% Mizar problem: t15_glib_005,glib_005,3758,23 fof(t15_glib_005,conjecture,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & v1_glib_005(A) & m1_glib_000(A) ) => ! [B,C,D] : ( ( v5_glib_001(D,A) & v7_glib_005(D,A) & m3_glib_001(D,A) ) => ( ( r1_glib_005(A,B,C) & r1_glib_001(A,B,C,D) ) => ( B = C | r1_glib_005(k12_glib_005(A,D),B,C) ) ) ) ) ), 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_finseq_1,cc1_finset_1,cc1_glib_001,cc1_membered,cc1_nat_1,cc1_polynom1,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_glib_001,cc2_glib_005,cc2_int_1,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_glib_001,cc3_glib_005,cc3_int_1,cc3_membered,cc3_nat_1,cc3_polynom1,cc3_xreal_0,cc4_glib_001,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_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,connectedness_r1_xreal_0,d15_glib_000,d16_glib_000,d18_glib_005,d19_glib_005,d1_funct_4,d1_tarski,d20_glib_005,d21_glib_005,d23_glib_001,d28_glib_001,d36_glib_000,d3_glib_001,d3_pboole,d5_funct_1,d5_real_1,d6_glib_001,d7_glib_001,d7_glib_005,d8_glib_003,dt_k10_glib_000,dt_k11_glib_000,dt_k11_glib_005,dt_k12_glib_001,dt_k12_glib_005,dt_k13_glib_000,dt_k13_glib_001,dt_k14_glib_001,dt_k1_card_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_glib_005,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_k27_glib_000,dt_k28_glib_000,dt_k29_glib_000,dt_k2_nat_1,dt_k2_relat_1,dt_k2_seq_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k30_glib_000,dt_k31_glib_000,dt_k32_glib_000,dt_k35_glib_000,dt_k37_glib_000,dt_k38_glib_000,dt_k39_glib_000,dt_k3_cqc_lang,dt_k3_finseq_1,dt_k3_glib_001,dt_k3_glib_003,dt_k3_nat_1,dt_k3_pre_circ,dt_k3_real_1,dt_k3_uproots,dt_k3_xcmplx_0,dt_k4_glib_001,dt_k4_relset_1,dt_k5_glib_003,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_relset_1,dt_k6_glib_000,dt_k6_glib_003,dt_k6_xcmplx_0,dt_k7_glib_000,dt_k7_relat_1,dt_k8_glib_000,dt_k8_glib_005,dt_k9_glib_000,dt_k9_glib_005,dt_m1_finseq_1,dt_m1_glib_000,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_glib_001,dt_m2_relset_1,dt_m2_subset_1,dt_m3_glib_001,existence_m1_finseq_1,existence_m1_glib_000,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_glib_001,existence_m2_relset_1,existence_m2_subset_1,existence_m3_glib_001,fc10_abian,fc10_glib_005,fc10_membered,fc10_xreal_0,fc11_abian,fc11_finseq_1,fc11_membered,fc11_xreal_0,fc12_abian,fc12_xreal_0,fc13_abian,fc13_glib_005,fc14_abian,fc14_finset_1,fc14_polynom1,fc15_abian,fc15_xreal_0,fc16_xreal_0,fc17_abian,fc17_finseq_1,fc17_glib_005,fc17_xreal_0,fc18_xreal_0,fc19_glib_005,fc19_xreal_0,fc1_abian,fc1_amistd_2,fc1_bagorder,fc1_finset_1,fc1_glib_000,fc1_glib_001,fc1_glib_002,fc1_glib_003,fc1_glib_005,fc1_int_1,fc1_jordan1d,fc1_nat_1,fc1_ordinal2,fc1_rfinseq,fc20_polynom1,fc20_xreal_0,fc21_xreal_0,fc22_membered,fc22_xreal_0,fc23_membered,fc23_xreal_0,fc24_membered,fc24_xreal_0,fc25_membered,fc26_membered,fc29_glib_003,fc2_abian,fc2_amistd_2,fc2_bagorder,fc2_finseq_1,fc2_glib_000,fc2_int_1,fc2_jordan1d,fc2_membered,fc2_nat_1,fc35_glib_003,fc36_glib_003,fc3_abian,fc3_amistd_2,fc3_glib_003,fc3_glib_005,fc3_nat_1,fc3_polynom1,fc3_xreal_0,fc41_glib_003,fc44_glib_003,fc45_glib_003,fc48_glib_003,fc4_abian,fc4_glib_000,fc4_glib_005,fc4_int_1,fc4_nat_1,fc4_xreal_0,fc52_glib_003,fc53_glib_003,fc55_glib_003,fc56_glib_003,fc58_glib_003,fc5_abian,fc5_glib_000,fc5_glib_005,fc5_membered,fc5_polynom1,fc5_xreal_0,fc6_abian,fc6_glib_003,fc6_int_1,fc6_membered,fc7_abian,fc7_funcop_1,fc7_int_1,fc7_membered,fc7_xreal_0,fc8_abian,fc8_int_1,fc8_membered,fc8_polynom1,fc8_xreal_0,fc9_abian,fc9_finset_1,fc9_int_1,fc9_membered,fc9_xreal_0,idempotence_k1_funct_4,idempotence_k2_xboole_0,rc10_polynom1,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc1_abian,rc1_finseq_1,rc1_finset_1,rc1_funcop_1,rc1_glib_000,rc1_int_1,rc1_membered,rc1_nat_1,rc1_xreal_0,rc2_abian,rc2_finseq_1,rc2_finset_1,rc2_int_1,rc2_nat_1,rc2_polynom1,rc2_xreal_0,rc3_abian,rc3_finseq_1,rc3_finset_1,rc3_glib_005,rc3_nat_1,rc3_polynom1,rc3_xreal_0,rc4_abian,rc4_finseq_1,rc4_finset_1,rc4_polynom1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,rc8_polynom1,rc9_polynom1,redefinition_k10_glib_000,redefinition_k11_glib_000,redefinition_k1_glib_005,redefinition_k1_nat_1,redefinition_k1_seq_1,redefinition_k2_nat_1,redefinition_k2_seq_1,redefinition_k3_finseq_1,redefinition_k3_pre_circ,redefinition_k3_real_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_nat_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r5_glib_000,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r5_glib_000,t101_glib_001,t104_glib_001,t106_glib_001,t10_xreal_1,t11_glib_000,t128_glib_001,t12_funct_4,t139_glib_001,t13_glib_005,t14_funct_4,t14_glib_005,t18_glib_001,t18_int_1,t19_glib_000,t1_arithm,t1_boole,t1_glib_001,t1_heyting3,t1_numerals,t1_real,t1_subset,t22_pepin,t29_nat_1,t2_arithm,t2_real,t2_subset,t2_xreal_1,t38_nat_1,t3_arithm,t3_real,t3_subset,t46_zfmisc_1,t49_nat_1,t4_arithm,t4_real,t4_subset,t59_glib_000,t5_cqc_lang,t5_real,t5_subset,t60_glib_000,t61_glib_000,t62_glib_000,t6_boole,t6_cqc_lang,t6_real,t72_funct_1,t78_glib_001,t7_boole,t7_glib_004,t7_real,t88_glib_001,t8_boole,t8_real,t91_glib_000,t92_real_1,t99_glib_000,t9_funct_1,t9_glib_004,t9_xreal_1]), [file(glib_005,t15_glib_005)]). 