% Mizar problem: t53_glib_004,glib_004,3896,31 fof(t53_glib_004,conjecture,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_003(B) & v4_glib_003(B,A) & m3_glib_000(B,A,k14_glib_003(k14_glib_004(A)),k11_glib_003(k14_glib_004(A))) ) => ( v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v1_glib_004(B,A) & m2_glib_000(B,A) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,antisymmetry_r2_xboole_0,cc10_membered,cc11_glib_000,cc11_membered,cc12_glib_000,cc12_membered,cc13_membered,cc14_membered,cc15_glib_000,cc15_membered,cc16_glib_000,cc16_membered,cc17_glib_000,cc17_membered,cc18_glib_000,cc18_membered,cc19_glib_000,cc19_membered,cc1_abian,cc1_card_1,cc1_finset_1,cc1_funct_1,cc1_glib_000,cc1_glib_001,cc1_glib_004,cc1_membered,cc1_polynom1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_card_1,cc2_finset_1,cc2_funct_1,cc2_glib_000,cc2_glib_001,cc2_glib_003,cc2_glib_004,cc2_int_1,cc2_membered,cc2_xreal_0,cc3_card_1,cc3_glib_000,cc3_glib_001,cc3_glib_002,cc3_glib_003,cc3_int_1,cc3_membered,cc3_polynom1,cc3_xreal_0,cc4_glib_000,cc4_glib_001,cc4_glib_002,cc4_glib_003,cc4_int_1,cc4_membered,cc4_polynom1,cc4_xreal_0,cc5_glib_000,cc5_glib_002,cc5_polynom1,cc5_xreal_0,cc6_glib_001,cc6_membered,cc6_polynom1,cc6_xreal_0,cc7_glib_002,cc7_xreal_0,cc8_glib_000,cc8_glib_003,cc8_xreal_0,cc9_glib_000,cc9_glib_003,cc9_membered,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xboole_0,commutativity_k3_xcmplx_0,commutativity_k5_subset_1,connectedness_r1_xreal_0,d10_glib_003,d10_glib_004,d11_glib_004,d12_glib_004,d13_glib_004,d14_glib_004,d15_glib_000,d15_glib_004,d16_glib_004,d17_glib_000,d17_glib_004,d1_glib_002,d1_tarski,d1_xboole_0,d20_glib_000,d20_glib_003,d23_glib_001,d24_glib_001,d26_glib_000,d27_glib_000,d28_glib_001,d2_glib_002,d2_xboole_0,d31_glib_001,d34_glib_000,d35_glib_000,d36_glib_000,d39_glib_000,d3_glib_001,d3_tarski,d3_xboole_0,d4_xboole_0,d58_glib_000,d59_glib_000,d5_real_1,d6_glib_001,d7_glib_001,d7_xboole_0,d8_xboole_0,d9_glib_004,dt_k10_domain_1,dt_k10_glib_000,dt_k10_glib_001,dt_k10_glib_004,dt_k11_glib_000,dt_k11_glib_003,dt_k11_glib_004,dt_k12_glib_003,dt_k12_glib_004,dt_k13_glib_000,dt_k13_glib_003,dt_k13_glib_004,dt_k14_glib_000,dt_k14_glib_001,dt_k14_glib_003,dt_k14_glib_004,dt_k15_glib_000,dt_k16_glib_000,dt_k17_glib_000,dt_k18_glib_000,dt_k1_card_1,dt_k1_card_fil,dt_k1_funct_1,dt_k1_glib_000,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_k22_glib_000,dt_k25_glib_000,dt_k26_glib_000,dt_k2_glib_000,dt_k2_glib_003,dt_k2_nat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_cqc_lang,dt_k3_enumset1,dt_k3_finseq_1,dt_k3_glib_000,dt_k3_glib_001,dt_k3_glib_003,dt_k3_real_1,dt_k3_uproots,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k40_glib_000,dt_k41_glib_000,dt_k42_glib_000,dt_k4_card_1,dt_k4_finseq_1,dt_k4_glib_000,dt_k4_glib_001,dt_k4_glib_003,dt_k4_relset_1,dt_k4_xboole_0,dt_k5_glib_003,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_subset_1,dt_k6_glib_000,dt_k6_glib_003,dt_k6_xcmplx_0,dt_k7_glib_000,dt_k7_glib_003,dt_k7_glib_004,dt_k7_relat_1,dt_k8_glib_000,dt_k8_glib_004,dt_k8_subset_1,dt_k9_glib_000,dt_k9_glib_004,dt_m1_finseq_1,dt_m1_glib_000,dt_m1_glib_004,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_glib_000,dt_m2_relset_1,dt_m2_subset_1,dt_m3_glib_000,dt_m3_glib_001,dt_m4_glib_001,existence_m1_finseq_1,existence_m1_glib_000,existence_m1_glib_004,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_glib_000,existence_m2_relset_1,existence_m2_subset_1,existence_m3_glib_000,existence_m3_glib_001,existence_m4_glib_001,fc100_glib_003,fc10_abian,fc10_finset_1,fc10_glib_000,fc10_glib_003,fc10_glib_004,fc10_membered,fc10_xreal_0,fc11_abian,fc11_finset_1,fc11_membered,fc11_xreal_0,fc12_abian,fc12_finset_1,fc12_relat_1,fc12_xreal_0,fc13_abian,fc13_relat_1,fc14_abian,fc14_finset_1,fc14_polynom1,fc15_abian,fc15_xreal_0,fc16_xreal_0,fc17_abian,fc17_glib_003,fc17_xreal_0,fc18_glib_003,fc18_xreal_0,fc19_glib_003,fc19_xreal_0,fc1_abian,fc1_finset_1,fc1_glib_000,fc1_glib_001,fc1_glib_002,fc1_glib_003,fc1_int_1,fc1_ordinal2,fc1_relat_1,fc1_subset_1,fc1_xboole_0,fc20_glib_003,fc20_polynom1,fc20_xreal_0,fc21_glib_003,fc21_xreal_0,fc22_glib_003,fc22_membered,fc22_xreal_0,fc23_glib_003,fc23_membered,fc23_xreal_0,fc24_glib_003,fc24_membered,fc24_xreal_0,fc25_glib_003,fc25_membered,fc26_glib_003,fc26_membered,fc27_glib_003,fc27_membered,fc28_glib_003,fc28_membered,fc29_glib_003,fc29_membered,fc2_abian,fc2_card_1,fc2_glib_000,fc2_glib_003,fc2_int_1,fc2_membered,fc2_relat_1,fc2_subset_1,fc2_xboole_0,fc30_glib_003,fc30_membered,fc31_glib_003,fc31_membered,fc32_glib_003,fc32_membered,fc33_glib_003,fc33_membered,fc34_glib_003,fc34_membered,fc35_glib_003,fc35_membered,fc36_glib_003,fc36_membered,fc37_glib_003,fc37_membered,fc38_glib_003,fc38_membered,fc39_glib_003,fc39_membered,fc3_abian,fc3_glib_003,fc3_polynom1,fc3_relat_1,fc3_xboole_0,fc3_xreal_0,fc40_glib_003,fc40_membered,fc41_glib_003,fc41_membered,fc42_glib_003,fc43_glib_003,fc44_glib_003,fc45_glib_003,fc46_glib_003,fc47_glib_003,fc48_glib_003,fc49_glib_003,fc4_abian,fc4_funct_1,fc4_glib_000,fc4_glib_003,fc4_int_1,fc4_relat_1,fc4_subset_1,fc4_xreal_0,fc50_glib_003,fc51_glib_003,fc52_glib_003,fc53_glib_003,fc54_glib_003,fc55_glib_003,fc56_glib_003,fc57_glib_003,fc58_glib_003,fc59_glib_003,fc5_abian,fc5_finset_1,fc5_glib_000,fc5_glib_003,fc5_membered,fc5_polynom1,fc5_relat_1,fc5_xreal_0,fc62_glib_003,fc63_glib_003,fc64_glib_003,fc65_glib_003,fc66_glib_003,fc67_glib_003,fc6_abian,fc6_glib_003,fc6_int_1,fc6_membered,fc6_relat_1,fc70_glib_003,fc71_glib_003,fc72_glib_003,fc73_glib_003,fc74_glib_003,fc75_glib_003,fc76_glib_003,fc78_glib_003,fc79_glib_003,fc7_abian,fc7_glib_003,fc7_glib_004,fc7_int_1,fc7_membered,fc7_relat_1,fc7_xreal_0,fc80_glib_003,fc81_glib_003,fc84_glib_003,fc85_glib_003,fc86_glib_003,fc87_glib_003,fc88_glib_003,fc89_glib_003,fc8_abian,fc8_glib_003,fc8_glib_004,fc8_int_1,fc8_membered,fc8_polynom1,fc8_relat_1,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_abian,fc9_finset_1,fc9_glib_003,fc9_glib_004,fc9_int_1,fc9_membered,fc9_xreal_0,fraenkel_a_1_2_glib_004,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k5_subset_1,irreflexivity_r2_xboole_0,l37_glib_004,l38_glib_004,l54_glib_004,l56_glib_004,l58_glib_004,l59_glib_004,l63_glib_004,l67_glib_004,l68_glib_004,rc10_glib_003,rc10_polynom1,rc11_glib_003,rc11_polynom1,rc12_polynom1,rc13_polynom1,rc1_abian,rc1_card_1,rc1_finset_1,rc1_funct_1,rc1_glib_000,rc1_glib_003,rc1_glib_004,rc1_int_1,rc1_membered,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc1_xreal_0,rc20_glib_003,rc2_abian,rc2_card_1,rc2_finset_1,rc2_funct_1,rc2_glib_003,rc2_glib_004,rc2_int_1,rc2_polynom1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,rc2_xreal_0,rc3_abian,rc3_finset_1,rc3_funct_1,rc3_glib_003,rc3_polynom1,rc3_relat_1,rc3_xreal_0,rc4_abian,rc4_finset_1,rc4_funct_1,rc4_polynom1,rc4_xreal_0,rc5_glib_000,rc6_glib_000,rc7_polynom1,rc8_polynom1,rc9_polynom1,redefinition_k10_domain_1,redefinition_k10_glib_000,redefinition_k11_glib_000,redefinition_k16_glib_000,redefinition_k18_glib_000,redefinition_k1_card_fil,redefinition_k1_nat_1,redefinition_k1_seq_1,redefinition_k25_glib_000,redefinition_k26_glib_000,redefinition_k2_nat_1,redefinition_k3_finseq_1,redefinition_k3_real_1,redefinition_k4_card_1,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_subset_1,redefinition_m1_glib_004,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r5_glib_000,s4_cqc_sim1__e13_84_2__glib_004,s5_nat_1__e22_84_2__glib_004,s5_nat_1__e3_84_2_13_1_1__glib_004,s5_nat_1__e3_84_2_13_1_2__glib_004,s5_nat_1__e9_84_2_3__glib_004,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,symmetry_r1_xboole_0,symmetry_r5_glib_000,t100_glib_001,t101_glib_001,t10_xreal_1,t111_glib_001,t112_glib_001,t120_glib_001,t127_glib_001,t133_glib_001,t139_glib_001,t13_finset_1,t151_glib_001,t15_glib_003,t161_glib_001,t16_glib_000,t16_glib_003,t176_glib_001,t177_glib_001,t18_glib_001,t18_int_1,t1_arithm,t1_boole,t1_heyting3,t1_numerals,t1_real,t1_subset,t1_xboole_1,t1_xreal_1,t20_glib_000,t20_glib_001,t22_nat_1,t23_glib_002,t23_xboole_1,t27_finseq_3,t2_arithm,t2_boole,t2_real,t2_subset,t2_tarski,t2_xboole_1,t2_xreal_1,t33_glib_004,t34_glib_000,t34_glib_004,t36_glib_004,t37_glib_000,t37_zfmisc_1,t38_nat_1,t3_arithm,t3_boole,t3_real,t3_subset,t46_glib_002,t47_glib_000,t47_glib_002,t48_glib_002,t4_arithm,t4_boole,t4_real,t4_subset,t50_xboole_1,t52_glib_003,t52_glib_004,t52_zfmisc_1,t53_card_2,t54_card_2,t54_glib_000,t56_glib_000,t56_glib_003,t5_glib_002,t5_real,t5_subset,t60_relat_1,t63_card_2,t65_glib_001,t66_glib_001,t67_card_2,t67_glib_001,t6_boole,t6_real,t72_funct_1,t75_glib_000,t76_glib_000,t79_card_1,t7_boole,t7_funct_2,t7_real,t7_xboole_1,t89_glib_000,t8_boole,t8_glib_001,t8_real,t8_xboole_1,t8_xreal_1,t91_glib_000,t92_real_1,t9_xreal_1]), [file(glib_004,t53_glib_004)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(antisymmetry_r2_xboole_0,axiom,( ! [A,B] : ( r2_xboole_0(A,B) => ~ r2_xboole_0(B,A) ) ), file(xboole_0,r2_xboole_0), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v5_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => v5_glib_000(B) ) ) ), file(glib_000,cc11_glib_000), []). 