% Mizar problem: t18_glib_004,glib_004,1037,60 fof(t18_glib_004,conjecture,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r1_tarski(k14_glib_003(k42_glib_000(k5_glib_004(A,B),C)),k2_glib_002(A,B)) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_abian,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_glib_003,cc2_int_1,cc2_membered,cc2_xreal_0,cc3_card_1,cc3_glib_003,cc3_int_1,cc3_membered,cc3_polynom1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_polynom1,cc4_xreal_0,cc5_polynom1,cc5_xreal_0,cc6_membered,cc6_polynom1,cc6_xreal_0,cc7_xreal_0,cc8_glib_003,cc8_xreal_0,cc9_glib_003,cc9_membered,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_real_1,connectedness_r1_xreal_0,d16_glib_000,d18_glib_000,d23_glib_003,d36_glib_000,d3_tarski,d4_glib_004,d5_glib_004,d6_glib_004,d7_glib_004,dt_k10_glib_000,dt_k11_glib_000,dt_k12_glib_003,dt_k13_glib_000,dt_k13_glib_003,dt_k14_glib_003,dt_k1_card_fil,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_seq_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_glib_002,dt_k2_glib_004,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_cqc_lang,dt_k3_glib_003,dt_k3_glib_004,dt_k3_real_1,dt_k42_glib_000,dt_k4_glib_003,dt_k4_glib_004,dt_k4_xboole_0,dt_k5_glib_003,dt_k5_glib_004,dt_k5_numbers,dt_k5_ordinal2,dt_k6_domain_1,dt_k6_glib_000,dt_k7_glib_000,dt_k7_glib_003,dt_k8_glib_000,dt_k8_subset_1,dt_k9_glib_000,dt_m1_glib_000,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_glib_000,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc100_glib_003,fc10_glib_000,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_finset_1,fc12_relat_1,fc12_xreal_0,fc14_finset_1,fc14_polynom1,fc17_abian,fc1_finset_1,fc1_glib_000,fc1_glib_002,fc1_glib_004,fc1_int_1,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc20_polynom1,fc29_glib_003,fc2_glib_000,fc2_membered,fc2_subset_1,fc30_glib_003,fc34_glib_003,fc35_glib_003,fc36_glib_003,fc37_membered,fc38_glib_003,fc38_membered,fc39_glib_003,fc39_membered,fc3_glib_003,fc3_glib_004,fc3_polynom1,fc3_relat_1,fc3_xreal_0,fc40_glib_003,fc40_membered,fc41_glib_003,fc41_membered,fc42_glib_003,fc44_glib_003,fc45_glib_003,fc46_glib_003,fc47_glib_003,fc48_glib_003,fc49_glib_003,fc4_glib_000,fc4_glib_003,fc4_relat_1,fc4_subset_1,fc50_glib_003,fc51_glib_003,fc52_glib_003,fc54_glib_003,fc55_glib_003,fc57_glib_003,fc58_glib_003,fc59_glib_003,fc5_glib_000,fc5_membered,fc5_polynom1,fc5_relat_1,fc63_glib_003,fc65_glib_003,fc66_glib_003,fc6_glib_003,fc6_int_1,fc6_membered,fc74_glib_003,fc75_glib_003,fc76_glib_003,fc78_glib_003,fc79_glib_003,fc7_glib_003,fc7_membered,fc7_relat_1,fc7_xreal_0,fc80_glib_003,fc88_glib_003,fc89_glib_003,fc8_membered,fc8_xreal_0,fc90_glib_003,fc92_glib_003,fc93_glib_003,fc94_glib_003,fc95_glib_003,fc96_glib_003,fc97_glib_003,fc99_glib_003,fc9_membered,fc9_xreal_0,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc1_card_1,rc1_finset_1,rc1_funct_1,rc1_glib_000,rc1_glib_003,rc1_int_1,rc1_membered,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc20_glib_003,rc2_card_1,rc2_finset_1,rc2_funct_1,rc2_int_1,rc2_polynom1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc2_xreal_0,rc3_finset_1,rc3_funct_1,rc3_relat_1,rc3_xreal_0,rc4_finset_1,rc4_funct_1,rc4_xreal_0,rc6_glib_000,rc7_polynom1,rc8_polynom1,rc9_polynom1,redefinition_k10_glib_000,redefinition_k11_glib_000,redefinition_k1_card_fil,redefinition_k1_nat_1,redefinition_k1_seq_1,redefinition_k3_real_1,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r5_glib_000,s1_nat_1__e7_31__glib_004,spc0_boole,spc1_boole,spc1_numerals,symmetry_r5_glib_000,t15_glib_004,t17_glib_004,t18_glib_002,t19_glib_002,t1_arithm,t1_numerals,t1_real,t1_subset,t2_real,t2_subset,t37_zfmisc_1,t3_boole,t3_real,t3_subset,t43_glib_003,t4_boole,t4_real,t4_subset,t5_real,t5_subset,t62_glib_003,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]), [file(glib_004,t18_glib_004)]). 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_abian,axiom,( ! [A] : ( v2_setfam_1(A) => v1_realset1(A) ) ), file(abian,cc1_abian), []). fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(card_1,cc1_card_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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_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_card_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_card_1(A) ) ) ), file(card_1,cc2_card_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_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_glib_003,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) ) => ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & v10_glib_003(A) ) ) ) ), file(glib_003,cc2_glib_003), []). fof(cc2_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_card_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_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_glib_003,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & v10_glib_003(A) ) => ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) ) ) ) ), file(glib_003,cc3_glib_003), []). 