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_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_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) => ( v1_relat_1(B) & v4_glib_001(B,A) ) ) ) ) ), file(glib_001,cc1_glib_001), []). 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_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). 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_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_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => ( v1_relat_1(B) & v5_glib_001(B,A) ) ) ) ) ), file(glib_001,cc2_glib_001), []). fof(cc2_glib_005,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v2_glib_003(A) & v4_glib_005(A) ) => ( v1_glib_000(A) & v2_glib_003(A) & v9_glib_003(A) ) ) ) ), file(glib_005,cc2_glib_005), []). 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_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => ( v1_relat_1(B) & v6_glib_001(B,A) ) ) ) ) ), file(glib_001,cc3_glib_001), []). fof(cc3_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => ( v1_relat_1(B) & v7_glib_005(B,A) ) ) ) ) ), file(glib_005,cc3_glib_005), []). 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_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_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v6_glib_001(B,A) => ( v1_relat_1(B) & v5_glib_001(B,A) ) ) ) ) ), file(glib_001,cc4_glib_001), []). 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_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) ), file(nat_1,k2_nat_1), []). fof(commutativity_k2_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_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(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d15_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r1_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 ) | ( k1_funct_1(k10_glib_000(A),D) = C & k1_funct_1(k11_glib_000(A),D) = B ) ) ) ) ) ), file(glib_000,d15_glib_000), []). 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_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v7_glib_005(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( C = k8_glib_005(A,B) <=> ( k4_relset_1(k5_numbers,k1_numbers,C) = k4_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_relset_1(k5_numbers,k1_numbers,C)) => ( ( r2_glib_000(A,k1_funct_1(B,k5_real_1(k2_nat_1(2,D),1)),k1_funct_1(B,k1_nat_1(k2_nat_1(2,D),1)),k1_funct_1(B,k2_nat_1(2,D))) => k2_seq_1(k5_numbers,k1_numbers,C,D) = k5_real_1(k1_seq_1(k5_glib_003(A),k1_funct_1(B,k2_nat_1(2,D))),k1_seq_1(k6_glib_003(A),k1_funct_1(B,k2_nat_1(2,D)))) ) & ( ~ r2_glib_000(A,k1_funct_1(B,k5_real_1(k2_nat_1(2,D),1)),k1_funct_1(B,k1_nat_1(k2_nat_1(2,D),1)),k1_funct_1(B,k2_nat_1(2,D))) => k2_seq_1(k5_numbers,k1_numbers,C,D) = k1_seq_1(k6_glib_003(A),k1_funct_1(B,k2_nat_1(2,D))) ) ) ) ) ) ) ) ) ) ), file(glib_005,d18_glib_005), []). fof(d19_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v7_glib_005(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( ( ~ v3_glib_001(B,A) => ( C = k9_glib_005(A,B) <=> ( r2_hidden(C,k5_relset_1(k5_numbers,k1_numbers,k8_glib_005(A,B))) & ! [D] : ( m1_subset_1(D,k1_numbers) => ( r2_hidden(D,k5_relset_1(k5_numbers,k1_numbers,k8_glib_005(A,B))) => r1_xreal_0(C,D) ) ) ) ) ) & ( v3_glib_001(B,A) => ( C = k9_glib_005(A,B) <=> C = 0 ) ) ) ) ) ) ), file(glib_005,d19_glib_005), []). 