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_glib_000,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k22_glib_000(A,B))) ) => ! [D] : ( m3_glib_000(D,A,B,C) => v2_glib_000(D) ) ) ), file(glib_000,cc12_glib_000), []). 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_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m3_glib_000(C,A,B,k1_xboole_0) => v7_glib_000(C) ) ) ), file(glib_000,cc15_glib_000), []). 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_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k1_zfmisc_1(k7_glib_000(A))) ) => ! [C] : ( m3_glib_000(C,A,k6_glib_000(A),B) => v9_glib_000(C,A) ) ) ), file(glib_000,cc16_glib_000), []). 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_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_000(B,A,k6_glib_000(A),k1_xboole_0) => v9_glib_000(B,A) ) ) ), file(glib_000,cc17_glib_000), []). 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_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [C] : ( m3_glib_000(C,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),k1_tarski(B))) => v9_glib_000(C,A) ) ) ), file(glib_000,cc18_glib_000), []). 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_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [C] : ( m3_glib_000(C,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),B)) => v9_glib_000(C,A) ) ) ), file(glib_000,cc19_glib_000), []). 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_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v5_glib_000(A) ) => ( v1_glib_000(A) & v6_glib_000(A) ) ) ) ), file(glib_000,cc1_glib_000), []). 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_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,k5_numbers) ) => ! [C] : ( m3_glib_000(C,A,k14_glib_003(k42_glib_000(k13_glib_004(A),B)),k22_glib_000(A,k14_glib_003(k42_glib_000(k13_glib_004(A),B)))) => ( v2_glib_000(C) & v1_glib_002(C) ) ) ) ), file(glib_004,cc1_glib_004), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). 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_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v7_glib_000(A) ) => ( v1_glib_000(A) & v3_glib_000(A) & v5_glib_000(A) ) ) ) ), file(glib_000,cc2_glib_000), []). 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_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_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,k5_numbers) ) => ! [C] : ( m3_glib_000(C,A,k14_glib_003(k42_glib_000(k13_glib_004(A),B)),k11_glib_003(k42_glib_000(k13_glib_004(A),B))) => ( v2_glib_000(C) & v1_glib_002(C) ) ) ) ), file(glib_004,cc2_glib_004), []). 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_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v3_glib_000(A) & v5_glib_000(A) ) => ( v1_glib_000(A) & v7_glib_000(A) ) ) ) ), file(glib_000,cc3_glib_000), []). 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_002,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v2_glib_002(A) ) => ( v1_glib_000(A) & v3_glib_000(A) & v5_glib_000(A) & v6_glib_000(A) & v7_glib_000(A) & v8_glib_000(A) ) ) ) ), file(glib_002,cc3_glib_002), []). 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_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v3_glib_000(A) & v6_glib_000(A) ) => ( v1_glib_000(A) & v8_glib_000(A) ) ) ) ), file(glib_000,cc4_glib_000), []). 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_glib_002,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v3_glib_002(A) ) => ( v1_glib_000(A) & v3_glib_000(A) & v5_glib_000(A) & v6_glib_000(A) & v7_glib_000(A) & v8_glib_000(A) & v1_glib_002(A) & v2_glib_002(A) ) ) ) ), file(glib_002,cc4_glib_002), []). fof(cc4_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ( ( v1_glib_003(B) & v4_glib_003(B,A) ) => ( v1_glib_003(B) & v4_glib_003(B,A) & v7_glib_003(B) ) ) ) ) ), file(glib_003,cc4_glib_003), []). 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_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v8_glib_000(A) ) => ( v1_glib_000(A) & v3_glib_000(A) & v6_glib_000(A) ) ) ) ), file(glib_000,cc5_glib_000), []). fof(cc5_glib_002,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v1_glib_002(A) & v2_glib_002(A) ) => ( v1_glib_000(A) & v3_glib_000(A) & v5_glib_000(A) & v6_glib_000(A) & v7_glib_000(A) & v8_glib_000(A) & v1_glib_002(A) & v2_glib_002(A) & v3_glib_002(A) ) ) ) ), file(glib_002,cc5_glib_002), []). 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_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v8_glib_001(B,A) => ( v1_relat_1(B) & v1_glib_001(B,A) & ~ v3_glib_001(B,A) & v5_glib_001(B,A) ) ) ) ) ), file(glib_001,cc6_glib_001), []). 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_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_002(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ( v3_glib_000(B) & v5_glib_000(B) & v2_glib_002(B) ) ) ) ), file(glib_002,cc7_glib_002), []). 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_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => v2_glib_000(B) ) ) ), file(glib_000,cc8_glib_000), []). 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_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v3_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => v3_glib_000(B) ) ) ), file(glib_000,cc9_glib_000), []). 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_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_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_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(d10_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_003(B) & m2_glib_000(B,A) ) => ( v4_glib_003(B,A) <=> k5_glib_003(B) = k7_relat_1(k5_glib_003(A),k26_glib_000(A,B)) ) ) ) ), file(glib_003,d10_glib_003), []). fof(d10_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( B = k8_glib_004(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_glib_003(D) & v4_glib_003(D,A) & m2_glib_000(D,A) & C = D & k1_relat_1(D) = k7_glib_004 ) ) ) ) ) ), file(glib_004,d10_glib_004), []). fof(d11_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => k9_glib_004(A) = k3_uproots(k7_glib_000(A),k5_glib_003(A)) ) ), file(glib_004,d11_glib_004), []). fof(d12_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v3_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k7_glib_000(A))) => ( B = k10_glib_004(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r3_glib_000(A,k14_glib_003(A),k1_card_fil(k6_glib_000(A),k14_glib_003(A)),C) & ! [D] : ( r3_glib_000(A,k14_glib_003(A),k1_card_fil(k6_glib_000(A),k14_glib_003(A)),D) => r1_xreal_0(k1_seq_1(k5_glib_003(A),C),k1_seq_1(k5_glib_003(A),D)) ) ) ) ) ) ) ), file(glib_004,d12_glib_004), []). fof(d13_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => k11_glib_004(A) = k13_glib_000(k13_glib_000(A,k4_glib_003,k3_cqc_lang(k8_subset_1(k6_glib_000(A)),1)),k3_glib_003,k1_xboole_0) ) ), file(glib_004,d13_glib_004), []). fof(d14_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) ) => ( ( k10_glib_004(A) = k1_xboole_0 => k12_glib_004(A) = A ) & ( r2_hidden(k1_funct_1(k10_glib_000(A),k8_subset_1(k10_glib_004(A))),k14_glib_003(A)) => ( k10_glib_004(A) = k1_xboole_0 | k12_glib_004(A) = k13_glib_003(k12_glib_003(A,k8_subset_1(k10_glib_004(A)),1),k1_funct_1(k11_glib_000(A),k8_subset_1(k10_glib_004(A))),1) ) ) & ~ ( k10_glib_004(A) != k1_xboole_0 & ~ ( k10_glib_004(A) != k1_xboole_0 & r2_hidden(k1_funct_1(k10_glib_000(A),k8_subset_1(k10_glib_004(A))),k14_glib_003(A)) ) & k12_glib_004(A) != k13_glib_003(k12_glib_003(A,k8_subset_1(k10_glib_004(A)),1),k1_funct_1(k10_glib_000(A),k8_subset_1(k10_glib_004(A))),1) ) ) ) ), file(glib_004,d14_glib_004), []). 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(d15_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v12_glib_000(B) & v12_glib_003(B) & v13_glib_003(B) & v14_glib_003(B) & v19_glib_003(B) & m1_pboole(B,k5_numbers) ) => ( B = k13_glib_004(A) <=> ( k42_glib_000(B,0) = k11_glib_004(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k42_glib_000(B,k1_nat_1(C,1)) = k12_glib_004(k42_glib_000(B,C)) ) ) ) ) ) ), file(glib_004,d15_glib_004), []). fof(d16_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => k14_glib_004(A) = k41_glib_000(k13_glib_004(A)) ) ), file(glib_004,d16_glib_004), []). fof(d17_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r3_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) ) | ( r2_hidden(k1_funct_1(k10_glib_000(A),D),C) & r2_hidden(k1_funct_1(k11_glib_000(A),D),B) ) ) ) ) ) ), file(glib_000,d17_glib_000), []). fof(d17_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & m2_glib_000(B,A) ) => ( v1_glib_004(B,A) <=> ! [C] : ( ( v9_glib_000(C,A) & v3_glib_002(C) & v1_glib_003(C) & v4_glib_003(C,A) & m2_glib_000(C,A) ) => r1_xreal_0(k9_glib_004(B),k9_glib_004(C)) ) ) ) ) ), file(glib_004,d17_glib_004), []). fof(d1_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_glib_002(A) <=> ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ? [D] : ( m3_glib_001(D,A) & r1_glib_001(A,B,C,D) ) ) ) ) ) ), file(glib_002,d1_glib_002), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_xboole_0,axiom,( ! [A] : ( A = k1_xboole_0 <=> ! [B] : ~ r2_hidden(B,A) ) ), file(xboole_0,d1_xboole_0), []). fof(d20_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v3_glib_000(A) <=> ! [B] : ~ ( r2_hidden(B,k7_glib_000(A)) & k1_funct_1(k10_glib_000(A),B) = k1_funct_1(k11_glib_000(A),B) ) ) ) ), file(glib_000,d20_glib_000), []). fof(d20_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => k11_glib_003(A) = k1_relat_1(k6_glib_003(A)) ) ), file(glib_003,d20_glib_003), []). 