% Mizar problem: t88_comput_1,comput_1,4177,34 fof(t88_comput_1,conjecture,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v9_comput_1(A) & v12_comput_1(A) ) => r2_hidden(k16_comput_1(A),k11_comput_1) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_comput_1,cc10_membered,cc11_comput_1,cc11_membered,cc12_comput_1,cc12_membered,cc13_comput_1,cc13_membered,cc14_comput_1,cc14_membered,cc15_comput_1,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_altcat_1,cc1_comput_1,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_funct_7,cc1_membered,cc1_nat_1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_comput_1,cc2_finset_1,cc2_funct_1,cc2_funct_7,cc2_membered,cc2_nat_1,cc2_xreal_0,cc3_comput_1,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_comput_1,cc4_membered,cc4_xreal_0,cc5_comput_1,cc5_xreal_0,cc6_comput_1,cc6_membered,cc6_xreal_0,cc7_comput_1,cc7_xreal_0,cc8_comput_1,cc8_xreal_0,cc9_comput_1,cc9_membered,commutativity_k2_tarski,connectedness_r1_xreal_0,d11_comput_1,d17_comput_1,d18_comput_1,d19_comput_1,d26_comput_1,d28_comput_1,d2_tarski,d6_comput_1,d8_comput_1,d9_comput_1,dt_k10_finseq_1,dt_k11_comput_1,dt_k13_finseq_1,dt_k16_comput_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_comput_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_pralg_3,dt_k4_finseq_2,dt_k4_partfun1,dt_k4_rfunct_3,dt_k5_comput_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k6_comput_1,dt_k6_funct_6,dt_k7_comput_1,dt_k8_comput_1,dt_m1_comput_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_rfunct_3,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_rfunct_3,dt_m2_subset_1,existence_m1_comput_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_rfunct_3,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_rfunct_3,existence_m2_subset_1,fc10_comput_1,fc10_membered,fc10_relat_1,fc11_finseq_1,fc11_membered,fc12_comput_1,fc12_membered,fc12_relat_1,fc13_comput_1,fc13_membered,fc14_comput_1,fc14_finset_1,fc14_membered,fc15_comput_1,fc15_membered,fc16_comput_1,fc16_finseq_1,fc16_membered,fc17_comput_1,fc17_finseq_1,fc18_comput_1,fc19_comput_1,fc1_finseq_2,fc1_finset_1,fc1_funcop_1,fc1_funct_1,fc1_ordinal2,fc1_partfun1,fc1_subset_1,fc20_comput_1,fc21_comput_1,fc22_comput_1,fc23_comput_1,fc24_comput_1,fc25_comput_1,fc26_comput_1,fc27_comput_1,fc28_comput_1,fc2_altcat_1,fc2_comput_1,fc2_finseq_1,fc2_finset_1,fc2_funcop_1,fc2_membered,fc2_subset_1,fc32_comput_1,fc33_comput_1,fc34_comput_1,fc3_comput_1,fc3_funcop_1,fc3_funct_7,fc3_pre_circ,fc3_subset_1,fc4_comput_1,fc4_ordinal2,fc4_relat_1,fc4_subset_1,fc5_comput_1,fc5_finseq_1,fc5_funct_7,fc5_membered,fc5_relat_1,fc6_comput_1,fc6_funct_1,fc6_membered,fc6_relat_1,fc7_comput_1,fc7_finseq_1,fc7_funcop_1,fc7_funct_7,fc7_membered,fc7_relat_1,fc8_comput_1,fc8_funcop_1,fc8_membered,fc8_relat_1,fc9_comput_1,fc9_finseq_1,fc9_funcop_1,fc9_membered,fc9_relat_1,fraenkel_a_0_1_comput_1,fraenkel_a_1_4_comput_1,rc10_comput_1,rc11_comput_1,rc12_comput_1,rc13_comput_1,rc14_comput_1,rc15_comput_1,rc16_comput_1,rc17_comput_1,rc18_comput_1,rc19_comput_1,rc1_finseq_1,rc1_finseq_2,rc1_finset_1,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_funct_7,rc1_membered,rc1_nat_1,rc1_partfun1,rc1_pre_circ,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc20_comput_1,rc21_comput_1,rc22_comput_1,rc23_comput_1,rc24_comput_1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_funct_7,rc2_nat_1,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_comput_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_relat_1,rc3_xreal_0,rc4_comput_1,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_xreal_0,rc5_comput_1,rc5_funct_1,rc6_comput_1,rc6_finseq_1,rc7_comput_1,rc7_finseq_1,rc8_comput_1,rc8_finseq_1,rc9_comput_1,redefinition_k2_pre_circ,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_rfunct_3,redefinition_k5_numbers,redefinition_m1_comput_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,t121_finseq_2,t12_msualg_1,t147_finseq_2,t1_numerals,t1_real,t1_subset,t2_real,t2_subset,t2_tarski,t3_real,t3_subset,t40_comput_1,t4_real,t4_subset,t5_real,t5_subset,t61_finseq_1,t6_boole,t6_real,t76_comput_1,t7_boole,t7_real,t8_boole,t8_real]), [file(comput_1,t88_comput_1)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k11_comput_1) => ( v1_relat_1(A) & v1_funct_1(A) & v2_unialg_1(A,k5_numbers) & v7_seqm_3(A) & v2_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) ) ) ), file(comput_1,cc10_comput_1), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_comput_1(k5_numbers)) => ( v9_comput_1(A) => ( v1_relat_1(A) & v1_funct_1(A) & v2_unialg_1(A,k5_numbers) & v4_comput_1(A) ) ) ) ), file(comput_1,cc11_comput_1), []). 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_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_comput_1(A) & v9_comput_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_comput_1(A) & v3_comput_1(A) ) ) ), file(comput_1,cc12_comput_1), []). 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_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) & v11_comput_1(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) ) ) ), file(comput_1,cc13_comput_1), []). 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_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) & v12_comput_1(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) ) ) ), file(comput_1,cc14_comput_1), []). 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_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) & v13_comput_1(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) ) ) ), file(comput_1,cc15_comput_1), []). 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_altcat_1,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_fraenkel(B) ) ) ), file(altcat_1,cc1_altcat_1), []). fof(cc1_comput_1,axiom,( ! [A,B,C] : ( m1_rfunct_3(C,A,B) => ( ~ v1_xboole_0(C) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ) ), file(comput_1,cc1_comput_1), []). 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_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_comput_1,axiom,( ! [A] : ( m1_relset_1(A,k3_finseq_2(k5_numbers),k5_numbers) => ( v1_funct_1(A) => ( v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) ) ) ) ), file(comput_1,cc2_comput_1), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(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) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_comput_1,axiom,( ! [A] : ( m1_relset_1(A,k3_finseq_2(k5_numbers),k5_numbers) => ( ( v1_funct_1(A) & v2_unialg_1(A,k5_numbers) ) => ( v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) ) ) ) ), file(comput_1,cc3_comput_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_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_comput_1,axiom,( ! [A,B] : ( m1_subset_1(B,k5_comput_1(A)) => ( v1_relat_1(B) & v1_funct_1(B) & v4_comput_1(B) ) ) ), file(comput_1,cc4_comput_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_comput_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_comput_1(A))) ) => ! [C] : ( m1_subset_1(C,B) => ( v1_relat_1(C) & v1_funct_1(C) & v4_comput_1(C) ) ) ) ), file(comput_1,cc5_comput_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_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k11_comput_1) => ( v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) ) ) ), file(comput_1,cc6_comput_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_comput_1,axiom,( ! [A] : ( v9_comput_1(A) => ( v1_relat_1(A) & v1_funct_1(A) ) ) ), file(comput_1,cc7_comput_1), []). 