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(d20_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m1_pboole(C,k7_glib_000(A)) => ( C = k11_glib_005(A,B) <=> ( ! [D] : ( r2_hidden(D,k7_glib_000(A)) => ( r2_hidden(D,k14_glib_001(A,B)) | k1_funct_1(C,D) = k1_seq_1(k6_glib_003(A),D) ) ) & ! [D] : ( ( ~ v1_abian(D) & m2_subset_1(D,k1_numbers,k5_numbers) ) => ( ~ r1_xreal_0(k3_finseq_1(B),D) => ( ( r2_glib_000(A,k1_funct_1(B,D),k1_funct_1(B,k1_nat_1(D,2)),k1_funct_1(B,k1_nat_1(D,1))) => k1_funct_1(C,k1_funct_1(B,k1_nat_1(D,1))) = k3_real_1(k1_seq_1(k6_glib_003(A),k1_funct_1(B,k1_nat_1(D,1))),k9_glib_005(A,B)) ) & ( ~ r2_glib_000(A,k1_funct_1(B,D),k1_funct_1(B,k1_nat_1(D,2)),k1_funct_1(B,k1_nat_1(D,1))) => k1_funct_1(C,k1_funct_1(B,k1_nat_1(D,1))) = k5_real_1(k1_seq_1(k6_glib_003(A),k1_funct_1(B,k1_nat_1(D,1))),k9_glib_005(A,B)) ) ) ) ) ) ) ) ) ) ), file(glib_005,d20_glib_005), []). fof(d21_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => k12_glib_005(A,B) = k13_glib_000(A,k3_glib_003,k11_glib_005(A,B)) ) ) ), file(glib_005,d21_glib_005), []). fof(d23_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( m3_glib_001(D,A) => ( r1_glib_001(A,B,C,D) <=> ( k3_glib_001(A,D) = B & k4_glib_001(A,D) = C ) ) ) ) ), file(glib_001,d23_glib_001), []). fof(d28_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) <=> ( v4_glib_001(B,A) & ! [C] : ( ( ~ v1_abian(C) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ! [D] : ( ( ~ v1_abian(D) & m2_subset_1(D,k1_numbers,k5_numbers) ) => ( ( r1_xreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => ( r1_xreal_0(D,C) | ( C = 1 & D = k3_finseq_1(B) ) ) ) ) ) ) ) ) ) ), file(glib_001,d28_glib_001), []). 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_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_finseq_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) => ( m3_glib_001(B,A) <=> ( ~ v1_abian(k3_finseq_1(B)) & r2_hidden(k1_funct_1(B,1),k6_glib_000(A)) & ! [C] : ( ( ~ v1_abian(C) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( ~ r1_xreal_0(k3_finseq_1(B),C) => r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,2)),k1_funct_1(B,k1_nat_1(C,1))) ) ) ) ) ) ) ), file(glib_001,d3_glib_001), []). fof(d3_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d6_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k3_glib_001(A,B) = k1_funct_1(B,1) ) ) ), file(glib_001,d6_glib_001), []). fof(d7_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k4_glib_001(A,B) = k1_funct_1(B,k3_finseq_1(B)) ) ) ), file(glib_001,d7_glib_001), []). fof(d7_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & v1_glib_005(A) & m1_glib_000(A) ) => ! [B,C] : ( r1_glib_005(A,B,C) <=> ( m1_subset_1(B,k6_glib_000(A)) & m1_subset_1(C,k6_glib_000(A)) & ! [D] : ( r2_hidden(D,k7_glib_000(A)) => ( r1_xreal_0(0,k1_seq_1(k1_glib_005(A),D)) & r1_xreal_0(k1_seq_1(k1_glib_005(A),D),k1_seq_1(k5_glib_003(A),D)) ) ) & ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ~ ( D != B & D != C & k3_uproots(k27_glib_000(A,D),k3_pre_circ(k7_glib_000(A),k1_glib_005(A),k27_glib_000(A,D))) != k3_uproots(k28_glib_000(A,D),k3_pre_circ(k7_glib_000(A),k1_glib_005(A),k28_glib_000(A,D))) ) ) ) ) ) ), file(glib_005,d7_glib_005), []). fof(d8_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => k6_glib_003(A) = k1_funct_1(A,k3_glib_003) ) ), file(glib_003,d8_glib_003), []). 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_k11_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => m1_pboole(k11_glib_005(A,B),k7_glib_000(A)) ) ), file(glib_005,k11_glib_005), []). fof(dt_k12_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => m2_glib_001(k12_glib_001(A,B),A) ) ), file(glib_001,k12_glib_001), []). fof(dt_k12_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => ( v1_glib_000(k12_glib_005(A,B)) & v1_glib_003(k12_glib_005(A,B)) & v2_glib_003(k12_glib_005(A,B)) & v7_glib_003(k12_glib_005(A,B)) & v9_glib_003(k12_glib_005(A,B)) & v1_glib_005(k12_glib_005(A,B)) & m1_glib_000(k12_glib_005(A,B)) ) ) ), file(glib_005,k12_glib_005), []). 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_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => ( v1_finset_1(k13_glib_001(A,B)) & m1_subset_1(k13_glib_001(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ) ), file(glib_001,k13_glib_001), []). fof(dt_k14_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => ( v1_finset_1(k14_glib_001(A,B)) & m1_subset_1(k14_glib_001(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ) ), file(glib_001,k14_glib_001), []). 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_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & v1_glib_005(A) & m1_glib_000(A) ) => m1_pboole(k1_glib_005(A),k7_glib_000(A)) ) ), file(glib_005,k1_glib_005), []). 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_k27_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k27_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_000,k27_glib_000), []). fof(dt_k28_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k28_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_000,k28_glib_000), []). fof(dt_k29_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k29_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_000,k29_glib_000), []). fof(dt_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k2_nat_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ), file(seq_1,k2_seq_1), []). 