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(d24_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_glib_001(B,A) <=> k3_glib_001(A,B) = k4_glib_001(A,B) ) ) ) ), file(glib_001,d24_glib_001), []). fof(d26_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => k15_glib_000(A) = k1_card_1(k6_glib_000(A)) ) ), file(glib_000,d26_glib_000), []). fof(d27_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => k17_glib_000(A) = k1_card_1(k7_glib_000(A)) ) ), file(glib_000,d27_glib_000), []). 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(d2_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v2_glib_002(A) <=> ! [B] : ( m3_glib_001(B,A) => ~ v8_glib_001(B,A) ) ) ) ), file(glib_002,d2_glib_002), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d31_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v8_glib_001(B,A) <=> ( v1_glib_001(B,A) & v5_glib_001(B,A) & ~ v3_glib_001(B,A) ) ) ) ) ), file(glib_001,d31_glib_001), []). fof(d34_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ( m2_glib_000(B,A) <=> ( r1_tarski(k6_glib_000(B),k6_glib_000(A)) & r1_tarski(k7_glib_000(B),k7_glib_000(A)) & ! [C] : ( r2_hidden(C,k7_glib_000(B)) => ( k1_funct_1(k10_glib_000(B),C) = k1_funct_1(k10_glib_000(A),C) & k1_funct_1(k11_glib_000(B),C) = k1_funct_1(k11_glib_000(A),C) ) ) ) ) ) ) ), file(glib_000,d34_glib_000), []). fof(d35_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ( v9_glib_000(B,A) <=> k25_glib_000(A,B) = k6_glib_000(A) ) ) ) ), file(glib_000,d35_glib_000), []). 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(d39_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( m2_glib_000(D,A) => ( ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) & r1_tarski(C,k22_glib_000(A,B)) ) => ( m3_glib_000(D,A,B,C) <=> ( k25_glib_000(A,D) = B & k26_glib_000(A,D) = C ) ) ) & ( ~ ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) & r1_tarski(C,k22_glib_000(A,B)) ) => ( m3_glib_000(D,A,B,C) <=> r5_glib_000(D,A) ) ) ) ) ) ), file(glib_000,d39_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_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(d58_glib_000,axiom,( ! [A] : ( m1_pboole(A,k5_numbers) => k41_glib_000(A) = k1_funct_1(A,k40_glib_000(A)) ) ), file(glib_000,d58_glib_000), []). fof(d59_glib_000,axiom,( ! [A] : ( ( v12_glib_000(A) & m1_pboole(A,k5_numbers) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k42_glib_000(A,B) = k1_funct_1(A,B) ) ) ), file(glib_000,d59_glib_000), []). 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_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), []). fof(d8_xboole_0,axiom,( ! [A,B] : ( r2_xboole_0(A,B) <=> ( r1_tarski(A,B) & A != B ) ) ), file(xboole_0,d8_xboole_0), []). fof(d9_glib_004,axiom,( k7_glib_004 = k10_domain_1(k5_numbers,k1_glib_000,k2_glib_000,k3_glib_000,k4_glib_000,k2_glib_003) ), file(glib_004,d9_glib_004), []). fof(dt_k10_domain_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) ) => m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)) ) ), file(domain_1,k10_domain_1), []). 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_k10_glib_001,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => m3_glib_001(k10_glib_001(A,B,C),A) ) ), file(glib_001,k10_glib_001), []). fof(dt_k10_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v3_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => m1_subset_1(k10_glib_004(A),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_004,k10_glib_004), []). 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_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => m1_subset_1(k11_glib_003(A),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_003,k11_glib_003), []). fof(dt_k11_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_glib_000(k11_glib_004(A)) & v1_glib_003(k11_glib_004(A)) & v2_glib_003(k11_glib_004(A)) & v3_glib_003(k11_glib_004(A)) & v11_glib_003(k11_glib_004(A)) & m1_glib_000(k11_glib_004(A)) ) ) ), file(glib_004,k11_glib_004), []). 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_k12_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(k12_glib_004(A)) & v1_glib_003(k12_glib_004(A)) & v2_glib_003(k12_glib_004(A)) & v3_glib_003(k12_glib_004(A)) & v11_glib_003(k12_glib_004(A)) & m1_glib_000(k12_glib_004(A)) ) ) ), file(glib_004,k12_glib_004), []). 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_k13_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v12_glib_000(k13_glib_004(A)) & v12_glib_003(k13_glib_004(A)) & v13_glib_003(k13_glib_004(A)) & v14_glib_003(k13_glib_004(A)) & v19_glib_003(k13_glib_004(A)) & m1_pboole(k13_glib_004(A),k5_numbers) ) ) ), file(glib_004,k13_glib_004), []). fof(dt_k14_glib_000,axiom,( ! [A,B] : ( m1_glib_000(A) => m1_glib_000(k14_glib_000(A,B)) ) ), file(glib_000,k14_glib_000), []). 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_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_k14_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_glib_000(k14_glib_004(A)) & v1_glib_003(k14_glib_004(A)) & v2_glib_003(k14_glib_004(A)) & v3_glib_003(k14_glib_004(A)) & v11_glib_003(k14_glib_004(A)) & m1_glib_000(k14_glib_004(A)) ) ) ), file(glib_004,k14_glib_004), []). fof(dt_k15_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => v1_card_1(k15_glib_000(A)) ) ), file(glib_000,k15_glib_000), []). fof(dt_k16_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( ~ v1_xboole_0(k16_glib_000(A)) & m2_subset_1(k16_glib_000(A),k1_numbers,k5_numbers) ) ) ), file(glib_000,k16_glib_000), []). fof(dt_k17_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => v1_card_1(k17_glib_000(A)) ) ), file(glib_000,k17_glib_000), []). fof(dt_k18_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => m2_subset_1(k18_glib_000(A),k1_numbers,k5_numbers) ) ), file(glib_000,k18_glib_000), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). 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_glib_000,axiom,( m2_subset_1(k1_glib_000,k1_numbers,k5_numbers) ), file(glib_000,k1_glib_000), []). 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_k22_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => m1_subset_1(k22_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_000,k22_glib_000), []). fof(dt_k25_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m2_glib_000(B,A) ) => ( ~ v1_xboole_0(k25_glib_000(A,B)) & m1_subset_1(k25_glib_000(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ) ), file(glib_000,k25_glib_000), []). fof(dt_k26_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m2_glib_000(B,A) ) => m1_subset_1(k26_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_000,k26_glib_000), []). fof(dt_k2_glib_000,axiom,( m2_subset_1(k2_glib_000,k1_numbers,k5_numbers) ), file(glib_000,k2_glib_000), []). fof(dt_k2_glib_003,axiom,( m2_subset_1(k2_glib_003,k1_numbers,k5_numbers) ), file(glib_003,k2_glib_003), []). 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_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). fof(dt_k3_enumset1,axiom,( $true ), file(enumset1,k3_enumset1), []). 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_000,axiom,( m2_subset_1(k3_glib_000,k1_numbers,k5_numbers) ), file(glib_000,k3_glib_000), []). 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_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_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k40_glib_000,axiom,( ! [A] : ( m1_pboole(A,k5_numbers) => m2_subset_1(k40_glib_000(A),k1_numbers,k5_numbers) ) ), file(glib_000,k40_glib_000), []). fof(dt_k41_glib_000,axiom,( $true ), file(glib_000,k41_glib_000), []). 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_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers) ) ), file(card_1,k4_card_1), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_glib_000,axiom,( m2_subset_1(k4_glib_000,k1_numbers,k5_numbers) ), file(glib_000,k4_glib_000), []). 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_glib_003,axiom,( m2_subset_1(k4_glib_003,k1_numbers,k5_numbers) ), file(glib_003,k4_glib_003), []). 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_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_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_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_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_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_k7_glib_004,axiom, ( ~ v1_xboole_0(k7_glib_004) & v1_finset_1(k7_glib_004) & m1_subset_1(k7_glib_004,k1_zfmisc_1(k5_numbers)) ), file(glib_004,k7_glib_004), []). 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_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ~ v1_xboole_0(k8_glib_004(A)) ) ), file(glib_004,k8_glib_004), []). 