqc_lang,d2_cqc_lang), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). fof(d7_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), []). fof(dt_k10_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => m1_struct_0(k10_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(amistd_1,k10_amistd_1), []). fof(dt_k10_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => m1_ami_1(k10_amistd_2(A,B,C,D),A,B) ) ), file(amistd_2,k10_amistd_2), []). fof(dt_k11_amistd_2,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => m1_ami_1(k11_amistd_2(A,B,C),A,B) ) ), file(amistd_2,k11_amistd_2), []). fof(dt_k12_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & ~ v1_xboole_0(D) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => m1_ami_1(k12_amistd_2(A,B,C,D),A,B) ) ), file(amistd_2,k12_amistd_2), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k14_ami_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => ( v1_ami_3(k14_ami_3(A,B,C,D),A,B) & m1_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) ), file(ami_3,k14_ami_3), []). fof(dt_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_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_scmfsa_4,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => ( v1_ami_3(k1_scmfsa_4(A,B,C,D),A,B) & m1_ami_1(k1_scmfsa_4(A,B,C,D),A,B) ) ) ), file(scmfsa_4,k1_scmfsa_4), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). 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_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). 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_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). 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_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). 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_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & v4_ordinal2(C) ) => m1_struct_0(k5_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(amistd_1,k5_amistd_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_k6_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => m1_ami_1(k6_amistd_2(A,B),A,B) ) ), file(amistd_2,k6_amistd_2), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( ~ v1_xboole_0(k7_amistd_2(A,B)) & v1_ami_3(k7_amistd_2(A,B),A,B) & v9_amistd_1(k7_amistd_2(A,B),A,B) & v10_amistd_1(k7_amistd_2(A,B),A,B) & v11_amistd_1(k7_amistd_2(A,B),A,B) & m1_ami_1(k7_amistd_2(A,B),A,B) ) ) ), file(amistd_2,k7_amistd_2), []). fof(dt_k9_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => m1_ami_1(k9_amistd_2(A,B,C,D),A,B) ) ), file(amistd_2,k9_amistd_2), []). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ), file(ami_1,m1_ami_1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_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(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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k7_ami_1(A)) & v1_fraenkel(k7_ami_1(A)) ) ) ), file(ami_1,fc10_ami_1), []). fof(fc10_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). 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_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). 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_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( v1_relat_1(k6_amistd_2(A,B)) & v1_funct_1(k6_amistd_2(A,B)) & ~ v1_xboole_0(k6_amistd_2(A,B)) & v1_finset_1(k6_amistd_2(A,B)) & v1_setfam_1(k6_amistd_2(A,B)) & v1_ami_3(k6_amistd_2(A,B),A,B) & v9_amistd_1(k6_amistd_2(A,B),A,B) & v11_amistd_1(k6_amistd_2(A,B),A,B) & v1_realset1(k6_amistd_2(A,B)) ) ) ), file(amistd_2,fc15_amistd_2), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( v1_relat_1(k6_amistd_2(A,B)) & v1_funct_1(k6_amistd_2(A,B)) & ~ v1_xboole_0(k6_amistd_2(A,B)) & v1_finset_1(k6_amistd_2(A,B)) & v1_setfam_1(k6_amistd_2(A,B)) & v1_ami_3(k6_amistd_2(A,B),A,B) & v6_amistd_1(k6_amistd_2(A,B),A,B) & v9_amistd_1(k6_amistd_2(A,B),A,B) & v11_amistd_1(k6_amistd_2(A,B),A,B) & v1_realset1(k6_amistd_2(A,B)) ) ) ), file(amistd_2,fc16_amistd_2), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc18_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( v1_relat_1(k6_amistd_2(A,B)) & v1_funct_1(k6_amistd_2(A,B)) & ~ v1_xboole_0(k6_amistd_2(A,B)) & v1_finset_1(k6_amistd_2(A,B)) & v1_setfam_1(k6_amistd_2(A,B)) & v1_ami_3(k6_amistd_2(A,B),A,B) & v9_amistd_1(k6_amistd_2(A,B),A,B) & v10_amistd_1(k6_amistd_2(A,B),A,B) & v11_amistd_1(k6_amistd_2(A,B),A,B) & v1_realset1(k6_amistd_2(A,B)) ) ) ), file(amistd_2,fc18_amistd_2), []). fof(fc1_amistd_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k2_funcop_1(A,B)) ) ), file(amistd_1,fc1_amistd_1), []). fof(fc1_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & ~ v1_xboole_0(k1_funct_4(A,B)) & v1_setfam_1(k1_funct_4(A,B)) ) ) ), file(amistd_2,fc1_amistd_2), []). fof(fc1_card_4,axiom, ( ~ v1_xboole_0(k5_ordinal2) & v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_finset_1(k5_ordinal2) & v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(card_4,fc1_card_4), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_funct_7,axiom,( ! [A,B] : ( ~ v1_xboole_0(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) ) ), file(funct_7,fc1_funct_7), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_1), []). 