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_k30_glib_000,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k30_glib_000(A,B,C),k6_glib_000(A)) ) ), file(glib_000,k30_glib_000), []). fof(dt_k31_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => v1_card_1(k31_glib_000(A,B)) ) ), file(glib_000,k31_glib_000), []). fof(dt_k32_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => v1_card_1(k32_glib_000(A,B)) ) ), file(glib_000,k32_glib_000), []). fof(dt_k35_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => v1_card_1(k35_glib_000(A,B)) ) ), file(glib_000,k35_glib_000), []). fof(dt_k37_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k37_glib_000(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ), file(glib_000,k37_glib_000), []). fof(dt_k38_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k38_glib_000(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ), file(glib_000,k38_glib_000), []). fof(dt_k39_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k39_glib_000(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ), file(glib_000,k39_glib_000), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => m1_subset_1(k3_glib_001(A,B),k6_glib_000(A)) ) ), file(glib_001,k3_glib_001), []). 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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => m2_subset_1(k3_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k3_nat_1), []). fof(dt_k3_pre_circ,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_pboole(k3_pre_circ(A,B,C),C) ) ), file(pre_circ,k3_pre_circ), []). 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_k3_uproots,axiom,( ! [A,B] : ( ( v1_seq_1(B) & v1_polynom1(B) & m1_pboole(B,A) ) => v1_xreal_0(k3_uproots(A,B)) ) ), file(uproots,k3_uproots), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => m1_subset_1(k4_glib_001(A,B),k6_glib_000(A)) ) ), file(glib_001,k4_glib_001), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). 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_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_1), []). fof(dt_k6_glib_000,axiom,( $true ), file(glib_000,k6_glib_000), []). fof(dt_k6_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k6_glib_003(A)) & v1_funct_1(k6_glib_003(A)) ) ) ), file(glib_003,k6_glib_003), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_glib_000,axiom,( $true ), file(glib_000,k7_glib_000), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k8_glib_000,axiom,( $true ), file(glib_000,k8_glib_000), []). fof(dt_k8_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => m2_finseq_1(k8_glib_005(A,B),k1_numbers) ) ), file(glib_005,k8_glib_005), []). fof(dt_k9_glib_000,axiom,( $true ), file(glib_000,k9_glib_000), []). fof(dt_k9_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => m1_subset_1(k9_glib_005(A,B),k1_numbers) ) ), file(glib_005,k9_glib_005), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_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_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_001(B,A) => m2_finseq_1(B,k7_glib_000(A)) ) ) ), file(glib_001,m2_glib_001), []). 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_m3_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => m2_finseq_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) ) ) ), file(glib_001,m3_glib_001), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_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_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : m2_glib_001(B,A) ) ), file(glib_001,m2_glib_001), []). 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(existence_m3_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : m3_glib_001(B,A) ) ), file(glib_001,m3_glib_001), []). fof(fc10_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(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)) & ~ v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc10_abian), []). fof(fc10_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & v4_glib_005(A) & m1_glib_000(A) ) => ( v1_relat_1(k6_glib_003(A)) & v1_funct_1(k6_glib_003(A)) & v1_seq_1(k6_glib_003(A)) & v7_seqm_3(k6_glib_003(A)) ) ) ), file(glib_005,fc10_glib_005), []). 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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(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)) & ~ v1_abian(k2_xcmplx_0(B,A)) ) ) ), file(abian,fc11_abian), []). 