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_k9_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => m1_subset_1(k9_glib_004(A),k1_numbers) ) ), file(glib_004,k9_glib_004), []). 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_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k8_glib_004(A))) ) => ! [C] : ( m1_glib_004(C,A,B) => ( v1_glib_003(C) & v4_glib_003(C,A) & m2_glib_000(C,A) ) ) ) ), file(glib_004,m1_glib_004), []). 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_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ( v1_glib_000(B) & m1_glib_000(B) ) ) ) ), file(glib_000,m2_glib_000), []). 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_000,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [D] : ( m3_glib_000(D,A,B,C) => m2_glib_000(D,A) ) ) ), file(glib_000,m3_glib_000), []). 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(dt_m4_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => ! [C] : ( m4_glib_001(C,A,B) => m3_glib_001(C,A) ) ) ), file(glib_001,m4_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_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k8_glib_004(A))) ) => ? [C] : m1_glib_004(C,A,B) ) ), file(glib_004,m1_glib_004), []). 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_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : m2_glib_000(B,A) ) ), file(glib_000,m2_glib_000), []). 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_000,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [D] : m3_glib_000(D,A,B,C) ) ), file(glib_000,m3_glib_000), []). 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(existence_m4_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => ? [C] : m4_glib_001(C,A,B) ) ), file(glib_001,m4_glib_001), []). 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_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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v3_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)) & v3_glib_000(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc10_glib_003), []). fof(fc10_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k14_glib_004(A)) & v1_funct_1(k14_glib_004(A)) & v1_finset_1(k14_glib_004(A)) & v1_polynom1(k14_glib_004(A)) & v1_glib_000(k14_glib_004(A)) & v2_glib_000(k14_glib_004(A)) & v1_glib_003(k14_glib_004(A)) & v2_glib_003(k14_glib_004(A)) & v3_glib_003(k14_glib_004(A)) & v7_glib_003(k14_glib_004(A)) & v9_glib_003(k14_glib_004(A)) & v10_glib_003(k14_glib_004(A)) & v11_glib_003(k14_glib_004(A)) ) ) ), file(glib_004,fc10_glib_004), []). 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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_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_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(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_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)) ) ) ), file(relat_1,fc13_relat_1), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v5_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v5_glib_000(k13_glib_000(A,k2_glib_003,B)) & v6_glib_000(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc17_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v5_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)) & v5_glib_000(k13_glib_000(A,k3_glib_003,B)) & v6_glib_000(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc18_glib_003), []). 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_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v5_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)) & v5_glib_000(k13_glib_000(A,k4_glib_003,B)) & v6_glib_000(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc19_glib_003), []). 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_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_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_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_1), []). fof(fc1_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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v6_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v6_glib_000(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc20_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v6_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)) & v6_glib_000(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc21_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v6_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)) & v6_glib_000(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc22_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_002(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v1_glib_002(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc23_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_002(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_002(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc24_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_002(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_002(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc25_glib_003), []). 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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_002(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v3_glib_000(k13_glib_000(A,k2_glib_003,B)) & v5_glib_000(k13_glib_000(A,k2_glib_003,B)) & v6_glib_000(k13_glib_000(A,k2_glib_003,B)) & v7_glib_000(k13_glib_000(A,k2_glib_003,B)) & v8_glib_000(k13_glib_000(A,k2_glib_003,B)) & v2_glib_002(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc26_glib_003), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc27_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_002(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_000(k13_glib_000(A,k3_glib_003,B)) & v5_glib_000(k13_glib_000(A,k3_glib_003,B)) & v6_glib_000(k13_glib_000(A,k3_glib_003,B)) & v7_glib_000(k13_glib_000(A,k3_glib_003,B)) & v8_glib_000(k13_glib_000(A,k3_glib_003,B)) & v2_glib_002(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc27_glib_003), []). fof(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_002(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)) & v3_glib_000(k13_glib_000(A,k4_glib_003,B)) & v5_glib_000(k13_glib_000(A,k4_glib_003,B)) & v6_glib_000(k13_glib_000(A,k4_glib_003,B)) & v7_glib_000(k13_glib_000(A,k4_glib_003,B)) & v8_glib_000(k13_glib_000(A,k4_glib_003,B)) & v2_glib_002(k13_glib_000(A,k4_glib_003,B)) ) ) ), file(glib_003,fc28_glib_003), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_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(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). fof(fc2_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_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) ), file(card_1,fc2_card_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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc2_glib_003), []). fof(fc2_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) ), file(relat_1,fc2_relat_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc30_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(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_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,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v1_glib_003(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc31_glib_003), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_glib_003,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,k2_glib_003,C)) & v1_funct_1(k13_glib_000(A,k2_glib_003,C)) & v1_finset_1(k13_glib_000(A,k2_glib_003,C)) & v1_polynom1(k13_glib_000(A,k2_glib_003,C)) & v1_glib_000(k13_glib_000(A,k2_glib_003,C)) & v1_glib_003(k13_glib_000(A,k2_glib_003,C)) ) ) ), file(glib_003,fc32_glib_003), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v2_glib_003(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc33_glib_003), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_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(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_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(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_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(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc37_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v3_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v3_glib_003(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc37_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_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_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_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_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc40_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(fc43_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & v1_funct_1(B) & v1_funct_2(B,k7_glib_000(A),k1_numbers) & m1_relset_1(B,k7_glib_000(A),k1_numbers) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v1_glib_003(k13_glib_000(A,k2_glib_003,B)) & v7_glib_003(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc43_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_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_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). 