% Mizar problem: t32_amistd_3,amistd_3,1369,47 fof(t32_amistd_3,conjecture,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => k5_amistd_3(A,B,k7_amistd_2(A,B)) = k9_trees_2(u2_ami_1(A,B),k1_amistd_3,k5_amistd_1(A,B,0)) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_amistd_1,cc1_arytm_3,cc1_card_1,cc1_card_5,cc1_finseq_1,cc1_finset_1,cc1_membered,cc1_necklace,cc1_ordinal1,cc1_relat_1,cc1_relset_1,cc1_scmfsa_4,cc1_xreal_0,cc20_membered,cc2_amistd_1,cc2_arytm_3,cc2_card_1,cc2_card_5,cc2_finset_1,cc2_membered,cc2_necklace,cc2_ordinal1,cc2_xreal_0,cc3_arytm_3,cc3_card_1,cc3_membered,cc3_ordinal1,cc3_xreal_0,cc4_amistd_1,cc4_membered,cc4_xreal_0,cc5_amistd_1,cc5_xreal_0,cc6_amistd_1,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_amistd_1,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d10_xboole_0,d13_amistd_1,d13_amistd_2,d1_amistd_3,d1_tarski,d21_ordinal2,d3_amistd_3,d3_finseq_1,d3_tarski,d4_amistd_3,d5_ami_5,d5_amistd_3,d6_trees_2,dt_k12_finseq_1,dt_k13_finseq_1,dt_k14_ami_3,dt_k15_cqc_sim1,dt_k1_amistd_1,dt_k1_amistd_3,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_trees_2,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_amistd_3,dt_k2_finseq_1,dt_k2_finseq_2,dt_k2_funcop_1,dt_k2_partfun1,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_2,dt_k2_wellord2,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_amistd_3,dt_k3_cqc_lang,dt_k3_finseq_1,dt_k3_tarski,dt_k3_trees_2,dt_k3_wellord1,dt_k4_amistd_3,dt_k4_finseq_1,dt_k4_ordinal2,dt_k5_ami_1,dt_k5_ami_5,dt_k5_amistd_1,dt_k5_amistd_3,dt_k5_finseq_1,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_amistd_1,dt_k6_amistd_2,dt_k6_finseq_1,dt_k7_ami_1,dt_k7_amistd_1,dt_k7_amistd_2,dt_k7_finseq_1,dt_k7_relat_1,dt_k8_finseq_1,dt_k9_finseq_1,dt_k9_trees_2,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_finseq_1,dt_m1_ordinal1,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_m2_trees_2,dt_m3_trees_2,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,existence_l1_ami_1,existence_l1_struct_0,existence_m1_ami_1,existence_m1_finseq_1,existence_m1_ordinal1,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,existence_m2_trees_2,existence_m3_trees_2,fc10_ami_1,fc10_amistd_3,fc10_membered,fc10_xreal_0,fc11_amistd_3,fc11_finseq_1,fc11_membered,fc11_xreal_0,fc12_amistd_3,fc12_finseq_1,fc12_membered,fc12_relat_1,fc12_xreal_0,fc13_amistd_3,fc13_finseq_1,fc13_membered,fc13_relat_1,fc14_amistd_3,fc14_finseq_1,fc14_finset_1,fc14_membered,fc15_amistd_3,fc15_membered,fc16_amistd_3,fc16_finseq_1,fc16_membered,fc17_amistd_3,fc17_finseq_1,fc1_amistd_1,fc1_amistd_3,fc1_arytm_3,fc1_card_4,fc1_finseq_1,fc1_finset_1,fc1_funcop_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_ami_1,fc2_amistd_1,fc2_amistd_3,fc2_card_1,fc2_finseq_1,fc2_finset_1,fc2_funcop_1,fc2_membered,fc2_necklace,fc2_ordinal1,fc2_relat_1,fc2_trees_2,fc3_amistd_3,fc3_finseq_1,fc3_finseq_6,fc3_funcop_1,fc3_trees_2,fc3_xreal_0,fc4_finseq_1,fc4_ordinal1,fc4_relat_1,fc4_trees_2,fc5_amistd_1,fc5_membered,fc5_ordinal1,fc5_relat_1,fc5_trees_2,fc6_ami_1,fc6_amistd_3,fc6_membered,fc6_relat_1,fc7_amistd_3,fc7_membered,fc7_relat_1,fc7_xreal_0,fc8_amistd_3,fc8_membered,fc8_relat_1,fc8_xreal_0,fc9_amistd_3,fc9_finseq_1,fc9_finset_1,fc9_funcop_1,fc9_membered,fc9_xreal_0,fraenkel_a_0_0_amistd_3,fraenkel_a_2_0_trees_2,fraenkel_a_3_3_amistd_3,fraenkel_a_3_4_amistd_3,fraenkel_a_3_5_amistd_3,fraenkel_a_3_6_amistd_3,fraenkel_a_5_0_amistd_3,idempotence_k2_xboole_0,rc1_amistd_1,rc1_amistd_3,rc1_arytm_3,rc1_card_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_heyting2,rc1_membered,rc1_ordinal1,rc1_relat_1,rc1_scmfsa_4,rc1_xreal_0,rc2_ami_1,rc2_amistd_1,rc2_card_1,rc2_card_5,rc2_finseq_1,rc2_finset_1,rc2_ordinal1,rc2_relat_1,rc2_xreal_0,rc3_ami_1,rc3_amistd_1,rc3_finseq_1,rc3_finset_1,rc3_ordinal1,rc3_relat_1,rc3_xreal_0,rc4_ami_1,rc4_finseq_1,rc4_finset_1,rc4_ordinal1,rc4_xreal_0,rc5_trees_2,rc6_amistd_1,rc6_finseq_1,rc6_trees_2,rc7_amistd_1,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_2,rc9_trees_2,redefinition_k12_finseq_1,redefinition_k14_ami_3,redefinition_k15_cqc_sim1,redefinition_k1_nat_1,redefinition_k1_struct_0,redefinition_k2_finseq_1,redefinition_k2_partfun1,redefinition_k3_finseq_1,redefinition_k3_trees_2,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k7_amistd_1,redefinition_k7_amistd_2,redefinition_k8_finseq_1,redefinition_k9_finseq_1,redefinition_k9_trees_2,redefinition_m1_struct_0,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_hilbert2__e8_56__amistd_3,s1_nat_1__e11_56__amistd_3,s1_nat_1__e7_56_4_1__amistd_3,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t14_trees_2,t15_amistd_1,t15_amistd_3,t17_amistd_3,t17_funcop_1,t17_qc_lang4,t18_amistd_3,t18_finseq_1,t1_arithm,t1_boole,t1_card_5,t1_numerals,t1_real,t1_subset,t20_amistd_3,t20_card_2,t20_finseq_2,t21_amistd_3,t29_amistd_3,t29_nat_1,t2_real,t2_subset,t2_tarski,t3_finseq_1,t3_real,t3_subset,t47_trees_1,t4_real,t4_subset,t50_card_1,t5_cqc_lang,t5_real,t5_subset,t61_finseq_3,t69_finseq_2,t6_boole,t6_cqc_lang,t6_real,t70_finseq_2,t72_finseq_2,t72_funct_1,t74_finseq_2,t7_boole,t7_finseq_1,t7_real,t8_boole,t8_finseq_2,t8_real,t91_relat_1]), [file(amistd_3,t32_amistd_3)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_amistd_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(A) & v1_setfam_1(A) ) ) ), file(amistd_1,cc1_amistd_1), []). fof(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). 