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_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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(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)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc12_abian), []). 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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & ~ v1_abian(k6_xcmplx_0(A,B)) ) ) ), file(abian,fc13_abian), []). fof(fc13_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v7_seqm_3(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)) & v1_glib_005(k13_glib_000(A,k3_glib_003,B)) & v4_glib_005(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_005,fc13_glib_005), []). fof(fc14_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) & ~ v1_abian(k6_xcmplx_0(B,A)) ) ) ), file(abian,fc14_abian), []). 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(fc15_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_abian(k6_xcmplx_0(A,B)) ) ) ), file(abian,fc15_abian), []). fof(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). fof(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_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(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(fc17_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => ( v1_relat_1(k11_glib_005(A,B)) & v1_funct_1(k11_glib_005(A,B)) & v1_seq_1(k11_glib_005(A,B)) ) ) ), file(glib_005,fc17_glib_005), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_glib_005,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) & v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => ( v1_relat_1(k12_glib_005(A,B)) & v1_funct_1(k12_glib_005(A,B)) & v1_finset_1(k12_glib_005(A,B)) & v1_polynom1(k12_glib_005(A,B)) & v1_glib_000(k12_glib_005(A,B)) & v2_glib_000(k12_glib_005(A,B)) & v1_glib_003(k12_glib_005(A,B)) & v2_glib_003(k12_glib_005(A,B)) & v7_glib_003(k12_glib_005(A,B)) & v9_glib_003(k12_glib_005(A,B)) & v1_glib_005(k12_glib_005(A,B)) ) ) ), file(glib_005,fc19_glib_005), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_abian,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k3_xcmplx_0(2,A)) & v1_xreal_0(k3_xcmplx_0(2,A)) & v1_int_1(k3_xcmplx_0(2,A)) & v1_abian(k3_xcmplx_0(2,A)) ) ) ), file(abian,fc1_abian), []). 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_bagorder,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) & v7_seqm_3(k7_relat_1(A,B)) ) ) ), file(bagorder,fc1_bagorder), []). 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_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => ( ~ v1_xboole_0(k1_card_1(B)) & v1_card_1(k1_card_1(B)) & ~ v1_abian(k1_card_1(B)) ) ) ), file(glib_001,fc1_glib_001), []). 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_003,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) ) ) ), file(glib_003,fc1_glib_003), []). fof(fc1_glib_005,axiom,( ! [A,B] : ( v1_xreal_0(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)) & v1_seq_1(k3_cqc_lang(A,B)) & v1_polynom1(k3_cqc_lang(A,B)) ) ) ), file(glib_005,fc1_glib_005), []). 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_jordan1d,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xreal_0(k2_xcmplx_0(A,2)) & v1_int_1(k2_xcmplx_0(A,2)) & v1_xcmplx_0(k2_xcmplx_0(A,2)) & v1_abian(k2_xcmplx_0(A,2)) ) ) ), file(jordan1d,fc1_jordan1d), []). 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_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_rfinseq,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_finset_1(k7_relat_1(A,B)) ) ) ), file(rfinseq,fc1_rfinseq), []). 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(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(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_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,1)) & v1_xreal_0(k2_xcmplx_0(A,1)) & v1_int_1(k2_xcmplx_0(A,1)) & ~ v1_abian(k2_xcmplx_0(A,1)) ) ) ), file(abian,fc2_abian), []). 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_bagorder,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_polynom1(k7_relat_1(A,B)) ) ) ), file(bagorder,fc2_bagorder), []). 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_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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_jordan1d,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xreal_0(k2_xcmplx_0(A,2)) & v1_int_1(k2_xcmplx_0(A,2)) & v1_xcmplx_0(k2_xcmplx_0(A,2)) & ~ v1_abian(k2_xcmplx_0(A,2)) ) ) ), file(jordan1d,fc2_jordan1d), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(nat_1,fc2_nat_1), []). 