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_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v9_comput_1(A) ) => ( v1_relat_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v4_comput_1(A) ) ) ), file(comput_1,cc8_comput_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_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k11_comput_1) => ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) ) ) ), file(comput_1,cc9_comput_1), []). 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_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). 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(d11_comput_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k8_comput_1(A,B) = k3_pralg_3(k2_finseq_2(A,k5_numbers),B) ) ) ), file(comput_1,d11_comput_1), []). fof(d17_comput_1,axiom,( ! [A] : ( v8_comput_1(A) <=> ( r2_hidden(k6_comput_1(0,0),A) & r2_hidden(k7_comput_1(1,1),A) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,B) ) => r2_hidden(k8_comput_1(B,C),A) ) ) ) & v6_comput_1(A) & v7_comput_1(A) ) ) ), file(comput_1,d17_comput_1), []). fof(d18_comput_1,axiom,( k11_comput_1 = k1_setfam_1(a_0_1_comput_1) ), file(comput_1,d18_comput_1), []). fof(d19_comput_1,axiom,( ! [A] : ( v9_comput_1(A) <=> r2_hidden(A,k11_comput_1) ) ), file(comput_1,d19_comput_1), []). fof(d26_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_comput_1(A) ) => ( v12_comput_1(A) <=> k3_comput_1(A) = 2 ) ) ), file(comput_1,d26_comput_1), []). fof(d28_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k16_comput_1(A) = k5_relat_1(k6_funct_6(k10_finseq_1(k8_comput_1(3,1),k8_comput_1(3,3))),A) ) ), file(comput_1,d28_comput_1), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). fof(d6_comput_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v5_comput_1(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,k2_relat_1(A)) & r2_hidden(C,k2_relat_1(A)) ) => ( ~ ( v1_xboole_0(B) & ~ v1_xboole_0(C) & k1_relat_1(C) != k1_tarski(k1_xboole_0) ) & ~ ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ~ v1_xboole_0(E) => ~ ( r1_tarski(k1_relat_1(B),k4_finseq_2(D,E)) & r1_tarski(k1_relat_1(C),k4_finseq_2(D,E)) ) ) ) ) ) ) ) ) ) ) ), file(comput_1,d6_comput_1), []). fof(d8_comput_1,axiom,( ! [A] : k5_comput_1(A) = a_1_4_comput_1(A) ), file(comput_1,d8_comput_1), []). fof(d9_comput_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k6_comput_1(A,B) = k2_pre_circ(k4_finseq_2(A,k5_numbers),B) ) ) ), file(comput_1,d9_comput_1), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k11_comput_1,axiom,( m1_subset_1(k11_comput_1,k1_zfmisc_1(k5_comput_1(k5_numbers))) ), file(comput_1,k11_comput_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k16_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k16_comput_1(A)) & v1_funct_1(k16_comput_1(A)) ) ) ), file(comput_1,k16_comput_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_setfam_1,axiom,( $true ), file(setfam_1,k1_setfam_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_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_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). 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_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_comput_1(A) ) => m2_subset_1(k3_comput_1(A),k1_numbers,k5_numbers) ) ), file(comput_1,k3_comput_1), []). 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_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_pralg_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k3_pralg_3(A,B)) & v1_funct_1(k3_pralg_3(A,B)) ) ) ), file(pralg_3,k3_pralg_3), []). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_partfun1,axiom,( $true ), file(partfun1,k4_partfun1), []). fof(dt_k4_rfunct_3,axiom,( ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ), file(rfunct_3,k4_rfunct_3), []). fof(dt_k5_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_comput_1(A)) & m1_rfunct_3(k5_comput_1(A),k3_finseq_2(A),A) ) ), file(comput_1,k5_comput_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_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(dt_k6_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k6_comput_1(A,B)) & v1_funct_1(k6_comput_1(A,B)) & v7_seqm_3(k6_comput_1(A,B)) & v2_comput_1(k6_comput_1(A,B)) & v4_comput_1(k6_comput_1(A,B)) ) ) ), file(comput_1,k6_comput_1), []). fof(dt_k6_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k6_funct_6(A)) & v1_funct_1(k6_funct_6(A)) ) ) ), file(funct_6,k6_funct_6), []). fof(dt_k7_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k7_comput_1(A,B)) & v1_funct_1(k7_comput_1(A,B)) & v7_seqm_3(k7_comput_1(A,B)) & v2_comput_1(k7_comput_1(A,B)) & v4_comput_1(k7_comput_1(A,B)) ) ) ), file(comput_1,k7_comput_1), []). fof(dt_k8_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_relat_1(k8_comput_1(A,B)) & v1_funct_1(k8_comput_1(A,B)) & v7_seqm_3(k8_comput_1(A,B)) & v2_comput_1(k8_comput_1(A,B)) & v4_comput_1(k8_comput_1(A,B)) ) ) ), file(comput_1,k8_comput_1), []). fof(dt_m1_comput_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(C)) ) => ! [E] : ( m1_comput_1(E,A,B,C,D) => m2_rfunct_3(E,A,B,C) ) ) ), file(comput_1,m1_comput_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_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rfunct_3,axiom,( $true ), file(rfunct_3,m1_rfunct_3), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). 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_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) => ( v1_funct_1(D) & m2_relset_1(D,A,B) ) ) ) ), file(rfunct_3,m2_rfunct_3), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(existence_m1_comput_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(C)) ) => ? [E] : m1_comput_1(E,A,B,C,D) ) ), file(comput_1,m1_comput_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rfunct_3,axiom,( ! [A,B] : ? [C] : m1_rfunct_3(C,A,B) ), file(rfunct_3,m1_rfunct_3), []). 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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ? [D] : m2_rfunct_3(D,A,B,C) ) ), file(rfunct_3,m2_rfunct_3), []). 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(fc10_comput_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v5_comput_1(B) & m1_finseq_1(B,k5_comput_1(A)) ) => ( v1_relat_1(k6_funct_6(B)) & v1_funct_1(k6_funct_6(B)) & v4_comput_1(k6_funct_6(B)) ) ) ), file(comput_1,fc10_comput_1), []). 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_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). 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(fc12_comput_1,axiom, ( ~ v1_xboole_0(k11_comput_1) & v1_fraenkel(k11_comput_1) & v8_comput_1(k11_comput_1) ), file(comput_1,fc12_comput_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(fc13_comput_1,axiom, ( ~ v1_xboole_0(k8_comput_1(1,1)) & v1_relat_1(k8_comput_1(1,1)) & v1_funct_1(k8_comput_1(1,1)) & v7_seqm_3(k8_comput_1(1,1)) & v2_comput_1(k8_comput_1(1,1)) & v3_comput_1(k8_comput_1(1,1)) & v4_comput_1(k8_comput_1(1,1)) & v9_comput_1(k8_comput_1(1,1)) ), file(comput_1,fc13_comput_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(fc14_comput_1,axiom, ( ~ v1_xboole_0(k8_comput_1(2,1)) & v1_relat_1(k8_comput_1(2,1)) & v1_funct_1(k8_comput_1(2,1)) & v7_seqm_3(k8_comput_1(2,1)) & v2_comput_1(k8_comput_1(2,1)) & v3_comput_1(k8_comput_1(2,1)) & v4_comput_1(k8_comput_1(2,1)) & v9_comput_1(k8_comput_1(2,1)) ), file(comput_1,fc14_comput_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_comput_1,axiom, ( ~ v1_xboole_0(k8_comput_1(2,2)) & v1_relat_1(k8_comput_1(2,2)) & v1_funct_1(k8_comput_1(2,2)) & v7_seqm_3(k8_comput_1(2,2)) & v2_comput_1(k8_comput_1(2,2)) & v3_comput_1(k8_comput_1(2,2)) & v4_comput_1(k8_comput_1(2,2)) & v9_comput_1(k8_comput_1(2,2)) ), file(comput_1,fc15_comput_1), []). 