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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(tex_2,fc1_tex_2), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc20_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc20_amistd_2), []). fof(fc21_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & v1_xboole_0(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) & v1_membered(k9_amistd_2(A,B,C,D)) & v2_membered(k9_amistd_2(A,B,C,D)) & v3_membered(k9_amistd_2(A,B,C,D)) & v4_membered(k9_amistd_2(A,B,C,D)) & v5_membered(k9_amistd_2(A,B,C,D)) & v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc21_amistd_2), []). fof(fc22_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & ~ v1_xboole_0(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc22_amistd_2), []). 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_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k9_amistd_2(A,B,C,D)) & v1_funct_1(k9_amistd_2(A,B,C,D)) & v1_finset_1(k9_amistd_2(A,B,C,D)) & v1_setfam_1(k9_amistd_2(A,B,C,D)) & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) & v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc23_amistd_2), []). 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(fc24_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k10_amistd_2(A,B,C,D)) & v1_funct_1(k10_amistd_2(A,B,C,D)) & v1_finset_1(k10_amistd_2(A,B,C,D)) & v1_setfam_1(k10_amistd_2(A,B,C,D)) & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc24_amistd_2), []). 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(fc25_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & v1_xboole_0(C) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k10_amistd_2(A,B,C,D)) & v1_funct_1(k10_amistd_2(A,B,C,D)) & v1_xboole_0(k10_amistd_2(A,B,C,D)) & v1_finset_1(k10_amistd_2(A,B,C,D)) & v1_setfam_1(k10_amistd_2(A,B,C,D)) & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) & v1_membered(k10_amistd_2(A,B,C,D)) & v2_membered(k10_amistd_2(A,B,C,D)) & v3_membered(k10_amistd_2(A,B,C,D)) & v4_membered(k10_amistd_2(A,B,C,D)) & v5_membered(k10_amistd_2(A,B,C,D)) & v9_amistd_1(k10_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc25_amistd_2), []). 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_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v4_ordinal2(D) ) => ( v1_relat_1(k10_amistd_2(A,B,C,D)) & v1_funct_1(k10_amistd_2(A,B,C,D)) & ~ v1_xboole_0(k10_amistd_2(A,B,C,D)) & v1_finset_1(k10_amistd_2(A,B,C,D)) & v1_setfam_1(k10_amistd_2(A,B,C,D)) & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc26_amistd_2), []). 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_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_amistd_2,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v1_realset1(C) & m1_ami_1(C,A,B) ) => ( v1_relat_1(k11_amistd_2(A,B,C)) & v1_funct_1(k11_amistd_2(A,B,C)) & v1_xboole_0(k11_amistd_2(A,B,C)) & v1_finset_1(k11_amistd_2(A,B,C)) & v1_setfam_1(k11_amistd_2(A,B,C)) & v1_ami_3(k11_amistd_2(A,B,C),A,B) & v1_membered(k11_amistd_2(A,B,C)) & v2_membered(k11_amistd_2(A,B,C)) & v3_membered(k11_amistd_2(A,B,C)) & v4_membered(k11_amistd_2(A,B,C)) & v5_membered(k11_amistd_2(A,B,C)) & v9_amistd_1(k11_amistd_2(A,B,C),A,B) ) ) ), file(amistd_2,fc28_amistd_2), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc29_amistd_2,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => ( v1_relat_1(k11_amistd_2(A,B,C)) & v1_funct_1(k11_amistd_2(A,B,C)) & v1_finset_1(k11_amistd_2(A,B,C)) & v1_setfam_1(k11_amistd_2(A,B,C)) & v1_ami_3(k11_amistd_2(A,B,C),A,B) ) ) ), file(amistd_2,fc29_amistd_2), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_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_amistd_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) & v1_realset1(k3_cqc_lang(A,B)) & v1_setfam_1(k3_cqc_lang(A,B)) ) ), file(amistd_1,fc2_amistd_1), []). fof(fc2_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) ) => ( v1_relat_1(k1_funct_4(B,A)) & v1_funct_1(k1_funct_4(B,A)) & ~ v1_xboole_0(k1_funct_4(B,A)) & v1_setfam_1(k1_funct_4(B,A)) ) ) ), file(amistd_2,fc2_amistd_2), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) ), file(relat_1,fc2_relat_1), []). 