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_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ) ), file(polynom1,cc3_polynom1), []). 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_polynom1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k5_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v7_seqm_3(B) ) ) ) ), file(polynom1,cc4_polynom1), []). 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_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) ) ), file(polynom1,cc5_polynom1), []). 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_polynom1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_pboole(B,A) => v1_polynom1(B) ) ) ), file(polynom1,cc6_polynom1), []). 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_glib_003,axiom,( ! [A] : ( m1_pboole(A,k5_numbers) => ( ( v12_glib_000(A) & v12_glib_003(A) & v13_glib_003(A) & v14_glib_003(A) & v19_glib_003(A) ) => ( v12_glib_000(A) & v12_glib_003(A) & v13_glib_003(A) & v14_glib_003(A) & v15_glib_003(A) & v17_glib_003(A) & v18_glib_003(A) ) ) ) ), file(glib_003,cc8_glib_003), []). 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_glib_003,axiom,( ! [A] : ( m1_pboole(A,k5_numbers) => ( ( v12_glib_000(A) & v12_glib_003(A) & v13_glib_003(A) & v14_glib_003(A) & v15_glib_003(A) & v17_glib_003(A) & v18_glib_003(A) ) => ( v12_glib_000(A) & v12_glib_003(A) & v13_glib_003(A) & v14_glib_003(A) & v19_glib_003(A) ) ) ) ), file(glib_003,cc9_glib_003), []). 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_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). fof(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(d16_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r2_glib_000(A,B,C,D) <=> ( r2_hidden(D,k7_glib_000(A)) & k1_funct_1(k10_glib_000(A),D) = B & k1_funct_1(k11_glib_000(A),D) = C ) ) ) ), file(glib_000,d16_glib_000), []). fof(d18_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r4_glib_000(A,B,C,D) <=> ( r2_hidden(D,k7_glib_000(A)) & r2_hidden(k1_funct_1(k10_glib_000(A),D),B) & r2_hidden(k1_funct_1(k11_glib_000(A),D),C) ) ) ) ), file(glib_000,d18_glib_000), []). fof(d23_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => k14_glib_003(A) = k1_relat_1(k7_glib_003(A)) ) ), file(glib_003,d23_glib_003), []). fof(d36_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ( r5_glib_000(A,B) <=> ( k6_glib_000(A) = k6_glib_000(B) & k7_glib_000(A) = k7_glib_000(B) & k10_glib_000(A) = k10_glib_000(B) & k11_glib_000(A) = k11_glib_000(B) ) ) ) ) ), file(glib_000,d36_glib_000), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k7_glib_000(A))) => ( B = k2_glib_004(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r4_glib_000(A,k14_glib_003(A),k1_card_fil(k6_glib_000(A),k14_glib_003(A)),C) & ! [D] : ( r4_glib_000(A,k14_glib_003(A),k1_card_fil(k6_glib_000(A),k14_glib_003(A)),D) => r1_xreal_0(k3_real_1(k1_seq_1(k7_glib_003(A),k1_funct_1(k10_glib_000(A),C)),k1_seq_1(k5_glib_003(A),C)),k3_real_1(k1_seq_1(k7_glib_003(A),k1_funct_1(k10_glib_000(A),D)),k1_seq_1(k5_glib_003(A),D))) ) ) ) ) ) ) ), file(glib_004,d4_glib_004), []). fof(d5_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) & m1_glib_000(A) ) => ( ( k2_glib_004(A) = k1_xboole_0 => k3_glib_004(A) = A ) & ( k2_glib_004(A) != k1_xboole_0 => k3_glib_004(A) = k13_glib_003(k12_glib_003(A,k8_subset_1(k2_glib_004(A)),1),k1_funct_1(k11_glib_000(A),k8_subset_1(k2_glib_004(A))),k3_real_1(k1_seq_1(k7_glib_003(A),k1_funct_1(k10_glib_000(A),k8_subset_1(k2_glib_004(A)))),k1_seq_1(k5_glib_003(A),k8_subset_1(k2_glib_004(A))))) ) ) ) ), file(glib_004,d5_glib_004), []). fof(d6_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k4_glib_004(A,B) = k13_glib_000(k13_glib_000(A,k3_glib_003,k1_xboole_0),k4_glib_003,k3_cqc_lang(B,0)) ) ) ), file(glib_004,d6_glib_004), []). fof(d7_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( ( v12_glib_000(C) & v12_glib_003(C) & v13_glib_003(C) & v14_glib_003(C) & v19_glib_003(C) & m1_pboole(C,k5_numbers) ) => ( C = k5_glib_004(A,B) <=> ( k42_glib_000(C,0) = k4_glib_004(A,B) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k42_glib_000(C,k1_nat_1(D,1)) = k3_glib_004(k42_glib_000(C,D)) ) ) ) ) ) ) ), file(glib_004,d7_glib_004), []). fof(dt_k10_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_funct_1(k10_glib_000(A)) & v1_funct_2(k10_glib_000(A),k7_glib_000(A),k6_glib_000(A)) & m2_relset_1(k10_glib_000(A),k7_glib_000(A),k6_glib_000(A)) ) ) ), file(glib_000,k10_glib_000), []). fof(dt_k11_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_funct_1(k11_glib_000(A)) & v1_funct_2(k11_glib_000(A),k7_glib_000(A),k6_glib_000(A)) & m2_relset_1(k11_glib_000(A),k7_glib_000(A),k6_glib_000(A)) ) ) ), file(glib_000,k11_glib_000), []). fof(dt_k12_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) & m1_glib_000(k12_glib_003(A,B,C)) ) ) ), file(glib_003,k12_glib_003), []). fof(dt_k13_glib_000,axiom,( ! [A,B,C] : ( ( m1_glib_000(A) & m1_subset_1(B,k5_numbers) ) => m1_glib_000(k13_glib_000(A,B,C)) ) ), file(glib_000,k13_glib_000), []). fof(dt_k13_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_glib_000(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) & m1_glib_000(k13_glib_003(A,B,C)) ) ) ), file(glib_003,k13_glib_003), []). fof(dt_k14_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => m1_subset_1(k14_glib_003(A),k1_zfmisc_1(k6_glib_000(A))) ) ), file(glib_003,k14_glib_003), []). fof(dt_k1_card_fil,axiom,( ! [A,B] : m1_subset_1(k1_card_fil(A,B),k1_zfmisc_1(A)) ), file(card_fil,k1_card_fil), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => m1_subset_1(k1_seq_1(A,B),k1_numbers) ) ), file(seq_1,k1_seq_1), []). 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_glib_002,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( ~ v1_xboole_0(k2_glib_002(A,B)) & m1_subset_1(k2_glib_002(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ) ), file(glib_002,k2_glib_002), []). fof(dt_k2_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) & m1_glib_000(A) ) => m1_subset_1(k2_glib_004(A),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_004,k2_glib_004), []). 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_glib_003,axiom,( m2_subset_1(k3_glib_003,k1_numbers,k5_numbers) ), file(glib_003,k3_glib_003), []). fof(dt_k3_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) & m1_glib_000(A) ) => ( v1_glib_000(k3_glib_004(A)) & v1_glib_003(k3_glib_004(A)) & v2_glib_003(k3_glib_004(A)) & v3_glib_003(k3_glib_004(A)) & v11_glib_003(k3_glib_004(A)) & m1_glib_000(k3_glib_004(A)) ) ) ), file(glib_004,k3_glib_004), []). fof(dt_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k42_glib_000,axiom,( ! [A,B] : ( ( v12_glib_000(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_glib_000(k42_glib_000(A,B)) & m1_glib_000(k42_glib_000(A,B)) ) ) ), file(glib_000,k42_glib_000), []). fof(dt_k4_glib_003,axiom,( m2_subset_1(k4_glib_003,k1_numbers,k5_numbers) ), file(glib_003,k4_glib_003), []). fof(dt_k4_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( v1_glib_000(k4_glib_004(A,B)) & v1_glib_003(k4_glib_004(A,B)) & v2_glib_003(k4_glib_004(A,B)) & v3_glib_003(k4_glib_004(A,B)) & v11_glib_003(k4_glib_004(A,B)) & m1_glib_000(k4_glib_004(A,B)) ) ) ), file(glib_004,k4_glib_004), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k5_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => m1_pboole(k5_glib_003(A),k7_glib_000(A)) ) ), file(glib_003,k5_glib_003), []). fof(dt_k5_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( v12_glib_000(k5_glib_004(A,B)) & v12_glib_003(k5_glib_004(A,B)) & v13_glib_003(k5_glib_004(A,B)) & v14_glib_003(k5_glib_004(A,B)) & v19_glib_003(k5_glib_004(A,B)) & m1_pboole(k5_glib_004(A,B),k5_numbers) ) ) ), file(glib_004,k5_glib_004), []). 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_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), []). fof(dt_k6_glib_000,axiom,( $true ), file(glib_000,k6_glib_000), []). fof(dt_k7_glib_000,axiom,( $true ), file(glib_000,k7_glib_000), []). fof(dt_k7_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k7_glib_003(A)) & v1_funct_1(k7_glib_003(A)) ) ) ), file(glib_003,k7_glib_003), []). fof(dt_k8_glib_000,axiom,( $true ), file(glib_000,k8_glib_000), []). fof(dt_k8_subset_1,axiom,( ! [A] : m1_subset_1(k8_subset_1(A),A) ), file(subset_1,k8_subset_1), []). fof(dt_k9_glib_000,axiom,( $true ), file(glib_000,k9_glib_000), []). fof(dt_m1_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(glib_000,m1_glib_000), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). 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(existence_m1_glib_000,axiom,( ? [A] : m1_glib_000(A) ), file(glib_000,m1_glib_000), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). 