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_card_5,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_xboole_0(A) ) ), file(card_5,cc1_card_5), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_necklace,axiom,( ! [A] : ( v4_ordinal2(A) => v1_card_1(A) ) ), file(necklace,cc1_necklace), []). fof(cc1_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) ), file(ordinal1,cc1_ordinal1), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) ) ) ), file(scmfsa_4,cc1_scmfsa_4), []). fof(cc1_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_amistd_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_xboole_0(C) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) ) ) ) ) ), file(amistd_1,cc2_amistd_1), []). fof(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). 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_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(card_5,cc2_card_5), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_necklace,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_realset1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_setfam_1(A) ) ) ), file(necklace,cc2_necklace), []). fof(cc2_ordinal1,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) ), file(ordinal1,cc2_ordinal1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). 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_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(ordinal1,cc3_ordinal1), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( l1_ami_1(B,A) => ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) ) => ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v3_amistd_1(B,A) ) ) ) ) ), file(amistd_1,cc4_amistd_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v5_amistd_1(C,A,B) => ( ~ v1_xboole_0(C) & ~ v3_ami_1(C,A,B) ) ) ) ) ), file(amistd_1,cc5_amistd_1), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_ami_1(A,B)) => ( v3_ami_1(C,A,B) => ( ~ v1_xboole_0(C) & ~ v5_amistd_1(C,A,B) ) ) ) ) ), file(amistd_1,cc6_amistd_1), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( v1_xboole_0(C) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_setfam_1(C) & v9_amistd_1(C,A,B) ) ) ) ) ), file(amistd_1,cc8_amistd_1), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(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_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d13_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => ! [D] : ( v4_ordinal2(D) => ( D = k6_amistd_1(A,B,C) <=> k5_amistd_1(A,B,D) = C ) ) ) ) ) ), file(amistd_1,d13_amistd_1), []). fof(d13_amistd_2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => k6_amistd_2(A,B) = k14_ami_3(A,B,k5_amistd_1(A,B,0),k5_ami_1(A,B)) ) ) ), file(amistd_2,d13_amistd_2), []). fof(d1_amistd_3,axiom,( k1_amistd_3 = a_0_0_amistd_3 ), file(amistd_3,d1_amistd_3), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d21_ordinal2,axiom,( ! [A] : ( v4_ordinal2(A) <=> r2_hidden(A,k5_ordinal2) ) ), file(ordinal2,d21_ordinal2), []). fof(d3_amistd_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) => k3_amistd_3(A,B,C) = a_3_3_amistd_3(A,B,C) ) ) ) ), file(amistd_3,d3_amistd_3), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_amistd_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) => ! [D] : ( m1_ordinal1(D,u2_ami_1(A,B)) => ( D = k4_amistd_3(A,B,C) <=> ( k1_relat_1(D) = k1_card_1(C) & ! [E] : ( r2_hidden(E,k1_card_1(C)) => k1_funct_1(D,E) = k5_amistd_1(A,B,k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))),k1_wellord2(k3_amistd_3(A,B,C))),E)) ) ) ) ) ) ) ) ), file(amistd_3,d4_amistd_3), []). fof(d5_ami_5,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ! [D] : ( m1_struct_0(D,B,u2_ami_1(A,B)) => ( r2_hidden(D,k1_relat_1(C)) => k5_ami_5(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) ) ), file(ami_5,d5_ami_5), []). fof(d5_amistd_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v3_trees_2(D) & m3_trees_2(D,u2_ami_1(A,B)) ) => ( D = k5_amistd_3(A,B,C) <=> ( k1_funct_1(D,k1_xboole_0) = k2_amistd_3(A,B,C) & ! [E] : ( m1_trees_1(E,k1_relat_1(D)) => ( k1_trees_2(k1_relat_1(D),E) = a_5_0_amistd_3(A,B,C,D,E) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r2_hidden(F,k1_card_1(k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E))))) => k1_funct_1(D,k8_finseq_1(k5_numbers,E,k12_finseq_1(k5_numbers,F))) = k1_funct_1(k4_amistd_3(A,B,k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))),F) ) ) ) ) ) ) ) ) ) ) ), file(amistd_3,d5_amistd_3), []). fof(d6_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k2_trees_2(A,B) = a_2_0_trees_2(A,B) ) ) ), file(trees_2,d6_trees_2), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k14_ami_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => ( v1_ami_3(k14_ami_3(A,B,C,D),A,B) & m1_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) ), file(ami_3,k14_ami_3), []). fof(dt_k15_cqc_sim1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k15_cqc_sim1(A,B),k5_finsub_1(A)) ) ), file(cqc_sim1,k15_cqc_sim1), []). fof(dt_k1_amistd_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => m1_subset_1(k1_amistd_1(A,B,C,D),k1_zfmisc_1(u2_ami_1(A,B))) ) ), file(amistd_1,k1_amistd_1), []). fof(dt_k1_amistd_3,axiom,( $true ), file(amistd_3,k1_amistd_3), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => m1_subset_1(k1_trees_2(A,B),k1_zfmisc_1(A)) ) ), file(trees_2,k1_trees_2), []). fof(dt_k1_wellord2,axiom,( ! [A] : v1_relat_1(k1_wellord2(A)) ), file(wellord2,k1_wellord2), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => m1_struct_0(k2_amistd_3(A,B,C),B,u2_ami_1(A,B)) ) ), file(amistd_3,k2_amistd_3), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => ( v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) ) ) ), file(finseq_2,k2_finseq_2), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_subset_1(B,k5_numbers) ) => m2_trees_2(k2_trees_2(A,B),A) ) ), file(trees_2,k2_trees_2), []). fof(dt_k2_wellord2,axiom,( ! [A] : ( v1_relat_1(A) => v3_ordinal1(k2_wellord2(A)) ) ), file(wellord2,k2_wellord2), []). 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_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) ) => m1_subset_1(k3_amistd_3(A,B,C),k1_zfmisc_1(k5_numbers)) ) ), file(amistd_3,k3_amistd_3), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_trees_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v3_trees_2(B) & m3_trees_2(B,A) & m1_subset_1(C,k1_relat_1(B)) ) => m1_subset_1(k3_trees_2(A,B,C),A) ) ), file(trees_2,k3_trees_2), []). fof(dt_k3_wellord1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( v1_relat_1(k3_wellord1(A,B)) & v1_funct_1(k3_wellord1(A,B)) ) ) ), file(wellord1,k3_wellord1), []). fof(dt_k4_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) ) => m1_ordinal1(k4_amistd_3(A,B,C),u2_ami_1(A,B)) ) ), file(amistd_3,k4_amistd_3), []). 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_ordinal2,axiom, ( v3_ordinal1(k4_ordinal2) & ~ v1_xboole_0(k4_ordinal2) ), file(ordinal2,k4_ordinal2), []). fof(dt_k5_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => m2_subset_1(k5_ami_1(A,B),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k5_ami_1), []). fof(dt_k5_ami_5,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_subset_1(D,u2_ami_1(A,B)) ) => m2_subset_1(k5_ami_5(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_5,k5_ami_5), []). fof(dt_k5_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & v4_ordinal2(C) ) => m1_struct_0(k5_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(amistd_1,k5_amistd_1), []). fof(dt_k5_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => ( v1_funct_1(k5_amistd_3(A,B,C)) & v3_trees_2(k5_amistd_3(A,B,C)) & m3_trees_2(k5_amistd_3(A,B,C),u2_ami_1(A,B)) ) ) ), file(amistd_3,k5_amistd_3), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k6_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) ) => v4_ordinal2(k6_amistd_1(A,B,C)) ) ), file(amistd_1,k6_amistd_1), []). fof(dt_k6_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => m1_ami_1(k6_amistd_2(A,B),A,B) ) ), file(amistd_2,k6_amistd_2), []). fof(dt_k6_finseq_1,axiom,( ! [A] : ( v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A) ) ), file(finseq_1,k6_finseq_1), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) ) => m2_subset_1(k7_amistd_1(A,B,C),k1_numbers,k5_numbers) ) ), file(amistd_1,k7_amistd_1), []). fof(dt_k7_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( ~ v1_xboole_0(k7_amistd_2(A,B)) & v1_ami_3(k7_amistd_2(A,B),A,B) & v9_amistd_1(k7_amistd_2(A,B),A,B) & v10_amistd_1(k7_amistd_2(A,B),A,B) & v11_amistd_1(k7_amistd_2(A,B),A,B) & m1_ami_1(k7_amistd_2(A,B),A,B) ) ) ), file(amistd_2,k7_amistd_2), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). 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_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_k9_trees_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_trees_1(B) & m1_subset_1(C,A) ) => ( v1_funct_1(k9_trees_2(A,B,C)) & v3_trees_2(k9_trees_2(A,B,C)) & m3_trees_2(k9_trees_2(A,B,C),A) ) ) ), file(trees_2,k9_trees_2), []). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ), file(ami_1,m1_ami_1), []). fof(dt_m1_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_ordinal1,axiom,( ! [A,B] : ( m1_ordinal1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) ) ) ), file(ordinal1,m1_ordinal1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k5_numbers) ) ) ), file(trees_1,m1_trees_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_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_m2_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_trees_2(B,A) => m1_subset_1(B,k1_zfmisc_1(A)) ) ) ), file(trees_2,m2_trees_2), []). fof(dt_m3_trees_2,axiom,( ! [A,B] : ( m3_trees_2(B,A) => v1_relat_1(B) ) ), file(trees_2,m3_trees_2), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ), file(ami_1,u2_ami_1), []). fof(dt_u3_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ~ v1_xboole_0(u3_ami_1(A,B)) ) ), file(ami_1,u3_ami_1), []). fof(dt_u4_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( ~ v1_xboole_0(u4_ami_1(A,B)) & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ), file(ami_1,u4_ami_1), []). fof(dt_u5_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u5_ami_1(A,B)) & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ), file(ami_1,u5_ami_1), []). fof(existence_l1_ami_1,axiom,( ! [A] : ? [B] : l1_ami_1(B,A) ), file(ami_1,l1_ami_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : m1_ami_1(C,A,B) ) ), file(ami_1,m1_ami_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_ordinal1,axiom,( ! [A] : ? [B] : m1_ordinal1(B,A) ), file(ordinal1,m1_ordinal1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_1(B,A) ) ), file(trees_1,m1_trees_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(existence_m2_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m2_trees_2(B,A) ) ), file(trees_2,m2_trees_2), []). fof(existence_m3_trees_2,axiom,( ! [A] : ? [B] : m3_trees_2(B,A) ), file(trees_2,m3_trees_2), []). fof(fc10_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k7_ami_1(A)) & v1_fraenkel(k7_ami_1(A)) ) ) ), file(ami_1,fc10_ami_1), []). fof(fc10_amistd_3,axiom, ( v1_relat_1(k2_wellord2(k1_xboole_0)) & v1_ordinal1(k2_wellord2(k1_xboole_0)) & v2_ordinal1(k2_wellord2(k1_xboole_0)) & v3_ordinal1(k2_wellord2(k1_xboole_0)) & v1_xboole_0(k2_wellord2(k1_xboole_0)) & v4_ordinal2(k2_wellord2(k1_xboole_0)) & v1_finset_1(k2_wellord2(k1_xboole_0)) & v1_card_1(k2_wellord2(k1_xboole_0)) & v1_xreal_0(k2_wellord2(k1_xboole_0)) & ~ v2_xreal_0(k2_wellord2(k1_xboole_0)) & ~ v3_xreal_0(k2_wellord2(k1_xboole_0)) & v1_setfam_1(k2_wellord2(k1_xboole_0)) & v1_xcmplx_0(k2_wellord2(k1_xboole_0)) & v1_membered(k2_wellord2(k1_xboole_0)) & v2_membered(k2_wellord2(k1_xboole_0)) & v3_membered(k2_wellord2(k1_xboole_0)) & v4_membered(k2_wellord2(k1_xboole_0)) & v5_membered(k2_wellord2(k1_xboole_0)) ), file(amistd_3,fc10_amistd_3), []). 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_amistd_3,axiom,( ! [A,B,C] : ( ( v3_ordinal1(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v1_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C)) & v2_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C)) & v3_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C)) ) ) ), file(amistd_3,fc11_amistd_3), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_amistd_3,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) & v2_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) & v3_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) & v4_ordinal2(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) & v1_card_1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) & v1_xreal_0(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) & v1_xcmplx_0(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) ) ) ), file(amistd_3,fc12_amistd_3), []). fof(fc12_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_amistd_3,axiom, ( ~ v1_xboole_0(k1_amistd_3) & v1_trees_1(k1_amistd_3) ), file(amistd_3,fc13_amistd_3), []). fof(fc13_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(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_amistd_3,axiom, ( ~ v1_xboole_0(k1_amistd_3) & ~ v1_finset_1(k1_amistd_3) & v1_trees_1(k1_amistd_3) ), file(amistd_3,fc14_amistd_3), []). fof(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) ) => ( v1_relat_1(k3_amistd_3(A,B,C)) & v1_ordinal1(k3_amistd_3(A,B,C)) & v2_ordinal1(k3_amistd_3(A,B,C)) & v3_ordinal1(k3_amistd_3(A,B,C)) & v1_xboole_0(k3_amistd_3(A,B,C)) & v4_ordinal2(k3_amistd_3(A,B,C)) & v1_finset_1(k3_amistd_3(A,B,C)) & v1_card_1(k3_amistd_3(A,B,C)) & v1_xreal_0(k3_amistd_3(A,B,C)) & ~ v2_xreal_0(k3_amistd_3(A,B,C)) & ~ v3_xreal_0(k3_amistd_3(A,B,C)) & v1_setfam_1(k3_amistd_3(A,B,C)) & v1_xcmplx_0(k3_amistd_3(A,B,C)) & v1_membered(k3_amistd_3(A,B,C)) & v2_membered(k3_amistd_3(A,B,C)) & v3_membered(k3_amistd_3(A,B,C)) & v4_membered(k3_amistd_3(A,B,C)) & v5_membered(k3_amistd_3(A,B,C)) ) ) ), file(amistd_3,fc15_amistd_3), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) ) => ( ~ v1_xboole_0(k3_amistd_3(A,B,C)) & v1_membered(k3_amistd_3(A,B,C)) & v2_membered(k3_amistd_3(A,B,C)) & v3_membered(k3_amistd_3(A,B,C)) & v4_membered(k3_amistd_3(A,B,C)) & v5_membered(k3_amistd_3(A,B,C)) ) ) ), file(amistd_3,fc16_amistd_3), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc17_amistd_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) ) => ( v1_relat_1(k4_amistd_3(A,B,C)) & v1_funct_1(k4_amistd_3(A,B,C)) & v2_funct_1(k4_amistd_3(A,B,C)) & v5_ordinal1(k4_amistd_3(A,B,C)) & v1_setfam_1(k4_amistd_3(A,B,C)) ) ) ), file(amistd_3,fc17_amistd_3), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc1_amistd_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k2_funcop_1(A,B)) ) ), file(amistd_1,fc1_amistd_1), []). fof(fc1_amistd_3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & m1_relset_1(B,A,k5_numbers) ) => ( v1_ordinal1(k1_funct_1(B,C)) & v2_ordinal1(k1_funct_1(B,C)) & v3_ordinal1(k1_funct_1(B,C)) & v4_ordinal2(k1_funct_1(B,C)) & v1_card_1(k1_funct_1(B,C)) & v1_xreal_0(k1_funct_1(B,C)) & v1_xcmplx_0(k1_funct_1(B,C)) ) ) ), file(amistd_3,fc1_amistd_3), []). fof(fc1_arytm_3,axiom, ( ~ v1_xboole_0(k4_ordinal2) & v1_ordinal1(k4_ordinal2) & v2_ordinal1(k4_ordinal2) & v3_ordinal1(k4_ordinal2) & v4_ordinal2(k4_ordinal2) ), file(arytm_3,fc1_arytm_3), []). fof(fc1_card_4,axiom, ( ~ v1_xboole_0(k5_ordinal2) & v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_finset_1(k5_ordinal2) & v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(card_4,fc1_card_4), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). 