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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc30_amistd_2,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & m1_ami_1(C,A,B) ) => ( v1_relat_1(k11_amistd_2(A,B,C)) & v1_funct_1(k11_amistd_2(A,B,C)) & v1_finset_1(k11_amistd_2(A,B,C)) & v1_setfam_1(k11_amistd_2(A,B,C)) & v1_ami_3(k11_amistd_2(A,B,C),A,B) & v9_amistd_1(k11_amistd_2(A,B,C),A,B) ) ) ), file(amistd_2,fc30_amistd_2), []). fof(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & ~ v1_xboole_0(D) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => ( v1_relat_1(k12_amistd_2(A,B,C,D)) & v1_funct_1(k12_amistd_2(A,B,C,D)) & ~ v1_xboole_0(k12_amistd_2(A,B,C,D)) & v1_finset_1(k12_amistd_2(A,B,C,D)) & v1_setfam_1(k12_amistd_2(A,B,C,D)) & v1_ami_3(k12_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc31_amistd_2), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & m1_ami_1(C,A,B) & ~ v1_xboole_0(D) & v1_ami_3(D,A,B) & v9_amistd_1(D,A,B) & m1_ami_1(D,A,B) ) => ( v1_relat_1(k12_amistd_2(A,B,C,D)) & v1_funct_1(k12_amistd_2(A,B,C,D)) & ~ v1_xboole_0(k12_amistd_2(A,B,C,D)) & v1_finset_1(k12_amistd_2(A,B,C,D)) & v1_setfam_1(k12_amistd_2(A,B,C,D)) & v1_ami_3(k12_amistd_2(A,B,C,D),A,B) & v9_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) ), file(amistd_2,fc32_amistd_2), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). fof(fc3_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & v1_finset_1(k1_funct_4(A,B)) & v1_setfam_1(k1_funct_4(A,B)) ) ) ), file(amistd_2,fc3_amistd_2), []). fof(fc3_funct_7,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k4_xboole_0(A,B)) ) ), file(relat_1,fc3_relat_1), []). 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_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc4_amistd_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k4_xboole_0(A,B)) & v1_funct_1(k4_xboole_0(A,B)) & v1_setfam_1(k4_xboole_0(A,B)) ) ) ), file(amistd_2,fc4_amistd_2), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). 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_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_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_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). 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_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v7_amistd_2(B,A) & l1_ami_1(B,A) ) => ~ v1_realset1(u2_ami_1(A,B)) ) ), file(amistd_2,fc9_amistd_2), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_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(fraenkel_a_3_8_amistd_2,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v4_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v10_ami_1(C,B) & v4_amistd_1(C,B) & v6_amistd_2(C,B) & v8_amistd_2(C,B) & l1_ami_1(C,B) & ~ v1_xboole_0(D) & v1_ami_3(D,B,C) & v9_amistd_1(D,B,C) & v10_amistd_1(D,B,C) & v11_amistd_1(D,B,C) & m1_ami_1(D,B,C) ) => ( r2_hidden(A,a_3_8_amistd_2(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & A = k5_amistd_1(B,C,k1_nat_1(E,k5_binarith(k4_card_1(D),1))) & r2_hidden(k5_amistd_1(B,C,E),k1_relat_1(k7_amistd_2(B,C))) ) ) ) ), file(amistd_2,a_3_8_amistd_2), []). fof(fraenkel_a_4_1_amistd_2,axiom,( ! [A,B,C,D,E] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) & m1_ami_1(D,B,C) & v4_ordinal2(E) ) => ( r2_hidden(A,a_4_1_amistd_2(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & A = k5_amistd_1(B,C,k2_xcmplx_0(F,E)) & r2_hidden(k5_amistd_1(B,C,F),k1_relat_1(D)) ) ) ) ), file(amistd_2,a_4_1_amistd_2), []). fof(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(idempotence_k1_scmfsa_4,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => k1_scmfsa_4(A,B,C,C) = C ) ), file(scmfsa_4,k1_scmfsa_4), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(l41_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( k1_relat_1(k6_amistd_2(A,B)) = k1_struct_0(B,k5_amistd_1(A,B,0)) & r2_hidden(k5_amistd_1(A,B,0),k1_relat_1(k6_amistd_2(A,B))) ) ) ) ), file(amistd_2,l41_amistd_2), []). fof(l42_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => k1_funct_1(k6_amistd_2(A,B),k5_amistd_1(A,B,0)) = k5_ami_1(A,B) ) ) ), file(amistd_2,l42_amistd_2), []). fof(l74_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => r1_tarski(k11_amistd_2(A,B,C),C) ) ) ) ), file(amistd_2,l74_amistd_2), []). fof(rc11_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v6_amistd_1(C,A,B) & v9_amistd_1(C,A,B) & v10_amistd_1(C,A,B) & v11_amistd_1(C,A,B) ) ) ), file(amistd_1,rc11_amistd_1), []). fof(rc1_amistd_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & ~ v1_realset1(A) ) ), file(amistd_1,rc1_amistd_1), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_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_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). 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_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_tex_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(tex_2,rc1_tex_2), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), []). fof(rc2_amistd_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v1_membered(C) & v2_membered(C) & v3_membered(C) & v4_membered(C) & v5_membered(C) ) ) ), file(amistd_1,rc2_amistd_1), []). fof(rc2_amistd_2,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)) & ~ v1_xboole_0(C) & v3_ami_1(C,A,B) ) ) ), file(amistd_2,rc2_amistd_2), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_tex_2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ), file(tex_2,rc2_tex_2), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) ) ) ), file(ami_1,rc3_ami_1), []). fof(rc3_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) ) ) ), file(amistd_1,rc3_amistd_1), []). fof(rc3_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v3_amistd_1(B,A) & v4_amistd_1(B,A) & v7_amistd_2(B,A) ) ) ), file(amistd_2,rc3_amistd_2), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc3_tex_2), []). 