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(fc100_glib_003,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v14_glib_003(A) & v18_glib_003(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_polynom1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v3_glib_003(k42_glib_000(A,B)) & v10_glib_003(k42_glib_000(A,B)) ) ) ), file(glib_003,fc100_glib_003), []). fof(fc10_glib_000,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v14_glib_000(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v2_glib_000(k42_glib_000(A,B)) ) ) ), file(glib_000,fc10_glib_000), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_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_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(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_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(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) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) ), file(polynom1,fc14_polynom1), []). fof(fc17_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_zfmisc_1(A)) & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ), file(abian,fc17_abian), []). 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_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ~ v1_xboole_0(k6_glib_000(A)) ) ), file(glib_000,fc1_glib_000), []). fof(fc1_glib_002,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A)) ) ), file(glib_002,fc1_glib_002), []). fof(fc1_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) & v11_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k3_glib_004(A)) & v1_funct_1(k3_glib_004(A)) & v1_finset_1(k3_glib_004(A)) & v1_polynom1(k3_glib_004(A)) & v1_glib_000(k3_glib_004(A)) & v2_glib_000(k3_glib_004(A)) & v1_glib_003(k3_glib_004(A)) & v2_glib_003(k3_glib_004(A)) & v3_glib_003(k3_glib_004(A)) & v7_glib_003(k3_glib_004(A)) & v9_glib_003(k3_glib_004(A)) & v10_glib_003(k3_glib_004(A)) & v11_glib_003(k3_glib_004(A)) ) ) ), file(glib_004,fc1_glib_004), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc20_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(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) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) & v1_polynom1(k1_xboole_0) ), file(polynom1,fc20_polynom1), []). fof(fc29_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v1_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc29_glib_003), []). fof(fc2_glib_000,axiom,( ! [A,B] : ( v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) & v1_finset_1(k3_cqc_lang(A,B)) ) ), file(glib_000,fc2_glib_000), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc30_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v1_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc30_glib_003), []). fof(fc34_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v2_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc34_glib_003), []). fof(fc35_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_funct_1(C) & m1_relset_1(C,k7_glib_000(A),B) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,C)) & v1_funct_1(k13_glib_000(A,k3_glib_003,C)) & v1_finset_1(k13_glib_000(A,k3_glib_003,C)) & v1_polynom1(k13_glib_000(A,k3_glib_003,C)) & v1_glib_000(k13_glib_000(A,k3_glib_003,C)) & v2_glib_003(k13_glib_000(A,k3_glib_003,C)) ) ) ), file(glib_003,fc35_glib_003), []). fof(fc36_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_pboole(B,k7_glib_000(A)) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v2_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc36_glib_003), []). fof(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v3_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc38_glib_003), []). 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_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_funct_1(C) & m1_relset_1(C,k6_glib_000(A),B) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,C)) & v1_funct_1(k13_glib_000(A,k4_glib_003,C)) & v1_finset_1(k13_glib_000(A,k4_glib_003,C)) & v1_polynom1(k13_glib_000(A,k4_glib_003,C)) & v1_glib_000(k13_glib_000(A,k4_glib_003,C)) & v3_glib_003(k13_glib_000(A,k4_glib_003,C)) ) ) ), file(glib_003,fc39_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc3_glib_003), []). fof(fc3_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( v1_relat_1(k5_glib_004(A,B)) & v1_funct_1(k5_glib_004(A,B)) & v12_glib_000(k5_glib_004(A,B)) & v14_glib_000(k5_glib_004(A,B)) & v12_glib_003(k5_glib_004(A,B)) & v13_glib_003(k5_glib_004(A,B)) & v14_glib_003(k5_glib_004(A,B)) & v15_glib_003(k5_glib_004(A,B)) & v17_glib_003(k5_glib_004(A,B)) & v18_glib_003(k5_glib_004(A,B)) & v19_glib_003(k5_glib_004(A,B)) ) ) ), file(glib_004,fc3_glib_004), []). fof(fc3_polynom1,axiom, ( 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_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(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) & v1_matrlin(k1_xboole_0) ), file(polynom1,fc3_polynom1), []). 