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_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc2_ami_1,axiom,( ! [A,B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ~ v1_xboole_0(u2_ami_1(A,B)) ) ), file(ami_1,fc2_ami_1), []). fof(fc2_amistd_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) & v1_realset1(k3_cqc_lang(A,B)) & v1_setfam_1(k3_cqc_lang(A,B)) ) ), file(amistd_1,fc2_amistd_1), []). fof(fc2_amistd_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_ordinal1(k7_relat_1(A,B)) & v2_ordinal1(k7_relat_1(A,B)) & v3_ordinal1(k7_relat_1(A,B)) & v1_xboole_0(k7_relat_1(A,B)) & v4_ordinal2(k7_relat_1(A,B)) & v1_finset_1(k7_relat_1(A,B)) & v1_card_1(k7_relat_1(A,B)) & v1_xreal_0(k7_relat_1(A,B)) & ~ v2_xreal_0(k7_relat_1(A,B)) & ~ v3_xreal_0(k7_relat_1(A,B)) & v1_setfam_1(k7_relat_1(A,B)) & v1_xcmplx_0(k7_relat_1(A,B)) & v1_membered(k7_relat_1(A,B)) & v2_membered(k7_relat_1(A,B)) & v3_membered(k7_relat_1(A,B)) & v4_membered(k7_relat_1(A,B)) & v5_membered(k7_relat_1(A,B)) ) ) ), file(amistd_3,fc2_amistd_3), []). 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_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_necklace,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_realset1(A) ) => v1_realset1(k1_relat_1(A)) ) ), file(necklace,fc2_necklace), []). fof(fc2_ordinal1,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_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) & v3_ordinal1(k1_xboole_0) ), file(ordinal1,fc2_ordinal1), []). 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_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) ) ) ), file(trees_2,fc2_trees_2), []). fof(fc3_amistd_3,axiom,( ! [A,B] : ( ~ v1_finset_1(A) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & ~ v1_xboole_0(k2_funcop_1(A,B)) & ~ v1_finset_1(k2_funcop_1(A,B)) & v1_setfam_1(k2_funcop_1(A,B)) ) ) ), file(amistd_3,fc3_amistd_3), []). fof(fc3_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). fof(fc3_finseq_6,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_ordinal2(B) ) => ( v1_relat_1(k7_relat_1(A,k2_finseq_1(B))) & v1_funct_1(k7_relat_1(A,k2_finseq_1(B))) & v1_finset_1(k7_relat_1(A,k2_finseq_1(B))) & v1_finseq_1(k7_relat_1(A,k2_finseq_1(B))) ) ) ), file(finseq_6,fc3_finseq_6), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v3_trees_2(k2_funcop_1(A,B)) ) ) ), file(trees_2,fc3_trees_2), []). 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(fc4_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), []). fof(fc4_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)) ) ) ), file(ordinal1,fc4_ordinal1), []). 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_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => v1_finset_1(k1_trees_2(A,B)) ) ), file(trees_2,fc4_trees_2), []). fof(fc5_amistd_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & m1_subset_1(D,u2_ami_1(A,B)) ) => ~ v1_xboole_0(k1_amistd_1(A,B,D,C)) ) ), file(amistd_1,fc5_amistd_1), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_ordinal1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ( v1_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) ) ) ), file(ordinal1,fc5_ordinal1), []). 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_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(trees_2,fc5_trees_2), []). fof(fc6_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => v3_ami_1(k5_ami_1(A,B),A,B) ) ), file(ami_1,fc6_ami_1), []). fof(fc6_amistd_3,axiom, ( v1_relat_1(k1_wellord2(k1_xboole_0)) & v1_ordinal1(k1_wellord2(k1_xboole_0)) & v2_ordinal1(k1_wellord2(k1_xboole_0)) & v3_ordinal1(k1_wellord2(k1_xboole_0)) & v1_xboole_0(k1_wellord2(k1_xboole_0)) & v4_ordinal2(k1_wellord2(k1_xboole_0)) & v1_finset_1(k1_wellord2(k1_xboole_0)) & v1_card_1(k1_wellord2(k1_xboole_0)) & v1_xreal_0(k1_wellord2(k1_xboole_0)) & ~ v2_xreal_0(k1_wellord2(k1_xboole_0)) & ~ v3_xreal_0(k1_wellord2(k1_xboole_0)) & v1_setfam_1(k1_wellord2(k1_xboole_0)) & v1_xcmplx_0(k1_wellord2(k1_xboole_0)) & v1_membered(k1_wellord2(k1_xboole_0)) & v2_membered(k1_wellord2(k1_xboole_0)) & v3_membered(k1_wellord2(k1_xboole_0)) & v4_membered(k1_wellord2(k1_xboole_0)) & v5_membered(k1_wellord2(k1_xboole_0)) ), file(amistd_3,fc6_amistd_3), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_amistd_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k1_wellord2(A)) & ~ v1_xboole_0(k1_wellord2(A)) & v1_setfam_1(k1_wellord2(A)) ) ) ), file(amistd_3,fc7_amistd_3), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_amistd_3,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_relat_1(k1_wellord2(A)) & v1_finset_1(k1_wellord2(A)) & v1_setfam_1(k1_wellord2(A)) ) ) ), file(amistd_3,fc8_amistd_3), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_amistd_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( v1_relat_1(k1_wellord2(A)) & ~ v1_xboole_0(k1_wellord2(A)) & ~ v1_finset_1(k1_wellord2(A)) & v1_setfam_1(k1_wellord2(A)) ) ) ), file(amistd_3,fc9_amistd_3), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_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_0_0_amistd_3,axiom,( ! [A] : ( r2_hidden(A,a_0_0_amistd_3) <=> ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & A = k2_finseq_2(B,0) ) ) ), file(amistd_3,a_0_0_amistd_3), []). fof(fraenkel_a_2_0_trees_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_2_0_trees_2(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & k3_finseq_1(D) = C ) ) ) ), file(trees_2,a_2_0_trees_2), []). fof(fraenkel_a_3_3_amistd_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C))) ) => ( r2_hidden(A,a_3_3_amistd_3(B,C,D)) <=> ? [E] : ( m1_struct_0(E,C,u2_ami_1(B,C)) & A = k7_amistd_1(B,C,E) & r2_hidden(E,D) ) ) ) ), file(amistd_3,a_3_3_amistd_3), []). fof(fraenkel_a_3_4_amistd_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v4_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v10_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) & m1_trees_1(D,k1_relat_1(k5_amistd_3(B,C,k7_amistd_2(B,C)))) ) => ( r2_hidden(A,a_3_4_amistd_3(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & A = k8_finseq_1(k5_numbers,D,k12_finseq_1(k5_numbers,E)) & r2_hidden(E,k1_card_1(k1_amistd_1(B,C,k3_trees_2(u2_ami_1(B,C),k5_amistd_3(B,C,k7_amistd_2(B,C)),D),k5_ami_5(B,C,k7_amistd_2(B,C),k3_trees_2(u2_ami_1(B,C),k5_amistd_3(B,C,k7_amistd_2(B,C)),D))))) ) ) ) ), file(amistd_3,a_3_4_amistd_3), []). fof(fraenkel_a_3_5_amistd_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v4_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v10_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) & m2_subset_1(D,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_3_5_amistd_3(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k1_relat_1(k5_amistd_3(B,C,k7_amistd_2(B,C)))) & A = E & k3_finseq_1(E) = k1_nat_1(D,1) ) ) ) ), file(amistd_3,a_3_5_amistd_3), []). fof(fraenkel_a_3_6_amistd_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v4_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v10_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) & m2_subset_1(D,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_3_6_amistd_3(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k1_relat_1(k5_amistd_3(B,C,k7_amistd_2(B,C)))) & A = E & k3_finseq_1(E) = D ) ) ) ), file(amistd_3,a_3_6_amistd_3), []). fof(fraenkel_a_5_0_amistd_3,axiom,( ! [A,B,C,D,E,F] : ( ( v1_setfam_1(B) & ~ v3_struct_0(C) & ~ v2_ami_1(C,B) & v5_ami_1(C,B) & v8_ami_1(C,B) & v4_amistd_1(C,B) & l1_ami_1(C,B) & m1_ami_1(D,B,C) & v1_funct_1(E) & v3_trees_2(E) & m3_trees_2(E,u2_ami_1(B,C)) & m1_trees_1(F,k1_relat_1(E)) ) => ( r2_hidden(A,a_5_0_amistd_3(B,C,D,E,F)) <=> ? [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) & A = k8_finseq_1(k5_numbers,F,k12_finseq_1(k5_numbers,G)) & r2_hidden(G,k1_card_1(k1_amistd_1(B,C,k3_trees_2(u2_ami_1(B,C),E,F),k5_ami_5(B,C,D,k3_trees_2(u2_ami_1(B,C),E,F))))) ) ) ) ), file(amistd_3,a_5_0_amistd_3), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(rc1_amistd_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & ~ v1_realset1(A) ) ), file(amistd_1,rc1_amistd_1), []). fof(rc1_amistd_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & ~ v1_finset_1(A) & v1_setfam_1(A) ) ), file(amistd_3,rc1_amistd_3), []). fof(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_card_5,axiom,( ? [A] : ~ v1_finset_1(A) ), file(card_5,rc1_card_5), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_heyting2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_fraenkel(A) ) ), file(heyting2,rc1_heyting2), []). 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_ordinal1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc1_ordinal1), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_scmfsa_4,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_ami_3(C,A,B) ) ) ), file(scmfsa_4,rc1_scmfsa_4), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), []). fof(rc2_amistd_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v1_membered(C) & v2_membered(C) & v3_membered(C) & v4_membered(C) & v5_membered(C) ) ) ), file(amistd_1,rc2_amistd_1), []). fof(rc2_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_card_5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) ) ), file(card_5,rc2_card_5), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc2_ordinal1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) ) ) ), file(ami_1,rc3_ami_1), []). fof(rc3_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) ) ) ), file(amistd_1,rc3_amistd_1), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc3_ordinal1), []). 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_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_subset_1(C,u4_ami_1(A,B)) & v3_ami_1(C,A,B) ) ) ), file(ami_1,rc4_ami_1), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) ), file(ordinal1,rc4_ordinal1), []). 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_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ), file(trees_2,rc5_trees_2), []). fof(rc6_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) ) ) ), file(amistd_1,rc6_amistd_1), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc6_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) ) ), file(trees_2,rc6_trees_2), []). fof(rc7_amistd_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_realset1(C) & v1_setfam_1(C) & v1_ami_3(C,A,B) & v9_amistd_1(C,A,B) & v10_amistd_1(C,A,B) & v11_amistd_1(C,A,B) ) ) ), file(amistd_1,rc7_amistd_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ), file(trees_2,rc7_trees_2), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(rc8_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) ) ), file(trees_2,rc8_trees_2), []). fof(rc9_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), []). fof(redefinition_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k14_ami_3,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) & m1_subset_1(D,u4_ami_1(A,B)) ) => k14_ami_3(A,B,C,D) = k3_cqc_lang(C,D) ) ), file(ami_3,k14_ami_3), []). fof(redefinition_k15_cqc_sim1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k15_cqc_sim1(A,B) = k1_tarski(B) ) ), file(cqc_sim1,k15_cqc_sim1), []). 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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). 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_trees_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v3_trees_2(B) & m3_trees_2(B,A) & m1_subset_1(C,k1_relat_1(B)) ) => k3_trees_2(A,B,C) = k1_funct_1(B,C) ) ), file(trees_2,k3_trees_2), []). 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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k7_amistd_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u2_ami_1(A,B)) ) => k7_amistd_1(A,B,C) = k6_amistd_1(A,B,C) ) ), file(amistd_1,k7_amistd_1), []). fof(redefinition_k7_amistd_2,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => k7_amistd_2(A,B) = k6_amistd_2(A,B) ) ), file(amistd_2,k7_amistd_2), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). fof(redefinition_k9_trees_2,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_trees_1(B) & m1_subset_1(C,A) ) => k9_trees_2(A,B,C) = k2_funcop_1(B,C) ) ), file(trees_2,k9_trees_2), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). fof(redefinition_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) <=> m1_subset_1(B,A) ) ) ), file(trees_1,m1_trees_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(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(s1_hilbert2__e8_56__amistd_3,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( ( r2_hidden(k1_funct_1(k5_amistd_3(A,B,k7_amistd_2(A,B)),k6_finseq_1(k5_numbers)),k1_relat_1(k7_amistd_2(A,B))) & ! [C] : ( m1_trees_1(C,k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) => ( r2_hidden(k1_funct_1(k5_amistd_3(A,B,k7_amistd_2(A,B)),C),k1_relat_1(k7_amistd_2(A,B))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)),k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) => r2_hidden(k1_funct_1(k5_amistd_3(A,B,k7_amistd_2(A,B)),k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D))),k1_relat_1(k7_amistd_2(A,B))) ) ) ) ) ) => ! [C] : ( m1_trees_1(C,k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) => r2_hidden(k1_funct_1(k5_amistd_3(A,B,k7_amistd_2(A,B)),C),k1_relat_1(k7_amistd_2(A,B))) ) ) ) ), file(amistd_3,s1_hilbert2__e8_56__amistd_3), []). fof(s1_nat_1__e11_56__amistd_3,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( ( k2_trees_2(k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B))),0) = k2_trees_2(k1_amistd_3,0) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k2_trees_2(k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B))),C) = k2_trees_2(k1_amistd_3,C) => k2_trees_2(k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B))),k1_nat_1(C,1)) = k2_trees_2(k1_amistd_3,k1_nat_1(C,1)) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k2_trees_2(k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B))),C) = k2_trees_2(k1_amistd_3,C) ) ) ) ), file(amistd_3,s1_nat_1__e11_56__amistd_3), []). fof(s1_nat_1__e7_56_4_1__amistd_3,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ( ( r2_hidden(k2_finseq_2(0,0),k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(k2_finseq_2(C,0),k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) => r2_hidden(k2_finseq_2(k1_nat_1(C,1),0),k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => r2_hidden(k2_finseq_2(C,0),k1_relat_1(k5_amistd_3(A,B,k7_amistd_2(A,B)))) ) ) ) ), file(amistd_3,s1_nat_1__e7_56_4_1__amistd_3), []). 