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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc4_tex_2), []). 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_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v7_amistd_2(B,A) & 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_setfam_1(C) & v1_ami_3(C,A,B) & ~ v1_realset1(C) ) ) ), file(amistd_2,rc5_amistd_2), []). 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(rc5_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) ) ) ), file(tex_2,rc5_tex_2), []). fof(rc6_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) ) ) ), file(amistd_1,rc6_amistd_1), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc6_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc6_tex_2), []). fof(rc7_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & v10_amistd_1(C,A,B) & v11_amistd_1(C,A,B) ) ) ), file(amistd_1,rc7_amistd_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_tex_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_realset1(B) & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ), file(tex_2,rc7_tex_2), []). fof(rc8_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v6_amistd_1(C,A,B) & v9_amistd_1(C,A,B) ) ) ), file(amistd_1,rc8_amistd_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(rc9_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v6_amistd_1(C,A,B) & v9_amistd_1(C,A,B) & v10_amistd_1(C,A,B) & v11_amistd_1(C,A,B) ) ) ), file(amistd_1,rc9_amistd_1), []). fof(redefinition_k14_ami_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => k14_ami_3(A,B,C,D) = k3_cqc_lang(C,D) ) ), file(ami_3,k14_ami_3), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_scmfsa_4,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => k1_scmfsa_4(A,B,C,D) = k1_funct_4(C,D) ) ), file(scmfsa_4,k1_scmfsa_4), []). fof(redefinition_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). 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_k7_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => k7_amistd_2(A,B) = k6_amistd_2(A,B) ) ), file(amistd_2,k7_amistd_2), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(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(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(t12_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ~ r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ), file(funct_4,t12_funct_4), []). fof(t14_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ), file(funct_4,t14_funct_4), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). 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_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t48_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => k1_relat_1(C) = k2_xboole_0(k1_relat_1(k11_amistd_2(A,B,C)),k1_struct_0(B,k10_amistd_1(A,B,C))) ) ) ) ), file(amistd_2,t48_amistd_2), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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(t50_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & v8_amistd_2(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & m1_ami_1(C,A,B) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_ami_3(D,A,B) & m1_ami_1(D,A,B) ) => r1_xboole_0(k1_relat_1(k11_amistd_2(A,B,C)),k1_relat_1(k10_amistd_2(A,B,k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),1)),k5_binarith(k4_card_1(C),1)))) ) ) ) ) ), file(amistd_2,t50_amistd_2), []). fof(t55_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & m1_ami_1(C,A,B) ) => k10_amistd_1(A,B,C) = k5_amistd_1(A,B,k5_binarith(k4_card_1(C),1)) ) ) ) ), file(amistd_1,t55_amistd_1), []). fof(t57_amistd_2,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v4_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v10_ami_1(C,B) & v4_amistd_1(C,B) & v6_amistd_2(C,B) & v8_amistd_2(C,B) & l1_ami_1(C,B) ) => k9_amistd_2(B,C,k7_amistd_2(B,C),A) = k7_amistd_2(B,C) ) ) ) ), file(amistd_2,t57_amistd_2), []). fof(t58_amistd_2,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v1_setfam_1(B) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v4_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) ) => k10_amistd_2(B,C,k7_amistd_2(B,C),A) = k14_ami_3(B,C,k5_amistd_1(B,C,A),k5_ami_1(B,C)) ) ) ) ), file(amistd_2,t58_amistd_2), []). fof(t5_cqc_lang,axiom,( ! [A,B] : ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A) & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ), file(cqc_lang,t5_cqc_lang), []). 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(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ), file(grfunc_1,t8_grfunc_1), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []).