% Mizar problem: t46_glib_002,glib_002,2538,58 fof(t46_glib_002,conjecture,( ! [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) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_glib_000,cc11_glib_000,cc11_glib_002,cc12_glib_000,cc13_glib_000,cc14_glib_000,cc15_glib_000,cc16_glib_000,cc17_glib_000,cc18_glib_000,cc19_glib_000,cc1_abian,cc1_card_1,cc1_finset_1,cc1_glib_000,cc1_glib_001,cc1_glib_002,cc1_nat_1,cc1_polynom1,cc1_relset_1,cc2_card_1,cc2_finset_1,cc2_glib_000,cc2_glib_001,cc2_glib_002,cc2_int_1,cc2_nat_1,cc3_card_1,cc3_glib_000,cc3_glib_001,cc3_glib_002,cc3_int_1,cc3_nat_1,cc3_polynom1,cc4_glib_000,cc4_glib_001,cc4_glib_002,cc4_int_1,cc4_polynom1,cc5_glib_000,cc5_glib_002,cc5_polynom1,cc6_glib_000,cc6_glib_001,cc6_glib_002,cc7_glib_000,cc7_glib_002,cc8_glib_000,cc8_glib_002,cc9_glib_000,cc9_glib_002,commutativity_k1_nat_1,commutativity_k23_binop_2,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,d15_glib_000,d1_glib_002,d1_tarski,d1_xboole_0,d26_glib_000,d27_glib_000,d2_glib_002,d3_glib_002,d53_glib_000,d54_glib_000,dt_k10_glib_000,dt_k11_glib_000,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_001,dt_k1_glib_002,dt_k1_nat_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_glib_000,dt_k23_binop_2,dt_k29_glib_000,dt_k2_glib_001,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k35_glib_000,dt_k36_glib_000,dt_k3_finseq_1,dt_k3_glib_001,dt_k4_card_1,dt_k4_glib_001,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k6_domain_1,dt_k6_glib_000,dt_k6_xcmplx_0,dt_k7_glib_000,dt_k8_glib_000,dt_k9_glib_000,dt_m1_finseq_1,dt_m1_glib_000,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,existence_m1_finseq_1,existence_m1_glib_000,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,fc10_abian,fc11_abian,fc12_abian,fc12_finset_1,fc13_abian,fc14_abian,fc14_finset_1,fc14_polynom1,fc15_abian,fc17_abian,fc1_finset_1,fc1_glib_000,fc1_glib_001,fc1_glib_002,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc20_polynom1,fc2_abian,fc2_card_1,fc2_glib_001,fc3_abian,fc3_glib_001,fc3_nat_1,fc3_polynom1,fc4_abian,fc4_glib_000,fc4_glib_001,fc4_int_1,fc4_nat_1,fc5_abian,fc5_glib_000,fc5_polynom1,fc6_glib_000,fc6_int_1,fc8_int_1,fc9_abian,fc9_finset_1,fc9_int_1,idempotence_k2_xboole_0,l36_glib_002,rc11_polynom1,rc12_polynom1,rc1_abian,rc1_card_1,rc1_finset_1,rc1_glib_000,rc1_glib_001,rc1_glib_002,rc1_int_1,rc1_nat_1,rc2_abian,rc2_card_1,rc2_finset_1,rc2_glib_000,rc2_glib_001,rc2_glib_002,rc2_int_1,rc2_nat_1,rc2_polynom1,rc3_abian,rc3_finset_1,rc3_glib_000,rc3_glib_002,rc3_nat_1,rc3_polynom1,rc4_abian,rc4_finset_1,rc4_glib_000,rc4_glib_002,rc4_polynom1,rc5_glib_000,rc6_glib_002,rc7_polynom1,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_k23_binop_2,redefinition_k36_glib_000,redefinition_k3_finseq_1,redefinition_k4_card_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_domain_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,s1_binarith__e7_79_1__glib_002,s1_binarith__e7_79__glib_002,spc0_boole,spc1_boole,spc1_numerals,t14_glib_001,t157_glib_001,t1_arithm,t1_boole,t1_numerals,t1_subset,t22_glib_000,t29_glib_000,t2_subset,t30_glib_000,t3_boole,t3_glib_002,t3_subset,t3_xcmplx_1,t4_arithm,t4_boole,t4_subset,t51_glib_000,t5_subset,t60_card_2,t6_boole,t78_card_1,t7_boole,t7_funct_2,t8_boole]), [file(glib_002,t46_glib_002)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v4_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => v4_glib_000(B) ) ) ), file(glib_000,cc10_glib_000), []). 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_glib_002,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v3_glib_002(A) & m1_glib_000(A) & v11_glib_000(B,A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m3_glib_000(C,A,k1_card_fil(k6_glib_000(A),k1_tarski(B)),k22_glib_000(A,k1_card_fil(k6_glib_000(A),k1_tarski(B)))) => ( v2_glib_000(C) & v3_glib_000(C) & v5_glib_000(C) & v2_glib_002(C) & v3_glib_002(C) ) ) ) ), file(glib_002,cc11_glib_002), []). 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(cc13_glib_000,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) & m1_subset_1(C,k1_zfmisc_1(k22_glib_000(A,k6_domain_1(k6_glib_000(A),B)))) ) => ! [D] : ( m3_glib_000(D,A,k6_domain_1(k6_glib_000(A),B),C) => v4_glib_000(D) ) ) ), file(glib_000,cc13_glib_000), []). fof(cc14_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m3_glib_000(C,A,k6_domain_1(k6_glib_000(A),B),k1_xboole_0) => ( v2_glib_000(C) & v4_glib_000(C) ) ) ) ), file(glib_000,cc14_glib_000), []). 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(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(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(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(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(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_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_002,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v4_glib_000(A) ) => ( v1_glib_000(A) & v1_glib_002(A) ) ) ) ), file(glib_002,cc1_glib_002), []). fof(cc1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_polynom1,axiom,( ! [A] : ( m1_finseq_1(A,k5_numbers) => v1_card_3(A) ) ), file(polynom1,cc1_polynom1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(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_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_002,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v3_glib_000(A) & v4_glib_000(A) ) => ( v1_glib_000(A) & v3_glib_002(A) ) ) ) ), file(glib_002,cc2_glib_002), []). 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_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), []). fof(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_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ) ), file(polynom1,cc3_polynom1), []). fof(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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). 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(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(cc6_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v3_glib_000(A) & v4_glib_000(A) ) => ( v1_glib_000(A) & v2_glib_000(A) ) ) ) ), file(glib_000,cc6_glib_000), []). 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_glib_002,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m3_glib_000(C,A,k6_domain_1(k6_glib_000(A),B),k1_xboole_0) => ( v2_glib_000(C) & v4_glib_000(C) & v7_glib_000(C) & v3_glib_002(C) ) ) ) ), file(glib_002,cc6_glib_002), []). fof(cc7_glib_000,axiom,( ! [A] : ( m1_glib_000(A) => ( ( v1_glib_000(A) & v4_glib_000(A) & v6_glib_000(A) ) => ( v1_glib_000(A) & v2_glib_000(A) ) ) ) ), file(glib_000,cc7_glib_000), []). 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(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_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A) => ( v4_glib_002(B,A) => v1_glib_002(B) ) ) ) ), file(glib_002,cc8_glib_002), []). 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_002,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m3_glib_000(C,A,k1_glib_002(A,B),k22_glib_000(A,k1_glib_002(A,B))) => ( v1_glib_002(C) & v4_glib_002(C,A) ) ) ) ), file(glib_002,cc9_glib_002), []). 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_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k23_binop_2(B,A) ) ), file(binop_2,k23_binop_2), []). 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(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(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(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(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(d3_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v3_glib_002(A) <=> ( v2_glib_002(A) & v1_glib_002(A) ) ) ) ), file(glib_002,d3_glib_002), []). fof(d53_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( v11_glib_000(B,A) <=> ? [C] : ( k29_glib_000(A,B) = k1_tarski(C) & ~ r1_glib_000(A,B,B,C) ) ) ) ) ), file(glib_000,d53_glib_000), []). fof(d54_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( v11_glib_000(B,A) <=> k36_glib_000(A,B) = 1 ) ) ) ), file(glib_000,d54_glib_000), []). fof(dt_k10_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_funct_1(k10_glib_000(A)) & v1_funct_2(k10_glib_000(A),k7_glib_000(A),k6_glib_000(A)) & m2_relset_1(k10_glib_000(A),k7_glib_000(A),k6_glib_000(A)) ) ) ), file(glib_000,k10_glib_000), []). fof(dt_k11_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_funct_1(k11_glib_000(A)) & v1_funct_2(k11_glib_000(A),k7_glib_000(A),k6_glib_000(A)) & m2_relset_1(k11_glib_000(A),k7_glib_000(A),k6_glib_000(A)) ) ) ), file(glib_000,k11_glib_000), []). fof(dt_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_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m3_glib_001(k1_glib_001(A,B),A) ) ), file(glib_001,k1_glib_001), []). fof(dt_k1_glib_002,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( ~ v1_xboole_0(k1_glib_002(A,B)) & m1_subset_1(k1_glib_002(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ) ), file(glib_002,k1_glib_002), []). 