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(fc3_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,1)) & v1_xreal_0(k2_xcmplx_0(A,1)) & v1_int_1(k2_xcmplx_0(A,1)) & v1_abian(k2_xcmplx_0(A,1)) ) ) ), file(abian,fc3_abian), []). 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_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_005,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) & v1_seq_1(k1_funct_4(A,B)) ) ) ), file(glib_005,fc3_glib_005), []). 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_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_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(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(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(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(fc4_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,1)) & v1_xreal_0(k6_xcmplx_0(A,1)) & v1_int_1(k6_xcmplx_0(A,1)) & ~ v1_abian(k6_xcmplx_0(A,1)) ) ) ), file(abian,fc4_abian), []). 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_005,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)) & v1_glib_005(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_005,fc4_glib_005), []). fof(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). fof(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(fc53_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k6_glib_003(A)) & v1_funct_1(k6_glib_003(A)) & v1_finset_1(k6_glib_003(A)) & v1_polynom1(k6_glib_003(A)) ) ) ), file(glib_003,fc53_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(fc56_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k6_glib_003(A)) & v1_funct_1(k6_glib_003(A)) & v1_seq_1(k6_glib_003(A)) ) ) ), file(glib_003,fc56_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(fc5_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,1)) & v1_xreal_0(k6_xcmplx_0(A,1)) & v1_int_1(k6_xcmplx_0(A,1)) & v1_abian(k6_xcmplx_0(A,1)) ) ) ), file(abian,fc5_abian), []). 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_glib_005,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k7_glib_000(A),B) & 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)) & v1_glib_005(k13_glib_000(A,k3_glib_003,C)) ) ) ), file(glib_005,fc5_glib_005), []). 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_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc6_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & v1_abian(k3_xcmplx_0(A,B)) ) ) ), file(abian,fc6_abian), []). 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(fc7_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) & v1_abian(k3_xcmplx_0(B,A)) ) ) ), file(abian,fc7_abian), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & ~ v1_abian(k3_xcmplx_0(A,B)) ) ) ), file(abian,fc8_abian), []). fof(fc8_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_polynom1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)) ) ) ), file(polynom1,fc8_polynom1), []). 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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & v1_abian(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)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc9_abian), []). 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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(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_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_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_abian,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) & v1_abian(A) ) ), file(abian,rc1_abian), []). 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_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_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_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_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_abian,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) & ~ v1_abian(A) ) ), file(abian,rc2_abian), []). 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_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_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_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) ), file(abian,rc3_abian), []). 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_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ? [B] : ( m3_glib_001(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_polynom1(B) & v4_glib_001(B,A) & v5_glib_001(B,A) & v6_glib_001(B,A) & v7_glib_005(B,A) ) ) ), file(glib_005,rc3_glib_005), []). 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_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc3_polynom1), []). 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_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) ), file(abian,rc4_abian), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_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_polynom1,axiom,( ? [A] : ( m1_finseq_1(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc4_polynom1), []). 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_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(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_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_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(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_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & v1_glib_005(A) & m1_glib_000(A) ) => k1_glib_005(A) = k6_glib_003(A) ) ), file(glib_005,k1_glib_005), []). 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_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ), file(nat_1,k2_nat_1), []). fof(redefinition_k2_seq_1,axiom,( ! [A,B,C,D] : ( ( v2_membered(B) & v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(seq_1,k2_seq_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_pre_circ,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k3_pre_circ(A,B,C) = k7_relat_1(B,C) ) ), file(pre_circ,k3_pre_circ), []). 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_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => r1_nat_1(A,A) ) ), file(nat_1,r1_nat_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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(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(t101_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k14_glib_001(A,B)) <=> ? [D] : ( ~ v1_abian(D) & m2_subset_1(D,k1_numbers,k5_numbers) & ~ r1_xreal_0(k3_finseq_1(B),D) & k1_funct_1(B,k1_nat_1(D,1)) = C ) ) ) ) ), file(glib_001,t101_glib_001), []). fof(t104_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ~ ( r2_hidden(C,k14_glib_001(A,B)) & ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ! [F] : ( ( ~ v1_abian(F) & m2_subset_1(F,k1_numbers,k5_numbers) ) => ~ ( r1_xreal_0(k1_nat_1(F,2),k3_finseq_1(B)) & D = k1_funct_1(B,F) & C = k1_funct_1(B,k1_nat_1(F,1)) & E = k1_funct_1(B,k1_nat_1(F,2)) & r1_glib_000(A,D,E,C) ) ) ) ) ) ) ) ), file(glib_001,t104_glib_001), []). fof(t106_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D,E] : ( ( r2_hidden(C,k14_glib_001(A,B)) & r1_glib_000(A,D,E,C) ) => ( r2_hidden(D,k13_glib_001(A,B)) & r2_hidden(E,k13_glib_001(A,B)) ) ) ) ) ), file(glib_001,t106_glib_001), []). fof(t10_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ), file(xreal_1,t10_xreal_1), []). fof(t11_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ! [B,C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k1_funct_1(k13_glib_000(A,C,B),C) = B ) ) ), file(glib_000,t11_glib_000), []). fof(t128_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( k3_glib_001(A,B) != k4_glib_001(A,B) & v3_glib_001(B,A) ) ) ) ), file(glib_001,t128_glib_001), []). 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(t139_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> ! [C] : ( ( v1_abian(C) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ! [D] : ( ( v1_abian(D) & m2_subset_1(D,k1_numbers,k5_numbers) ) => ~ ( r1_xreal_0(1,C) & ~ r1_xreal_0(D,C) & r1_xreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) ) ) ) ) ) ), file(glib_001,t139_glib_001), []). fof(t13_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & v7_glib_005(B,A) & m3_glib_001(B,A) ) => ( r5_glib_000(A,k12_glib_005(A,B)) & k5_glib_003(A) = k5_glib_003(k12_glib_005(A,B)) ) ) ) ), file(glib_005,t13_glib_005), []). 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(t14_glib_005,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v7_glib_003(A) & v9_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v7_glib_005(B,A) & m3_glib_001(B,A) ) => ~ ( ~ v3_glib_001(B,A) & r1_xreal_0(k9_glib_005(A,B),0) ) ) ) ), file(glib_005,t14_glib_005), []). fof(t18_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D] : ( r1_glib_001(A,C,D,B) <=> ( k1_funct_1(B,1) = C & k1_funct_1(B,k3_finseq_1(B)) = D ) ) ) ) ), file(glib_001,t18_glib_001), []). fof(t18_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xreal_0(A,B) => r2_hidden(k6_xcmplx_0(B,A),k5_numbers) ) ) ) ), file(int_1,t18_int_1), []). fof(t19_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r1_glib_000(A,C,D,B) <=> ( r2_glib_000(A,C,D,B) | r2_glib_000(A,D,C,B) ) ) ) ), file(glib_000,t19_glib_000), []). 