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_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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_pboole(B,k6_glib_000(A)) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v3_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc40_glib_003), []). 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_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_funct_1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_finset_1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_polynom1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_glib_000(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v2_glib_003(k13_glib_000(A,k3_glib_003,k1_xboole_0)) ) ) ), file(glib_003,fc41_glib_003), []). 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(fc42_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_funct_1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_finset_1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_polynom1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_glib_000(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v3_glib_003(k13_glib_000(A,k4_glib_003,k1_xboole_0)) ) ) ), file(glib_003,fc42_glib_003), []). fof(fc44_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_funct_1(B) & m1_relset_1(B,k7_glib_000(A),k1_numbers) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v2_glib_003(k13_glib_000(A,k3_glib_003,B)) & v9_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc44_glib_003), []). fof(fc45_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_seq_1(B) & m1_pboole(B,k7_glib_000(A)) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v2_glib_003(k13_glib_000(A,k3_glib_003,B)) & v9_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc45_glib_003), []). fof(fc46_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_funct_1(B) & m1_relset_1(B,k6_glib_000(A),k1_numbers) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v3_glib_003(k13_glib_000(A,k4_glib_003,B)) & v10_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc46_glib_003), []). fof(fc47_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_seq_1(B) & m1_pboole(B,k6_glib_000(A)) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v3_glib_003(k13_glib_000(A,k4_glib_003,B)) & v10_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc47_glib_003), []). fof(fc48_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_funct_1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_finset_1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_polynom1(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v1_glib_000(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v2_glib_003(k13_glib_000(A,k3_glib_003,k1_xboole_0)) & v9_glib_003(k13_glib_000(A,k3_glib_003,k1_xboole_0)) ) ) ), file(glib_003,fc48_glib_003), []). fof(fc49_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_funct_1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_finset_1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_polynom1(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v1_glib_000(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v3_glib_003(k13_glib_000(A,k4_glib_003,k1_xboole_0)) & v10_glib_003(k13_glib_000(A,k4_glib_003,k1_xboole_0)) ) ) ), file(glib_003,fc49_glib_003), []). fof(fc4_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( ~ v1_xboole_0(k6_glib_000(A)) & v1_finset_1(k6_glib_000(A)) ) ) ), file(glib_000,fc4_glib_000), []). fof(fc4_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc4_glib_003), []). 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_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(fc50_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) & v1_xreal_0(C) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_funct_1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_finset_1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_polynom1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_glib_000(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v3_glib_003(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) ) ) ), file(glib_003,fc50_glib_003), []). fof(fc51_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) & v1_xreal_0(C) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_funct_1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_finset_1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_polynom1(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v1_glib_000(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v3_glib_003(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) & v10_glib_003(k13_glib_000(A,k4_glib_003,k3_cqc_lang(B,C))) ) ) ), file(glib_003,fc51_glib_003), []). fof(fc52_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k5_glib_003(A)) & v1_funct_1(k5_glib_003(A)) & v1_finset_1(k5_glib_003(A)) & v1_polynom1(k5_glib_003(A)) ) ) ), file(glib_003,fc52_glib_003), []). fof(fc54_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k7_glib_003(A)) & v1_funct_1(k7_glib_003(A)) & v1_finset_1(k7_glib_003(A)) & v1_polynom1(k7_glib_003(A)) ) ) ), file(glib_003,fc54_glib_003), []). fof(fc55_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k5_glib_003(A)) & v1_funct_1(k5_glib_003(A)) & v1_seq_1(k5_glib_003(A)) ) ) ), file(glib_003,fc55_glib_003), []). fof(fc57_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v3_glib_003(A) & v10_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k7_glib_003(A)) & v1_funct_1(k7_glib_003(A)) & v1_seq_1(k7_glib_003(A)) ) ) ), file(glib_003,fc57_glib_003), []). fof(fc58_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v1_glib_003(k13_glib_000(A,k3_glib_003,B)) & v7_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc58_glib_003), []). fof(fc59_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v1_glib_003(k13_glib_000(A,k4_glib_003,B)) & v7_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc59_glib_003), []). fof(fc5_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => v1_finset_1(k7_glib_000(A)) ) ), file(glib_000,fc5_glib_000), []). 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_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & v1_finset_1(k1_funct_1(A,B)) & v1_finseq_1(k1_funct_1(A,B)) ) ) ), file(polynom1,fc5_polynom1), []). 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(fc63_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v2_glib_003(k13_glib_000(A,k4_glib_003,B)) & v9_glib_003(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc63_glib_003), []). fof(fc65_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v3_glib_003(A) & v10_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v3_glib_003(k13_glib_000(A,k3_glib_003,B)) & v10_glib_003(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc65_glib_003), []). fof(fc66_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v1_funct_1(k12_glib_003(A,B,C)) & v1_finset_1(k12_glib_003(A,B,C)) & v1_polynom1(k12_glib_003(A,B,C)) & v1_glib_000(k12_glib_003(A,B,C)) & v2_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc66_glib_003), []). fof(fc6_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k3_glib_003,B)) & v1_funct_1(k13_glib_000(A,k3_glib_003,B)) & v1_finset_1(k13_glib_000(A,k3_glib_003,B)) & v1_polynom1(k13_glib_000(A,k3_glib_003,B)) & v1_glib_000(k13_glib_000(A,k3_glib_003,B)) & v2_glib_000(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc6_glib_003), []). 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(fc74_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v1_funct_1(k12_glib_003(A,B,C)) & v1_finset_1(k12_glib_003(A,B,C)) & v1_polynom1(k12_glib_003(A,B,C)) & v1_glib_000(k12_glib_003(A,B,C)) & v1_glib_003(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc74_glib_003), []). fof(fc75_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v1_funct_1(k12_glib_003(A,B,C)) & v1_finset_1(k12_glib_003(A,B,C)) & v1_polynom1(k12_glib_003(A,B,C)) & v1_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) & v3_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc75_glib_003), []). fof(fc76_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v1_funct_1(k12_glib_003(A,B,C)) & v1_finset_1(k12_glib_003(A,B,C)) & v1_polynom1(k12_glib_003(A,B,C)) & v1_glib_000(k12_glib_003(A,B,C)) & v1_glib_003(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) & v7_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc76_glib_003), []). fof(fc78_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & m1_subset_1(C,k1_numbers) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v1_funct_1(k12_glib_003(A,B,C)) & v1_finset_1(k12_glib_003(A,B,C)) & v1_polynom1(k12_glib_003(A,B,C)) & v1_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) & v9_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc78_glib_003), []). fof(fc79_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) & v10_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v1_funct_1(k12_glib_003(A,B,C)) & v1_finset_1(k12_glib_003(A,B,C)) & v1_polynom1(k12_glib_003(A,B,C)) & v1_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) & v3_glib_003(k12_glib_003(A,B,C)) & v10_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc79_glib_003), []). fof(fc7_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k4_glib_003,B)) & v1_funct_1(k13_glib_000(A,k4_glib_003,B)) & v1_finset_1(k13_glib_000(A,k4_glib_003,B)) & v1_polynom1(k13_glib_000(A,k4_glib_003,B)) & v1_glib_000(k13_glib_000(A,k4_glib_003,B)) & v2_glib_000(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc7_glib_003), []). 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(fc80_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v1_funct_1(k13_glib_003(A,B,C)) & v1_finset_1(k13_glib_003(A,B,C)) & v1_polynom1(k13_glib_003(A,B,C)) & v1_glib_000(k13_glib_003(A,B,C)) & v2_glib_000(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc80_glib_003), []). fof(fc88_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_003(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v1_funct_1(k13_glib_003(A,B,C)) & v1_finset_1(k13_glib_003(A,B,C)) & v1_polynom1(k13_glib_003(A,B,C)) & v1_glib_000(k13_glib_003(A,B,C)) & v1_glib_003(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc88_glib_003), []). fof(fc89_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v1_funct_1(k13_glib_003(A,B,C)) & v1_finset_1(k13_glib_003(A,B,C)) & v1_polynom1(k13_glib_003(A,B,C)) & v1_glib_000(k13_glib_003(A,B,C)) & v2_glib_003(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc89_glib_003), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc90_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_003(A) & v3_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v1_funct_1(k13_glib_003(A,B,C)) & v1_finset_1(k13_glib_003(A,B,C)) & v1_polynom1(k13_glib_003(A,B,C)) & v1_glib_000(k13_glib_003(A,B,C)) & v1_glib_003(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) & v7_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc90_glib_003), []). fof(fc92_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v1_funct_1(k13_glib_003(A,B,C)) & v1_finset_1(k13_glib_003(A,B,C)) & v1_polynom1(k13_glib_003(A,B,C)) & v1_glib_000(k13_glib_003(A,B,C)) & v2_glib_003(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) & v9_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc92_glib_003), []). fof(fc93_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v3_glib_003(A) & v10_glib_003(A) & m1_glib_000(A) & m1_subset_1(C,k1_numbers) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v1_funct_1(k13_glib_003(A,B,C)) & v1_finset_1(k13_glib_003(A,B,C)) & v1_polynom1(k13_glib_003(A,B,C)) & v1_glib_000(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) & v10_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc93_glib_003), []). fof(fc94_glib_003,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v12_glib_003(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_polynom1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v1_glib_003(k42_glib_000(A,B)) ) ) ), file(glib_003,fc94_glib_003), []). fof(fc95_glib_003,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v13_glib_003(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_polynom1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v2_glib_003(k42_glib_000(A,B)) ) ) ), file(glib_003,fc95_glib_003), []). fof(fc96_glib_003,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v14_glib_003(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_polynom1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v3_glib_003(k42_glib_000(A,B)) ) ) ), file(glib_003,fc96_glib_003), []). fof(fc97_glib_003,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v12_glib_003(A) & v15_glib_003(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_polynom1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v1_glib_003(k42_glib_000(A,B)) & v7_glib_003(k42_glib_000(A,B)) ) ) ), file(glib_003,fc97_glib_003), []). fof(fc99_glib_003,axiom,( ! [A,B] : ( ( v12_glib_000(A) & v13_glib_003(A) & v17_glib_003(A) & m1_pboole(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k42_glib_000(A,B)) & v1_funct_1(k42_glib_000(A,B)) & v1_finset_1(k42_glib_000(A,B)) & v1_polynom1(k42_glib_000(A,B)) & v1_glib_000(k42_glib_000(A,B)) & v2_glib_003(k42_glib_000(A,B)) & v9_glib_003(k42_glib_000(A,B)) ) ) ), file(glib_003,fc99_glib_003), []). 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(rc10_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc10_polynom1), []). fof(rc11_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_seq_1(A) & v7_seqm_3(A) & v1_polynom1(A) ) ), file(polynom1,rc11_polynom1), []). fof(rc12_polynom1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc12_polynom1), []). fof(rc13_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc13_polynom1), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_glib_000,axiom,( ? [A] : ( m1_glib_000(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) ), file(glib_000,rc1_glib_000), []). fof(rc1_glib_003,axiom,( ? [A] : ( m1_glib_000(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_polynom1(A) & v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) ) ), file(glib_003,rc1_glib_003), []). 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_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_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_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(rc20_glib_003,axiom,( ? [A] : ( m1_pboole(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v12_glib_000(A) & v12_glib_003(A) & v13_glib_003(A) & v14_glib_003(A) ) ), file(glib_003,rc20_glib_003), []). fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) ), file(card_1,rc2_card_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_matrlin(A) ) ), file(polynom1,rc2_polynom1), []). 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_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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc6_glib_000,axiom,( ? [A] : ( m1_pboole(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v12_glib_000(A) ) ), file(glib_000,rc6_glib_000), []). fof(rc7_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v7_seqm_3(A) ) ), file(polynom1,rc7_polynom1), []). fof(rc8_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) & v7_seqm_3(B) ) ), file(polynom1,rc8_polynom1), []). fof(rc9_polynom1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) ), file(polynom1,rc9_polynom1), []). fof(redefinition_k10_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => k10_glib_000(A) = k8_glib_000(A) ) ), file(glib_000,k10_glib_000), []). fof(redefinition_k11_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => k11_glib_000(A) = k9_glib_000(A) ) ), file(glib_000,k11_glib_000), []). fof(redefinition_k1_card_fil,axiom,( ! [A,B] : k1_card_fil(A,B) = k4_xboole_0(A,B) ), file(card_fil,k1_card_fil), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => k1_seq_1(A,B) = k1_funct_1(A,B) ) ), file(seq_1,k1_seq_1), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(reflexivity_r5_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_glib_000(B) & m1_glib_000(B) ) => r5_glib_000(A,A) ) ), file(glib_000,r5_glib_000), []). fof(s1_nat_1__e7_31__glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( ( r1_tarski(k14_glib_003(k42_glib_000(k5_glib_004(A,B),0)),k2_glib_002(A,B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_tarski(k14_glib_003(k42_glib_000(k5_glib_004(A,B),C)),k2_glib_002(A,B)) => r1_tarski(k14_glib_003(k42_glib_000(k5_glib_004(A,B),k1_nat_1(C,1))),k2_glib_002(A,B)) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r1_tarski(k14_glib_003(k42_glib_000(k5_glib_004(A,B),C)),k2_glib_002(A,B)) ) ) ) ), file(glib_004,s1_nat_1__e7_31__glib_004), []). 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_r5_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_glib_000(B) & m1_glib_000(B) ) => ( r5_glib_000(A,B) => r5_glib_000(B,A) ) ) ), file(glib_000,r5_glib_000), []). fof(t15_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k14_glib_003(k4_glib_004(A,B)) = k6_domain_1(k6_glib_000(A),B) ) ) ), file(glib_004,t15_glib_004), []). fof(t17_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r5_glib_000(A,k42_glib_000(k5_glib_004(A,B),C)) & k5_glib_003(A) = k5_glib_003(k42_glib_000(k5_glib_004(A,B),C)) ) ) ) ) ), file(glib_004,t17_glib_004), []). fof(t18_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => r2_hidden(B,k2_glib_002(A,B)) ) ) ), file(glib_002,t18_glib_002), []). fof(t19_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D,E] : ( m1_subset_1(E,k6_glib_000(A)) => ( ( r2_hidden(B,k2_glib_002(A,E)) & r2_glib_000(A,B,D,C) ) => r2_hidden(D,k2_glib_002(A,E)) ) ) ) ), file(glib_002,t19_glib_002), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). 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(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(t37_zfmisc_1,axiom,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). 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(t43_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) & m1_glib_000(A) ) => ! [B,C] : k7_glib_003(A) = k7_glib_003(k12_glib_003(A,B,C)) ) ), file(glib_003,t43_glib_003), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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(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(t62_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r2_hidden(C,k14_glib_003(k13_glib_003(A,B,D))) => ( r2_hidden(C,k14_glib_003(A)) | ( B = C & r2_hidden(B,k6_glib_000(A)) ) ) ) ) ), file(glib_003,t62_glib_003), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).