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_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_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) ), file(binop_2,k23_binop_2), []). fof(dt_k29_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_subset_1(k29_glib_000(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ), file(glib_000,k29_glib_000), []). fof(dt_k2_glib_001,axiom,( ! [A,B,C,D] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => m3_glib_001(k2_glib_001(A,B,C,D),A) ) ), file(glib_001,k2_glib_001), []). 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_k35_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => v1_card_1(k35_glib_000(A,B)) ) ), file(glib_000,k35_glib_000), []). fof(dt_k36_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m2_subset_1(k36_glib_000(A,B),k1_numbers,k5_numbers) ) ), file(glib_000,k36_glib_000), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_glib_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m3_glib_001(B,A) ) => m1_subset_1(k3_glib_001(A,B),k6_glib_000(A)) ) ), file(glib_001,k3_glib_001), []). fof(dt_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_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_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). 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_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), []). fof(dt_k6_glib_000,axiom,( $true ), file(glib_000,k6_glib_000), []). fof(dt_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_k8_glib_000,axiom,( $true ), file(glib_000,k8_glib_000), []). fof(dt_k9_glib_000,axiom,( $true ), file(glib_000,k9_glib_000), []). 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_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(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_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(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(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(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(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(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(fc17_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_zfmisc_1(A)) & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ), file(abian,fc17_abian), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ~ v1_xboole_0(k6_glib_000(A)) ) ), file(glib_000,fc1_glib_000), []). fof(fc1_glib_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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). 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(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_001,axiom,( ! [A,B] : ( ( v1_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ( v1_relat_1(k1_glib_001(A,B)) & v1_funct_1(k1_glib_001(A,B)) & v1_finset_1(k1_glib_001(A,B)) & v1_finseq_1(k1_glib_001(A,B)) & v2_finseq_1(k1_glib_001(A,B)) & v1_glib_001(k1_glib_001(A,B),A) & v2_glib_001(k1_glib_001(A,B),A) & v3_glib_001(k1_glib_001(A,B),A) & v4_glib_001(k1_glib_001(A,B),A) & v5_glib_001(k1_glib_001(A,B),A) & v6_glib_001(k1_glib_001(A,B),A) ) ) ), file(glib_001,fc2_glib_001), []). 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_001,axiom,( ! [A,B,C,D] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k2_glib_001(A,B,D,C)) & v1_funct_1(k2_glib_001(A,B,D,C)) & v1_finset_1(k2_glib_001(A,B,D,C)) & v1_finseq_1(k2_glib_001(A,B,D,C)) & v2_finseq_1(k2_glib_001(A,B,D,C)) & v4_glib_001(k2_glib_001(A,B,D,C),A) & v5_glib_001(k2_glib_001(A,B,D,C),A) ) ) ), file(glib_001,fc3_glib_001), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_polynom1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_matrlin(k1_xboole_0) ), file(polynom1,fc3_polynom1), []). fof(fc4_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,1)) & v1_xreal_0(k6_xcmplx_0(A,1)) & v1_int_1(k6_xcmplx_0(A,1)) & ~ v1_abian(k6_xcmplx_0(A,1)) ) ) ), file(abian,fc4_abian), []). fof(fc4_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( ~ v1_xboole_0(k6_glib_000(A)) & v1_finset_1(k6_glib_000(A)) ) ) ), file(glib_000,fc4_glib_000), []). fof(fc4_glib_001,axiom,( ! [A,B,C] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ( v1_relat_1(k2_glib_001(A,B,B,C)) & v1_funct_1(k2_glib_001(A,B,B,C)) & v1_finset_1(k2_glib_001(A,B,B,C)) & v1_finseq_1(k2_glib_001(A,B,B,C)) & v2_finseq_1(k2_glib_001(A,B,B,C)) & v1_glib_001(k2_glib_001(A,B,B,C),A) & v4_glib_001(k2_glib_001(A,B,B,C),A) & v5_glib_001(k2_glib_001(A,B,B,C),A) ) ) ), file(glib_001,fc4_glib_001), []). fof(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc5_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,1)) & v1_xreal_0(k6_xcmplx_0(A,1)) & v1_int_1(k6_xcmplx_0(A,1)) & v1_abian(k6_xcmplx_0(A,1)) ) ) ), file(abian,fc5_abian), []). fof(fc5_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => v1_finset_1(k7_glib_000(A)) ) ), file(glib_000,fc5_glib_000), []). fof(fc5_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(fc6_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v4_glib_000(A) & m1_glib_000(A) ) => ( ~ v1_xboole_0(k6_glib_000(A)) & v1_finset_1(k6_glib_000(A)) ) ) ), file(glib_000,fc6_glib_000), []). 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(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(fc9_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc9_abian), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(l36_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v2_glib_002(A) & m1_glib_000(A) ) => ~ ( k7_glib_000(A) != k1_xboole_0 & ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & v11_glib_000(B,A) & v11_glib_000(C,A) & r2_hidden(C,k1_glib_002(A,B)) ) ) ) ) ) ), file(glib_002,l36_glib_002), []). 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(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_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_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : ( m3_glib_001(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_glib_001(B,A) & v2_glib_001(B,A) & v3_glib_001(B,A) & v4_glib_001(B,A) & v5_glib_001(B,A) & v6_glib_001(B,A) ) ) ), file(glib_001,rc1_glib_001), []). fof(rc1_glib_002,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) & v2_glib_000(A) & v3_glib_000(A) & v4_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,rc1_glib_002), []). 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_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(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_glib_000,axiom,( ? [A] : ( m1_glib_000(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v3_glib_000(A) & v4_glib_000(A) & v5_glib_000(A) & v6_glib_000(A) & v7_glib_000(A) & v8_glib_000(A) ) ), file(glib_000,rc2_glib_000), []). fof(rc2_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ? [B] : ( m3_glib_001(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_glib_001(B,A) & v5_glib_001(B,A) & v6_glib_001(B,A) ) ) ), file(glib_001,rc2_glib_001), []). fof(rc2_glib_002,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) & v2_glib_000(A) & v3_glib_000(A) & ~ v4_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,rc2_glib_002), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_matrlin(A) ) ), file(polynom1,rc2_polynom1), []). fof(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_glib_000,axiom,( ? [A] : ( m1_glib_000(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v3_glib_000(A) & ~ v4_glib_000(A) & v5_glib_000(A) & v6_glib_000(A) & v7_glib_000(A) & v8_glib_000(A) ) ), file(glib_000,rc3_glib_000), []). fof(rc3_glib_002,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) & v2_glib_000(B) & v3_glib_000(B) & v4_glib_000(B) & v5_glib_000(B) & v6_glib_000(B) & v7_glib_000(B) & v8_glib_000(B) & v1_glib_002(B) & v2_glib_002(B) & v3_glib_002(B) ) ) ), file(glib_002,rc3_glib_002), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_card_3(A) ) ), file(polynom1,rc3_polynom1), []). fof(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_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) & v2_glib_000(B) & v3_glib_000(B) & v4_glib_000(B) & v5_glib_000(B) & v6_glib_000(B) & v7_glib_000(B) & v8_glib_000(B) ) ) ), file(glib_000,rc4_glib_000), []). fof(rc4_glib_002,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_002(B) & v4_glib_002(B,A) ) ) ), file(glib_002,rc4_glib_002), []). 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(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_002,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v3_glib_002(A) & m1_glib_000(A) ) => ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & v11_glib_000(B,A) ) ) ), file(glib_002,rc6_glib_002), []). 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(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_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k23_binop_2), []). fof(redefinition_k36_glib_000,axiom,( ! [A,B] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => k36_glib_000(A,B) = k35_glib_000(A,B) ) ), file(glib_000,k36_glib_000), []). 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_k4_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k4_card_1(A) = k1_card_1(A) ) ), file(card_1,k4_card_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_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_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), []). fof(redefinition_m2_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(s1_binarith__e7_79_1__glib_002,axiom, ( ( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v3_glib_002(A) & m1_glib_000(A) ) => ( k16_glib_000(A) = 1 => 1 = k1_nat_1(k18_glib_000(A),1) ) ) & ! [B] : ( ( ~ v1_xboole_0(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ( ! [C] : ( ( v1_glib_000(C) & v2_glib_000(C) & v3_glib_002(C) & m1_glib_000(C) ) => ( k16_glib_000(C) = B => B = k1_nat_1(k18_glib_000(C),1) ) ) => ! [D] : ( ( v1_glib_000(D) & v2_glib_000(D) & v3_glib_002(D) & m1_glib_000(D) ) => ( k16_glib_000(D) = k23_binop_2(B,1) => k23_binop_2(B,1) = k1_nat_1(k18_glib_000(D),1) ) ) ) ) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ! [E] : ( ( v1_glib_000(E) & v2_glib_000(E) & v3_glib_002(E) & m1_glib_000(E) ) => ( k16_glib_000(E) = B => B = k1_nat_1(k18_glib_000(E),1) ) ) ) ), file(glib_002,s1_binarith__e7_79_1__glib_002), []). fof(s1_binarith__e7_79__glib_002,axiom, ( ( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v2_glib_002(A) & m1_glib_000(A) ) => ( ( k16_glib_000(A) = 1 & k16_glib_000(A) = k1_nat_1(k18_glib_000(A),1) ) => v1_glib_002(A) ) ) & ! [B] : ( ( ~ v1_xboole_0(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ( ! [C] : ( ( v1_glib_000(C) & v2_glib_000(C) & v2_glib_002(C) & m1_glib_000(C) ) => ( ( k16_glib_000(C) = B & k16_glib_000(C) = k1_nat_1(k18_glib_000(C),1) ) => v1_glib_002(C) ) ) => ! [D] : ( ( v1_glib_000(D) & v2_glib_000(D) & v2_glib_002(D) & m1_glib_000(D) ) => ( ( k16_glib_000(D) = k23_binop_2(B,1) & k16_glib_000(D) = k1_nat_1(k18_glib_000(D),1) ) => v1_glib_002(D) ) ) ) ) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_subset_1(B,k1_numbers,k5_numbers) ) => ! [E] : ( ( v1_glib_000(E) & v2_glib_000(E) & v2_glib_002(E) & m1_glib_000(E) ) => ( ( k16_glib_000(E) = B & k16_glib_000(E) = k1_nat_1(k18_glib_000(E),1) ) => v1_glib_002(E) ) ) ) ), file(glib_002,s1_binarith__e7_79__glib_002), []). 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(t14_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( k3_finseq_1(k1_glib_001(A,B)) = 1 & k1_funct_1(k1_glib_001(A,B),1) = B & k3_glib_001(A,k1_glib_001(A,B)) = B & k4_glib_001(A,k1_glib_001(A,B)) = B & r1_glib_001(A,B,B,k1_glib_001(A,B)) ) ) ) ), file(glib_001,t14_glib_001), []). fof(t157_glib_001,axiom,( ! [A] : ( ( v1_glib_000(A) & m1_glib_000(A) ) => ! [B,C] : ( r1_glib_000(A,C,C,B) => v8_glib_001(k2_glib_001(A,C,C,B),A) ) ) ), file(glib_001,t157_glib_001), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t22_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & v3_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k36_glib_000(A,B) = k4_card_1(k29_glib_000(A,B)) ) ) ), file(glib_000,t22_glib_000), []). fof(t29_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( k16_glib_000(A) = 1 <=> v4_glib_000(A) ) ) ), file(glib_000,t29_glib_000), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t30_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & m1_glib_000(A) ) => ( k16_glib_000(A) = 1 <=> ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & k6_glib_000(A) = k6_domain_1(k6_glib_000(A),B) ) ) ) ), file(glib_000,t30_glib_000), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_glib_002,axiom,( ! [A] : ( ( v1_glib_000(A) & ~ v4_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m3_glib_000(C,A,k1_card_fil(k6_glib_000(A),k1_tarski(B)),k22_glib_000(A,k1_card_fil(k6_glib_000(A),k1_tarski(B)))) => ( v1_glib_002(C) => ( ! [D] : ~ ( r2_hidden(D,k29_glib_000(A,B)) & ~ r1_glib_000(A,B,B,D) ) | v1_glib_002(A) ) ) ) ) ) ), file(glib_002,t3_glib_002), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A = k2_xcmplx_0(A,B) => B = 0 ) ) ) ), file(xcmplx_1,t3_xcmplx_1), []). 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_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_glib_000,axiom,( ! [A] : ( ( v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & m1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m3_glib_000(C,A,k1_card_fil(k6_glib_000(A),k1_tarski(B)),k22_glib_000(A,k1_card_fil(k6_glib_000(A),k1_tarski(B)))) => ( k1_nat_1(k16_glib_000(C),1) = k16_glib_000(A) & k1_nat_1(k18_glib_000(C),k4_card_1(k29_glib_000(A,B))) = k18_glib_000(A) ) ) ) ) ), file(glib_000,t51_glib_000), []). 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_card_2,axiom,( ! [A] : ( k1_card_1(A) = 1 <=> ? [B] : A = k1_tarski(B) ) ), file(card_2,t60_card_2), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t78_card_1,axiom,( k4_card_1(k1_xboole_0) = 0 ), file(card_1,t78_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(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).