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_glib_001,axiom,( ! [A] : ( ( ~ v1_abian(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => ! [B] : ( ( ~ v1_abian(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ( ~ r1_xreal_0(B,A) <=> r1_xreal_0(k1_nat_1(A,2),B) ) ) ) ), file(glib_001,t1_glib_001), []). fof(t1_heyting3,axiom,( ! [A] : ( ( ~ v1_abian(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => r1_xreal_0(1,A) ) ), file(heyting3,t1_heyting3), []). 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(t22_pepin,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( r1_nat_1(2,A) <=> v1_abian(A) ) ) ), file(pepin,t22_pepin), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t46_zfmisc_1,axiom,( ! [A,B] : ( r2_hidden(A,B) => k2_xboole_0(k1_tarski(A),B) = B ) ), file(zfmisc_1,t46_zfmisc_1), []). fof(t49_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_nat_1(A,B) <=> B = k3_xcmplx_0(A,k3_nat_1(B,A)) ) ) ) ), file(nat_1,t49_nat_1), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_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(t59_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k27_glib_000(A,C)) <=> ( r2_hidden(B,k7_glib_000(A)) & k1_funct_1(k11_glib_000(A),B) = C ) ) ) ) ), file(glib_000,t59_glib_000), []). 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_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(t60_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k27_glib_000(A,C)) <=> ? [D] : r2_glib_000(A,D,C,B) ) ) ) ), file(glib_000,t60_glib_000), []). fof(t61_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k28_glib_000(A,C)) <=> ( r2_hidden(B,k7_glib_000(A)) & k1_funct_1(k10_glib_000(A),B) = C ) ) ) ) ), file(glib_000,t61_glib_000), []). fof(t62_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k28_glib_000(A,C)) <=> ? [D] : r2_glib_000(A,C,D,B) ) ) ) ), file(glib_000,t62_glib_000), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_cqc_lang,axiom,( ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ), file(cqc_lang,t6_cqc_lang), []). 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(t72_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t72_funct_1), []). fof(t78_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v1_abian(C) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(B)) ) => ( r2_hidden(k3_nat_1(C,2),k4_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B))) & k1_funct_1(B,C) = k1_funct_1(k12_glib_001(A,B),k3_nat_1(C,2)) ) ) ) ) ) ), file(glib_001,t78_glib_001), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_glib_004,axiom,( ! [A,B,C] : ( ( v1_seq_1(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ! [D] : ( ( v1_seq_1(D) & v1_polynom1(D) & m1_pboole(D,B) ) => ( C = D => k3_uproots(A,C) = k3_uproots(B,D) ) ) ) ), file(glib_004,t7_glib_004), []). 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(t88_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k13_glib_001(A,B)) <=> ? [D] : ( ~ v1_abian(D) & m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C ) ) ) ) ), file(glib_001,t88_glib_001), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t91_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ! [C,D,E,F,G] : ( r5_glib_000(A,B) => ( ( r1_glib_000(A,D,E,C) => r1_glib_000(B,D,E,C) ) & ( r2_glib_000(A,D,E,C) => r2_glib_000(B,D,E,C) ) & ( r3_glib_000(A,F,G,C) => r3_glib_000(B,F,G,C) ) & ( r4_glib_000(A,F,G,C) => r4_glib_000(B,F,G,C) ) ) ) ) ) ), file(glib_000,t91_glib_000), []). fof(t92_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) ) & ~ ( ( ( ~ r1_xreal_0(B,A) & r1_xreal_0(C,D) ) | ( r1_xreal_0(A,B) & ~ r1_xreal_0(D,C) ) ) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ) ), file(real_1,t92_real_1), []). fof(t99_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ! [C,D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(B)) => ( ( D = E & r5_glib_000(A,B) ) => ( k27_glib_000(A,D) = k27_glib_000(B,E) & k28_glib_000(A,D) = k28_glib_000(B,E) & k29_glib_000(A,D) = k29_glib_000(B,E) & k30_glib_000(A,D,C) = k30_glib_000(B,E,C) & k31_glib_000(A,D) = k31_glib_000(B,E) & k32_glib_000(A,D) = k32_glib_000(B,E) & k35_glib_000(A,D) = k35_glib_000(B,E) & k37_glib_000(A,D) = k37_glib_000(B,E) & k38_glib_000(A,D) = k38_glib_000(B,E) & k39_glib_000(A,D) = k39_glib_000(B,E) ) ) ) ) ) ) ), file(glib_000,t99_glib_000), []). 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), []). fof(t9_glib_004,axiom,( ! [A,B,C] : ( ( v1_seq_1(C) & v1_polynom1(C) & m1_pboole(C,A) ) => ! [D] : ( ( v1_seq_1(D) & v1_polynom1(D) & m1_pboole(D,A) ) => ! [E] : ( v1_xreal_0(E) => ( D = k1_funct_4(C,k3_cqc_lang(B,E)) => k3_uproots(A,D) = k6_xcmplx_0(k2_xcmplx_0(k3_uproots(A,C),E),k1_seq_1(C,B)) ) ) ) ) ), file(glib_004,t9_glib_004), []). fof(t9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ), file(xreal_1,t9_xreal_1), []).