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_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_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(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(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(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(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(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(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_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_finset_1,axiom,( ! [A,B,C,D,E] : v1_finset_1(k3_enumset1(A,B,C,D,E)) ), file(finset_1,fc5_finset_1), []). 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_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v2_glib_000(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc5_glib_003), []). 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(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(fc62_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,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v2_glib_003(k13_glib_000(A,k2_glib_003,B)) & v9_glib_003(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc62_glib_003), []). 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(fc64_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,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v3_glib_003(k13_glib_000(A,k2_glib_003,B)) & v10_glib_003(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc64_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(fc67_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v3_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)) & v3_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc67_glib_003), []). 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(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc70_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v5_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)) & v5_glib_000(k12_glib_003(A,B,C)) & v6_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc70_glib_003), []). fof(fc71_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v6_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)) & v6_glib_000(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc71_glib_003), []). fof(fc72_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_002(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_002(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc72_glib_003), []). fof(fc73_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_002(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)) & v3_glib_000(k12_glib_003(A,B,C)) & v5_glib_000(k12_glib_003(A,B,C)) & v6_glib_000(k12_glib_003(A,B,C)) & v7_glib_000(k12_glib_003(A,B,C)) & v8_glib_000(k12_glib_003(A,B,C)) & v2_glib_002(k12_glib_003(A,B,C)) & v2_glib_003(k12_glib_003(A,B,C)) ) ) ), file(glib_003,fc73_glib_003), []). 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_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_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_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k14_glib_000(A,k7_glib_004)) & v1_funct_1(k14_glib_000(A,k7_glib_004)) & v1_finset_1(k14_glib_000(A,k7_glib_004)) & v1_polynom1(k14_glib_000(A,k7_glib_004)) & v1_glib_000(k14_glib_000(A,k7_glib_004)) & v1_glib_003(k14_glib_000(A,k7_glib_004)) ) ) ), file(glib_004,fc7_glib_004), []). 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_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(fc81_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v3_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)) & v3_glib_000(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc81_glib_003), []). fof(fc84_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v5_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)) & v5_glib_000(k13_glib_003(A,B,C)) & v6_glib_000(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc84_glib_003), []). fof(fc85_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v6_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)) & v6_glib_000(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc85_glib_003), []). fof(fc86_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_002(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_002(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc86_glib_003), []). fof(fc87_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_002(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)) & v3_glib_000(k13_glib_003(A,B,C)) & v5_glib_000(k13_glib_003(A,B,C)) & v6_glib_000(k13_glib_003(A,B,C)) & v7_glib_000(k13_glib_003(A,B,C)) & v8_glib_000(k13_glib_003(A,B,C)) & v2_glib_002(k13_glib_003(A,B,C)) & v3_glib_003(k13_glib_003(A,B,C)) ) ) ), file(glib_003,fc87_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_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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v3_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_000(A,k2_glib_003,B)) & v1_funct_1(k13_glib_000(A,k2_glib_003,B)) & v1_finset_1(k13_glib_000(A,k2_glib_003,B)) & v1_polynom1(k13_glib_000(A,k2_glib_003,B)) & v1_glib_000(k13_glib_000(A,k2_glib_003,B)) & v3_glib_000(k13_glib_000(A,k2_glib_003,B)) ) ) ), file(glib_003,fc8_glib_003), []). fof(fc8_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ( ~ v1_xboole_0(k8_glib_004(A)) & v1_finset_1(k8_glib_004(A)) ) ) ), file(glib_004,fc8_glib_004), []). 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_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(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_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_glib_003,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v3_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)) & v3_glib_000(k13_glib_000(A,k3_glib_003,B)) ) ) ), file(glib_003,fc9_glib_003), []). fof(fc9_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( v1_relat_1(k13_glib_004(A)) & v1_funct_1(k13_glib_004(A)) & v12_glib_000(k13_glib_004(A)) & v14_glib_000(k13_glib_004(A)) & v12_glib_003(k13_glib_004(A)) & v13_glib_003(k13_glib_004(A)) & v14_glib_003(k13_glib_004(A)) & v15_glib_003(k13_glib_004(A)) & v17_glib_003(k13_glib_004(A)) & v18_glib_003(k13_glib_004(A)) & v19_glib_003(k13_glib_004(A)) ) ) ), file(glib_004,fc9_glib_004), []). 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(fraenkel_a_1_2_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(B) & v2_glib_000(B) & v1_glib_002(B) & v1_glib_003(B) & v7_glib_003(B) & m1_glib_000(B) ) => ( r2_hidden(A,a_1_2_glib_004(B)) <=> ? [C] : ( m1_subset_1(C,k8_glib_004(B)) & A = C & v9_glib_000(C,B) & v3_glib_002(C) & v1_glib_003(C) & v4_glib_003(C,B) & v1_glib_004(C,B) & m2_glib_000(C,B) ) ) ) ), file(glib_004,a_1_2_glib_004), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(irreflexivity_r2_xboole_0,axiom,( ! [A,B] : ~ r2_xboole_0(A,A) ), file(xboole_0,r2_xboole_0), []). fof(l37_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ( r5_glib_000(A,k14_glib_000(A,k7_glib_004)) & k5_glib_003(A) = k5_glib_003(k14_glib_000(A,k7_glib_004)) ) ) ), file(glib_004,l37_glib_004), []). fof(l38_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => k1_relat_1(k14_glib_000(A,k7_glib_004)) = k7_glib_004 ) ), file(glib_004,l38_glib_004), []). fof(l54_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ( r5_glib_000(A,k11_glib_004(A)) & k5_glib_003(A) = k5_glib_003(k11_glib_004(A)) & k6_glib_003(k11_glib_004(A)) = k1_xboole_0 & k7_glib_003(k11_glib_004(A)) = k3_cqc_lang(k8_subset_1(k6_glib_000(A)),1) ) ) ), file(glib_004,l54_glib_004), []). fof(l56_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) ) => ~ ( k10_glib_004(A) != k1_xboole_0 & ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ~ ( ~ r2_hidden(B,k14_glib_003(A)) & k12_glib_004(A) = k13_glib_003(k12_glib_003(A,k8_subset_1(k10_glib_004(A)),1),B,1) ) ) ) ) ), file(glib_004,l56_glib_004), []). fof(l58_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r5_glib_000(A,k42_glib_000(k13_glib_004(A),B)) & k5_glib_003(k42_glib_000(k13_glib_004(A),B)) = k5_glib_003(A) ) ) ) ), file(glib_004,l58_glib_004), []). fof(l59_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ~ v1_xboole_0(k14_glib_003(k42_glib_000(k13_glib_004(A),B))) & m1_subset_1(k14_glib_003(k42_glib_000(k13_glib_004(A),B)),k1_zfmisc_1(k6_glib_000(A))) & r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),B)),k22_glib_000(A,k14_glib_003(k42_glib_000(k13_glib_004(A),B)))) ) ) ) ), file(glib_004,l59_glib_004), []). fof(l63_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r1_xreal_0(B,C) => ( r1_tarski(k14_glib_003(k42_glib_000(k13_glib_004(A),B)),k14_glib_003(k42_glib_000(k13_glib_004(A),C))) & r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),B)),k11_glib_003(k42_glib_000(k13_glib_004(A),C))) ) ) ) ) ) ), file(glib_004,l63_glib_004), []). fof(l67_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m3_glib_000(C,A,k14_glib_003(k42_glib_000(k13_glib_004(A),B)),k11_glib_003(k42_glib_000(k13_glib_004(A),B))) => v3_glib_002(C) ) ) ) ), file(glib_004,l67_glib_004), []). fof(l68_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => k14_glib_003(k14_glib_004(A)) = k6_glib_000(A) ) ), file(glib_004,l68_glib_004), []). fof(rc10_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [D] : ( m3_glib_000(D,A,B,C) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v1_polynom1(D) & v1_glib_000(D) & v1_glib_003(D) & v2_glib_003(D) & v3_glib_003(D) ) ) ), file(glib_003,rc10_glib_003), []). 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_glib_003,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ? [D] : ( m3_glib_000(D,A,B,C) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v1_polynom1(D) & v1_glib_000(D) & v1_glib_003(D) & v4_glib_003(D,A) ) ) ), file(glib_003,rc11_glib_003), []). 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_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_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ? [B] : ( m2_glib_000(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_polynom1(B) & v1_glib_000(B) & v2_glib_000(B) & v3_glib_000(B) & v5_glib_000(B) & v6_glib_000(B) & v7_glib_000(B) & v8_glib_000(B) & v9_glib_000(B,A) & v1_glib_002(B) & v2_glib_002(B) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v7_glib_003(B) ) ) ), file(glib_004,rc1_glib_004), []). 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_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_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_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : ( m2_glib_000(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_polynom1(B) & v1_glib_000(B) & v1_glib_003(B) & v2_glib_003(B) & v3_glib_003(B) ) ) ), file(glib_003,rc2_glib_003), []). fof(rc2_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ? [B] : ( m2_glib_000(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_polynom1(B) & v1_glib_000(B) & v2_glib_000(B) & v3_glib_000(B) & v5_glib_000(B) & v6_glib_000(B) & v7_glib_000(B) & v8_glib_000(B) & v9_glib_000(B,A) & v1_glib_002(B) & v2_glib_002(B) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v7_glib_003(B) & v1_glib_004(B,A) ) ) ), file(glib_004,rc2_glib_004), []). 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_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) ), file(abian,rc3_abian), []). 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_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ? [B] : ( m2_glib_000(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_polynom1(B) & v1_glib_000(B) & v1_glib_003(B) & v4_glib_003(B,A) ) ) ), file(glib_003,rc3_glib_003), []). 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_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_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) ), file(abian,rc4_abian), []). 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_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(rc5_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : ( m2_glib_000(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v9_glib_000(B,A) ) ) ), file(glib_000,rc5_glib_000), []). 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_domain_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) ) => k10_domain_1(A,B,C,D,E,F) = k3_enumset1(B,C,D,E,F) ) ), file(domain_1,k10_domain_1), []). 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_k16_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => k16_glib_000(A) = k15_glib_000(A) ) ), file(glib_000,k16_glib_000), []). fof(redefinition_k18_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => k18_glib_000(A) = k17_glib_000(A) ) ), file(glib_000,k18_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_k25_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m2_glib_000(B,A) ) => k25_glib_000(A,B) = k6_glib_000(B) ) ), file(glib_000,k25_glib_000), []). fof(redefinition_k26_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m2_glib_000(B,A) ) => k26_glib_000(A,B) = k7_glib_000(B) ) ), file(glib_000,k26_glib_000), []). 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_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_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_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_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_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_m1_glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k8_glib_004(A))) ) => ! [C] : ( m1_glib_004(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(glib_004,m1_glib_004), []). 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_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(s4_cqc_sim1__e13_84_2__glib_004,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & v1_glib_003(B) & v4_glib_003(B,A) & m3_glib_000(B,A,k14_glib_003(k14_glib_004(A)),k11_glib_003(k14_glib_004(A))) & ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k8_glib_004(A))) ) => ( ( v1_finset_1(C) & C != k1_xboole_0 & r1_tarski(C,C) & ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,C) => ( ~ ( r1_xreal_0(k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))),k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B)))) & ~ ( k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))) = k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(F,1))),k7_glib_000(D)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r1_xreal_0(H,F) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),H)),k7_glib_000(D)) ) ) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(G,1))),k7_glib_000(E)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r1_xreal_0(H,G) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),H)),k7_glib_000(E)) ) ) ) => r1_xreal_0(G,F) ) ) ) ) ) | ~ ( r1_xreal_0(k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))),k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B)))) & ~ ( k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))) = k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(I,1))),k7_glib_000(E)) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ( r1_xreal_0(K,I) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),K)),k7_glib_000(E)) ) ) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(J,1))),k7_glib_000(D)) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ( r1_xreal_0(K,J) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),K)),k7_glib_000(D)) ) ) ) => r1_xreal_0(J,I) ) ) ) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,C) => ! [L] : ( m1_subset_1(L,C) => ( ( ~ ( r1_xreal_0(k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))),k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B)))) & ~ ( k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))) = k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ! [N] : ( m2_subset_1(N,k1_numbers,k5_numbers) => ( ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(M,1))),k7_glib_000(D)) & ! [O] : ( m2_subset_1(O,k1_numbers,k5_numbers) => ( r1_xreal_0(O,M) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),O)),k7_glib_000(D)) ) ) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(N,1))),k7_glib_000(E)) & ! [O] : ( m2_subset_1(O,k1_numbers,k5_numbers) => ( r1_xreal_0(O,N) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),O)),k7_glib_000(E)) ) ) ) => r1_xreal_0(N,M) ) ) ) ) ) & ~ ( r1_xreal_0(k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))),k4_card_1(k3_xboole_0(k7_glib_000(L),k26_glib_000(A,B)))) & ~ ( k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))) = k4_card_1(k3_xboole_0(k7_glib_000(L),k26_glib_000(A,B))) & ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ! [Q] : ( m2_subset_1(Q,k1_numbers,k5_numbers) => ( ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(P,1))),k7_glib_000(E)) & ! [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) => ( r1_xreal_0(R,P) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),R)),k7_glib_000(E)) ) ) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(Q,1))),k7_glib_000(L)) & ! [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) => ( r1_xreal_0(R,Q) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),R)),k7_glib_000(L)) ) ) ) => r1_xreal_0(Q,P) ) ) ) ) ) ) => ~ ( r1_xreal_0(k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))),k4_card_1(k3_xboole_0(k7_glib_000(L),k26_glib_000(A,B)))) & ~ ( k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))) = k4_card_1(k3_xboole_0(k7_glib_000(L),k26_glib_000(A,B))) & ! [S] : ( m2_subset_1(S,k1_numbers,k5_numbers) => ! [T] : ( m2_subset_1(T,k1_numbers,k5_numbers) => ( ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(S,1))),k7_glib_000(D)) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ( r1_xreal_0(U,S) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),U)),k7_glib_000(D)) ) ) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(T,1))),k7_glib_000(L)) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ( r1_xreal_0(U,T) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),U)),k7_glib_000(L)) ) ) ) => r1_xreal_0(T,S) ) ) ) ) ) ) ) ) ) ) => ? [D] : ( m1_subset_1(D,C) & r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,C) => ( r2_hidden(E,C) => ~ ( r1_xreal_0(k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))),k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B)))) & ~ ( k4_card_1(k3_xboole_0(k7_glib_000(D),k26_glib_000(A,B))) = k4_card_1(k3_xboole_0(k7_glib_000(E),k26_glib_000(A,B))) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ! [W] : ( m2_subset_1(W,k1_numbers,k5_numbers) => ( ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(V,1))),k7_glib_000(D)) & ! [X] : ( m2_subset_1(X,k1_numbers,k5_numbers) => ( r1_xreal_0(X,V) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),X)),k7_glib_000(D)) ) ) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),k1_nat_1(W,1))),k7_glib_000(E)) & ! [X] : ( m2_subset_1(X,k1_numbers,k5_numbers) => ( r1_xreal_0(X,W) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),X)),k7_glib_000(E)) ) ) ) => r1_xreal_0(W,V) ) ) ) ) ) ) ) ) ) ) ), file(glib_004,s4_cqc_sim1__e13_84_2__glib_004), []). fof(s5_nat_1__e22_84_2__glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v1_glib_004(B,A) & m2_glib_000(B,A) ) => ( ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),C)),k26_glib_000(A,B)) ) => ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),C)),k26_glib_000(A,B)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),D)),k26_glib_000(A,B)) => r1_xreal_0(C,D) ) ) ) ) ) ), file(glib_004,s5_nat_1__e22_84_2__glib_004), []). fof(s5_nat_1__e3_84_2_13_1_1__glib_004,axiom,( ! [A,B,C,D,E] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v1_glib_004(B,A) & m2_glib_000(B,A) & m2_subset_1(C,k1_numbers,k5_numbers) & v1_glib_003(D) & v4_glib_003(D,A) & m3_glib_000(D,A,k6_glib_000(A),k2_xboole_0(k26_glib_000(A,B),k1_tarski(k8_subset_1(k10_glib_004(k42_glib_000(k13_glib_004(A),C)))))) & v5_glib_001(E,D) & m3_glib_001(E,D) ) => ( ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & ~ v1_abian(F) & r1_xreal_0(F,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,F),k14_glib_003(k42_glib_000(k13_glib_004(A),C))) ) => ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & ~ v1_abian(F) & r1_xreal_0(F,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,F),k14_glib_003(k42_glib_000(k13_glib_004(A),C))) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ( ~ v1_abian(G) & r1_xreal_0(G,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,G),k14_glib_003(k42_glib_000(k13_glib_004(A),C))) ) => r1_xreal_0(F,G) ) ) ) ) ) ), file(glib_004,s5_nat_1__e3_84_2_13_1_1__glib_004), []). fof(s5_nat_1__e3_84_2_13_1_2__glib_004,axiom,( ! [A,B,C,D,E] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v1_glib_004(B,A) & m2_glib_000(B,A) & m2_subset_1(C,k1_numbers,k5_numbers) & v1_glib_003(D) & v4_glib_003(D,A) & m3_glib_000(D,A,k6_glib_000(A),k2_xboole_0(k26_glib_000(A,B),k1_tarski(k8_subset_1(k10_glib_004(k42_glib_000(k13_glib_004(A),C)))))) & v5_glib_001(E,D) & m3_glib_001(E,D) ) => ( ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & ~ v1_abian(F) & r1_xreal_0(F,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,F),k1_card_fil(k6_glib_000(k42_glib_000(k13_glib_004(A),C)),k14_glib_003(k42_glib_000(k13_glib_004(A),C)))) ) => ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & ~ v1_abian(F) & r1_xreal_0(F,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,F),k1_card_fil(k6_glib_000(k42_glib_000(k13_glib_004(A),C)),k14_glib_003(k42_glib_000(k13_glib_004(A),C)))) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ( ~ v1_abian(G) & r1_xreal_0(G,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,G),k1_card_fil(k6_glib_000(k42_glib_000(k13_glib_004(A),C)),k14_glib_003(k42_glib_000(k13_glib_004(A),C)))) ) => r1_xreal_0(F,G) ) ) ) ) ) ), file(glib_004,s5_nat_1__e3_84_2_13_1_2__glib_004), []). fof(s5_nat_1__e9_84_2_3__glib_004,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) & v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v1_glib_004(B,A) & m2_glib_000(B,A) ) => ( ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),C)),k26_glib_000(A,B)) ) => ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),C)),k26_glib_000(A,B)) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ~ r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),D)),k26_glib_000(A,B)) => r1_xreal_0(C,D) ) ) ) ) ) ), file(glib_004,s5_nat_1__e9_84_2_3__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(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_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). 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(t100_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(1,D) & r1_xreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C ) ) ) ) ), file(glib_001,t100_glib_001), []). 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(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(t111_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k14_glib_001(A,C) = k14_glib_001(B,D) ) ) ) ) ) ), file(glib_001,t111_glib_001), []). fof(t112_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k14_glib_001(A,k10_glib_001(A,B,C)) = k2_xboole_0(k14_glib_001(A,B),k1_tarski(C)) ) ) ) ), file(glib_001,t112_glib_001), []). fof(t120_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_glib_001(B,A) <=> ? [C] : r1_glib_001(A,C,C,B) ) ) ) ), file(glib_001,t120_glib_001), []). fof(t127_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ~ ( ~ v3_glib_001(B,A) & k3_finseq_1(B) = 1 ) & ~ ( k3_finseq_1(B) != 1 & v3_glib_001(B,A) ) ) ) ) ), file(glib_001,t127_glib_001), []). fof(t133_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D] : ~ ( r1_glib_000(A,k4_glib_001(A,B),D,C) & v3_glib_001(k10_glib_001(A,B,C),A) ) ) ) ), file(glib_001,t133_glib_001), []). 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_finset_1,axiom,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), []). fof(t151_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C,D] : ( ( r1_glib_000(A,k4_glib_001(A,B),D,C) & ! [E] : ( ( ~ v1_abian(E) & m2_subset_1(E,k1_numbers,k5_numbers) ) => ~ ( ~ r1_xreal_0(E,1) & r1_xreal_0(E,k3_finseq_1(B)) & k1_funct_1(B,E) = D ) ) ) => ( r2_hidden(C,k14_glib_001(A,B)) | ( ~ v3_glib_001(B,A) & v1_glib_001(B,A) ) | v5_glib_001(k10_glib_001(A,B,C),A) ) ) ) ) ), file(glib_001,t151_glib_001), []). fof(t15_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & v1_glib_003(B) & m1_glib_000(B) ) => ! [C] : ( ( v1_glib_000(C) & v1_glib_003(C) & m1_glib_000(C) ) => ( ( r5_glib_000(A,B) & k5_glib_003(A) = k5_glib_003(B) & v1_glib_003(A) & v4_glib_003(A,C) & m2_glib_000(A,C) ) => ( v1_glib_003(B) & v4_glib_003(B,C) & m2_glib_000(B,C) ) ) ) ) ) ), file(glib_003,t15_glib_003), []). fof(t161_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D,E] : ( m4_glib_001(B,A,C) => ( r1_glib_001(A,D,E,B) <=> r1_glib_001(A,D,E,C) ) ) ) ) ) ), file(glib_001,t161_glib_001), []). fof(t16_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D] : ( r1_glib_000(A,C,D,B) => ( r2_hidden(C,k6_glib_000(A)) & r2_hidden(D,k6_glib_000(A)) ) ) ) ), file(glib_000,t16_glib_000), []). fof(t16_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_003(B) & v4_glib_003(B,A) & m2_glib_000(B,A) ) => ! [C] : ( ( v1_glib_003(C) & v4_glib_003(C,B) & m2_glib_000(C,B) ) => ( v1_glib_003(C) & v4_glib_003(C,A) & m2_glib_000(C,A) ) ) ) ) ), file(glib_003,t16_glib_003), []). fof(t176_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ! [C] : ( m3_glib_001(C,B) => ( ( v1_glib_001(C,B) => ( v1_glib_001(C,A) & m3_glib_001(C,A) ) ) & ( v2_glib_001(C,B) => ( v2_glib_001(C,A) & m3_glib_001(C,A) ) ) & ( v3_glib_001(C,B) => ( v3_glib_001(C,A) & m3_glib_001(C,A) ) ) & ( v4_glib_001(C,B) => ( v4_glib_001(C,A) & m3_glib_001(C,A) ) ) & ( v5_glib_001(C,B) => ( v5_glib_001(C,A) & m3_glib_001(C,A) ) ) & ( v6_glib_001(C,B) => ( v6_glib_001(C,A) & m3_glib_001(C,A) ) ) ) ) ) ) ), file(glib_001,t176_glib_001), []). fof(t177_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => ( ( v1_glib_001(C,A) => v1_glib_001(D,B) ) & ( v1_glib_001(D,B) => v1_glib_001(C,A) ) & ( v2_glib_001(C,A) => v2_glib_001(D,B) ) & ( v2_glib_001(D,B) => v2_glib_001(C,A) ) & ( v3_glib_001(C,A) => v3_glib_001(D,B) ) & ( v3_glib_001(D,B) => v3_glib_001(C,A) ) & ( v4_glib_001(C,A) => v4_glib_001(D,B) ) & ( v4_glib_001(D,B) => v4_glib_001(C,A) ) & ( v5_glib_001(C,A) => v5_glib_001(D,B) ) & ( v5_glib_001(D,B) => v5_glib_001(C,A) ) & ( v6_glib_001(C,A) => v6_glib_001(D,B) ) & ( v6_glib_001(D,B) => v6_glib_001(C,A) ) ) ) ) ) ) ) ), file(glib_001,t177_glib_001), []). 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(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_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(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,A) ) => A = B ) ) ) ), file(xreal_1,t1_xreal_1), []). fof(t20_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C,D,E,F] : ( r1_glib_000(A,C,D,B) => ( ( ~ ( r2_hidden(C,E) & r2_hidden(D,F) ) & ~ ( r2_hidden(C,F) & r2_hidden(D,E) ) ) | r3_glib_000(A,E,F,B) ) ) ) ), file(glib_000,t20_glib_000), []). fof(t20_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ! [C,D,E] : ( m3_glib_001(E,A) => ! [F] : ( m3_glib_001(F,B) => ( E = F => ( r1_glib_001(A,C,D,E) <=> r1_glib_001(B,C,D,F) ) ) ) ) ) ) ), file(glib_001,t20_glib_001), []). fof(t22_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ~ ( A != 0 & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => A != k1_nat_1(B,1) ) ) ) ), file(nat_1,t22_nat_1), []). fof(t23_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_002(B) & m2_glib_000(B,A) ) => ( v9_glib_000(B,A) => v1_glib_002(A) ) ) ) ), file(glib_002,t23_glib_002), []). fof(t23_xboole_1,axiom,( ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ), file(xboole_1,t23_xboole_1), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). 