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(t14_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),k1_trees_2(A,B)) <=> r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A) ) ) ) ) ), file(trees_2,t14_trees_2), []). fof(t15_amistd_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => ! [D] : ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) => ( v3_ami_1(D,A,B) => k1_amistd_1(A,B,C,D) = k1_struct_0(B,C) ) ) ) ) ) ), file(amistd_1,t15_amistd_1), []). fof(t15_amistd_3,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( r1_tarski(k1_tarski(A),B) => k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k1_tarski(A)))),k1_wellord2(k1_tarski(A))) = k3_cqc_lang(0,A) ) ) ), file(amistd_3,t15_amistd_3), []). fof(t17_amistd_3,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m1_trees_1(C,B) => r2_hidden(k2_partfun1(k5_numbers,k5_numbers,C,k2_finseq_1(A)),B) ) ) ) ), file(amistd_3,t17_amistd_3), []). fof(t17_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = B ) => A = k2_funcop_1(k1_relat_1(A),B) ) ) ), file(funcop_1,t17_funcop_1), []). fof(t17_qc_lang4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k2_trees_2(A,0) = k1_tarski(k1_xboole_0) ) ), file(qc_lang4,t17_qc_lang4), []). fof(t18_amistd_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k2_trees_2(A,C) = k2_trees_2(B,C) ) => A = B ) ) ) ), file(amistd_3,t18_amistd_3), []). fof(t18_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,k3_finseq_1(A)) ) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) ), file(finseq_1,t18_finseq_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_card_5,axiom, ( 1 = k1_tarski(0) & 2 = k2_tarski(0,1) ), file(card_5,t1_card_5), []). 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(t20_amistd_3,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k2_trees_2(k1_amistd_3,A) = k1_tarski(k2_finseq_2(A,0)) ) ), file(amistd_3,t20_amistd_3), []). fof(t20_card_2,axiom,( 1 = k4_ordinal2 ), file(card_2,t20_card_2), []). fof(t20_finseq_2,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) => ( C = D & A = B ) ) ) ) ), file(finseq_2,t20_finseq_2), []). fof(t21_amistd_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_ami_3(C,A,B) & m1_ami_1(C,A,B) ) => r2_hidden(k2_amistd_3(A,B,C),k1_relat_1(C)) ) ) ) ), file(amistd_3,t21_amistd_3), []). fof(t29_amistd_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v4_amistd_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_struct_0(C,B,u2_ami_1(A,B)) => ! [D] : ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) => ( ( v10_ami_1(B,A) & v3_ami_1(D,A,B) ) => k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,C)) ) ) ) ) ) ), file(amistd_3,t29_amistd_3), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_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(t3_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xreal_0(1,A) & r1_xreal_0(A,B) ) ) ) ) ), file(finseq_1,t3_finseq_1), []). 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(t47_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( r2_hidden(k1_xboole_0,A) & r2_hidden(k6_finseq_1(k5_numbers),A) ) ) ), file(trees_1,t47_trees_1), []). 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_card_1,axiom,( ! [A] : k1_card_1(k1_tarski(A)) = k4_ordinal2 ), file(card_1,t50_card_1), []). fof(t5_cqc_lang,axiom,( ! [A,B] : ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A) & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ), file(cqc_lang,t5_cqc_lang), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t61_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v4_ordinal2(C) => ( ( k3_finseq_1(A) = k2_xcmplx_0(C,1) & B = k7_relat_1(A,k2_finseq_1(C)) ) => A = k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,1)))) ) ) ) ) ), file(finseq_3,t61_finseq_3), []). fof(t69_finseq_2,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) ), file(finseq_2,t69_finseq_2), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_cqc_lang,axiom,( ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ), file(cqc_lang,t6_cqc_lang), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t70_finseq_2,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B,C] : ( r2_hidden(B,k2_finseq_1(A)) => k1_funct_1(k2_finseq_2(A,C),B) = C ) ) ), file(finseq_2,t70_finseq_2), []). fof(t72_finseq_2,axiom,( ! [A] : k2_finseq_2(0,A) = k1_xboole_0 ), file(finseq_2,t72_finseq_2), []). 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(t74_finseq_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : k2_finseq_2(k1_nat_1(A,1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) ) ), file(finseq_2,t74_finseq_2), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r1_xreal_0(A,B) <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ), file(finseq_1,t7_finseq_1), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_finseq_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,1))) & ~ r2_hidden(A,k2_finseq_1(B)) & A != k1_nat_1(B,1) ) ) ) ), file(finseq_2,t8_finseq_2), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t91_relat_1,axiom,( ! [A,B] : ( v1_relat_1(B) => ( r1_tarski(A,k1_relat_1(B)) => k1_relat_1(k7_relat_1(B,A)) = A ) ) ), file(relat_1,t91_relat_1), []).