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_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_xboole_1,axiom,( ! [A] : r1_tarski(k1_xboole_0,A) ), file(xboole_1,t2_xboole_1), []). 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(t33_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B,C] : ( ( v1_glib_003(C) & v4_glib_003(C,A) & m3_glib_000(C,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),k1_tarski(B))) ) => ( r2_hidden(B,k7_glib_000(A)) => k9_glib_004(A) = k3_real_1(k9_glib_004(C),k1_seq_1(k5_glib_003(A),B)) ) ) ) ), file(glib_004,t33_glib_004), []). fof(t34_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( ( r2_hidden(B,k7_glib_000(A)) & r2_hidden(k1_funct_1(k10_glib_000(A),B),C) & r2_hidden(k1_funct_1(k11_glib_000(A),B),C) ) <=> r2_hidden(B,k22_glib_000(A,C)) ) ) ), file(glib_000,t34_glib_000), []). fof(t34_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k22_glib_000(A,B))) => ! [D] : ( ( v1_glib_003(D) & v4_glib_003(D,A) & m3_glib_000(D,A,B,C) ) => ! [E,F] : ( ( v1_glib_003(F) & v4_glib_003(F,A) & m3_glib_000(F,A,B,k2_xboole_0(C,k1_tarski(E))) ) => ( r2_hidden(E,k22_glib_000(A,B)) => ( r2_hidden(E,C) | k3_real_1(k9_glib_004(D),k1_seq_1(k5_glib_003(A),E)) = k9_glib_004(F) ) ) ) ) ) ) ) ), file(glib_004,t34_glib_004), []). fof(t36_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( ( v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v1_glib_004(B,A) & m2_glib_000(B,A) ) => ! [C] : ( ( v1_glib_000(C) & v1_glib_003(C) & m1_glib_000(C) ) => ( ( r5_glib_000(B,C) & k5_glib_003(B) = k5_glib_003(C) ) => ( v9_glib_000(C,A) & v3_glib_002(C) & v1_glib_003(C) & v4_glib_003(C,A) & v1_glib_004(C,A) & m2_glib_000(C,A) ) ) ) ) ) ), file(glib_004,t36_glib_004), []). fof(t37_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => k7_glib_000(A) = k22_glib_000(A,k6_glib_000(A)) ) ), file(glib_000,t37_glib_000), []). fof(t37_zfmisc_1,axiom,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_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_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(t46_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( v3_glib_002(A) <=> ( v2_glib_002(A) & k16_glib_000(A) = k1_nat_1(k18_glib_000(A),1) ) ) ) ), file(glib_002,t46_glib_002), []). fof(t47_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ! [C] : ( m2_glib_000(C,A) => ( ( r1_tarski(k25_glib_000(A,B),k25_glib_000(A,C)) & r1_tarski(k26_glib_000(A,B),k26_glib_000(A,C)) ) => m2_glib_000(B,C) ) ) ) ) ), file(glib_000,t47_glib_000), []). fof(t47_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( v3_glib_002(A) <=> ( v1_glib_002(A) & k16_glib_000(A) = k1_nat_1(k18_glib_000(A),1) ) ) ) ), file(glib_002,t47_glib_002), []). fof(t48_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( ( v1_glib_000(B) & m1_glib_000(B) ) => ( ( r5_glib_000(A,B) & v3_glib_002(A) ) => v3_glib_002(B) ) ) ) ), file(glib_002,t48_glib_002), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). 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(t50_xboole_1,axiom,( ! [A,B,C] : k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ), file(xboole_1,t50_xboole_1), []). fof(t52_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & m1_glib_000(A) ) => ! [B,C] : ( r2_hidden(B,k7_glib_000(A)) => k11_glib_003(k12_glib_003(A,B,C)) = k2_xboole_0(k11_glib_003(A),k1_tarski(B)) ) ) ), file(glib_003,t52_glib_003), []). fof(t52_glib_004,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v1_glib_002(A) & v1_glib_003(A) & v7_glib_003(A) & m1_glib_000(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r1_tarski(k11_glib_003(k42_glib_000(k13_glib_004(A),B)),k11_glib_003(k14_glib_004(A))) ) ) ), file(glib_004,t52_glib_004), []). fof(t52_zfmisc_1,axiom,( ! [A,B] : ( r2_hidden(A,B) => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) ), file(zfmisc_1,t52_zfmisc_1), []). fof(t53_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_xboole_0(A,B) => k4_card_1(k2_xboole_0(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ) ), file(card_2,t53_card_2), []). fof(t54_card_2,axiom,( ! [A,B] : ( v1_finset_1(B) => ( ~ r2_hidden(A,B) => k4_card_1(k2_xboole_0(B,k1_tarski(A))) = k1_nat_1(k4_card_1(B),1) ) ) ), file(card_2,t54_card_2), []). fof(t54_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( m3_glib_000(C,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),k1_tarski(B))) => ( k25_glib_000(A,C) = k6_glib_000(A) & k26_glib_000(A,C) = k1_card_fil(k7_glib_000(A),k1_tarski(B)) ) ) ) ), file(glib_000,t54_glib_000), []). fof(t56_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( m3_glib_000(C,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),B)) => ( k25_glib_000(A,C) = k6_glib_000(A) & k26_glib_000(A,C) = k1_card_fil(k7_glib_000(A),B) ) ) ) ), file(glib_000,t56_glib_000), []). fof(t56_glib_003,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) & m1_glib_000(A) ) => ! [B,C] : k11_glib_003(A) = k11_glib_003(k13_glib_003(A,B,C)) ) ), file(glib_003,t56_glib_003), []). fof(t5_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & v1_glib_002(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D] : ( m3_glib_000(D,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),k1_tarski(C))) => ( ( v8_glib_001(B,A) & r2_hidden(C,k14_glib_001(A,B)) ) => v1_glib_002(D) ) ) ) ) ), file(glib_002,t5_glib_002), []). 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_relat_1,axiom, ( k1_relat_1(k1_xboole_0) = k1_xboole_0 & k2_relat_1(k1_xboole_0) = k1_xboole_0 ), file(relat_1,t60_relat_1), []). fof(t63_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,A) => k4_card_1(k4_xboole_0(A,B)) = k5_real_1(k4_card_1(A),k4_card_1(B)) ) ) ) ), file(card_2,t63_card_2), []). fof(t65_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k3_finseq_1(k10_glib_001(A,B,C)) = k1_nat_1(k3_finseq_1(B),2) ) ) ) ), file(glib_001,t65_glib_001), []). fof(t66_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => ( k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),1)) = C & k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),2)) = D & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) => k1_funct_1(k10_glib_001(A,B,C),E) = k1_funct_1(B,E) ) ) ) ) ) ) ), file(glib_001,t66_glib_001), []). fof(t67_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r2_xboole_0(A,B) => ( ~ r1_xreal_0(k4_card_1(B),k4_card_1(A)) & r2_hidden(k1_card_1(A),k1_card_1(B)) ) ) ) ) ), file(card_2,t67_card_2), []). fof(t67_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C,D,E,F] : ( ( r1_glib_001(A,C,D,B) & r1_glib_000(A,D,F,E) ) => r1_glib_001(A,C,F,k10_glib_001(A,B,E)) ) ) ) ), file(glib_001,t67_glib_001), []). 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(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(t75_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ! [C,D,E] : ( ( r1_glib_000(B,C,D,E) => r1_glib_000(A,C,D,E) ) & ( r2_glib_000(B,C,D,E) => r2_glib_000(A,C,D,E) ) & ( r3_glib_000(B,C,D,E) => r3_glib_000(A,C,D,E) ) & ( r4_glib_000(B,C,D,E) => r4_glib_000(A,C,D,E) ) ) ) ) ), file(glib_000,t75_glib_000), []). fof(t76_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ! [C,D,E] : ( r2_hidden(E,k26_glib_000(A,B)) => ( ( r1_glib_000(A,C,D,E) => r1_glib_000(B,C,D,E) ) & ( r2_glib_000(A,C,D,E) => r2_glib_000(B,C,D,E) ) & ( r3_glib_000(A,C,D,E) => r3_glib_000(B,C,D,E) ) & ( r4_glib_000(A,C,D,E) => r4_glib_000(B,C,D,E) ) ) ) ) ) ), file(glib_000,t76_glib_000), []). fof(t79_card_1,axiom,( ! [A] : k4_card_1(k1_tarski(A)) = 1 ), file(card_1,t79_card_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),B) ) ) ) ), file(funct_2,t7_funct_2), []). 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(t7_xboole_1,axiom,( ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ), file(xboole_1,t7_xboole_1), []). fof(t89_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ! [C] : ( m2_glib_000(C,A) => ( ( k25_glib_000(A,B) = k25_glib_000(A,C) & k26_glib_000(A,B) = k26_glib_000(A,C) ) => r5_glib_000(B,C) ) ) ) ) ), file(glib_000,t89_glib_000), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_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(C,k3_finseq_1(B)) => r2_hidden(k1_funct_1(B,C),k6_glib_000(A)) ) ) ) ) ), file(glib_001,t8_glib_001), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t8_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(C,B) ) => r1_tarski(k2_xboole_0(A,C),B) ) ), file(xboole_1,t8_xboole_1), []). fof(t8_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,B) <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t8_xreal_1), []). 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(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), []).