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_comput_1,axiom, ( ~ v1_xboole_0(k7_comput_1(1,1)) & v1_relat_1(k7_comput_1(1,1)) & v1_funct_1(k7_comput_1(1,1)) & v7_seqm_3(k7_comput_1(1,1)) & v2_comput_1(k7_comput_1(1,1)) & v3_comput_1(k7_comput_1(1,1)) & v4_comput_1(k7_comput_1(1,1)) & v9_comput_1(k7_comput_1(1,1)) ), file(comput_1,fc16_comput_1), []). 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_comput_1,axiom, ( ~ v1_xboole_0(k7_comput_1(3,3)) & v1_relat_1(k7_comput_1(3,3)) & v1_funct_1(k7_comput_1(3,3)) & v7_seqm_3(k7_comput_1(3,3)) & v2_comput_1(k7_comput_1(3,3)) & v3_comput_1(k7_comput_1(3,3)) & v4_comput_1(k7_comput_1(3,3)) & v9_comput_1(k7_comput_1(3,3)) ), file(comput_1,fc17_comput_1), []). 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(fc18_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k6_comput_1(0,A)) & v1_relat_1(k6_comput_1(0,A)) & v1_funct_1(k6_comput_1(0,A)) & v7_seqm_3(k6_comput_1(0,A)) & v2_comput_1(k6_comput_1(0,A)) & v3_comput_1(k6_comput_1(0,A)) & v4_comput_1(k6_comput_1(0,A)) & v10_comput_1(k6_comput_1(0,A)) ) ) ), file(comput_1,fc18_comput_1), []). fof(fc19_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k6_comput_1(1,A)) & v1_relat_1(k6_comput_1(1,A)) & v1_funct_1(k6_comput_1(1,A)) & v7_seqm_3(k6_comput_1(1,A)) & v2_comput_1(k6_comput_1(1,A)) & v3_comput_1(k6_comput_1(1,A)) & v4_comput_1(k6_comput_1(1,A)) & v11_comput_1(k6_comput_1(1,A)) ) ) ), file(comput_1,fc19_comput_1), []). fof(fc1_finseq_2,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k4_finseq_2(A,B)) ) ), file(finseq_2,fc1_finseq_2), []). 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(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_partfun1,axiom,( ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ), file(partfun1,fc1_partfun1), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc20_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k6_comput_1(2,A)) & v1_relat_1(k6_comput_1(2,A)) & v1_funct_1(k6_comput_1(2,A)) & v7_seqm_3(k6_comput_1(2,A)) & v2_comput_1(k6_comput_1(2,A)) & v3_comput_1(k6_comput_1(2,A)) & v4_comput_1(k6_comput_1(2,A)) & v12_comput_1(k6_comput_1(2,A)) ) ) ), file(comput_1,fc20_comput_1), []). fof(fc21_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k6_comput_1(3,A)) & v1_relat_1(k6_comput_1(3,A)) & v1_funct_1(k6_comput_1(3,A)) & v7_seqm_3(k6_comput_1(3,A)) & v2_comput_1(k6_comput_1(3,A)) & v3_comput_1(k6_comput_1(3,A)) & v4_comput_1(k6_comput_1(3,A)) & v13_comput_1(k6_comput_1(3,A)) ) ) ), file(comput_1,fc21_comput_1), []). fof(fc22_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k8_comput_1(1,A)) & v1_relat_1(k8_comput_1(1,A)) & v1_funct_1(k8_comput_1(1,A)) & v7_seqm_3(k8_comput_1(1,A)) & v2_comput_1(k8_comput_1(1,A)) & v3_comput_1(k8_comput_1(1,A)) & v4_comput_1(k8_comput_1(1,A)) & v11_comput_1(k8_comput_1(1,A)) ) ) ), file(comput_1,fc22_comput_1), []). fof(fc23_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k8_comput_1(2,A)) & v1_relat_1(k8_comput_1(2,A)) & v1_funct_1(k8_comput_1(2,A)) & v7_seqm_3(k8_comput_1(2,A)) & v2_comput_1(k8_comput_1(2,A)) & v3_comput_1(k8_comput_1(2,A)) & v4_comput_1(k8_comput_1(2,A)) & v12_comput_1(k8_comput_1(2,A)) ) ) ), file(comput_1,fc23_comput_1), []). fof(fc24_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k8_comput_1(3,A)) & v1_relat_1(k8_comput_1(3,A)) & v1_funct_1(k8_comput_1(3,A)) & v7_seqm_3(k8_comput_1(3,A)) & v2_comput_1(k8_comput_1(3,A)) & v3_comput_1(k8_comput_1(3,A)) & v4_comput_1(k8_comput_1(3,A)) & v13_comput_1(k8_comput_1(3,A)) ) ) ), file(comput_1,fc24_comput_1), []). fof(fc25_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k7_comput_1(1,A)) & v1_relat_1(k7_comput_1(1,A)) & v1_funct_1(k7_comput_1(1,A)) & v7_seqm_3(k7_comput_1(1,A)) & v2_comput_1(k7_comput_1(1,A)) & v3_comput_1(k7_comput_1(1,A)) & v4_comput_1(k7_comput_1(1,A)) & v11_comput_1(k7_comput_1(1,A)) ) ) ), file(comput_1,fc25_comput_1), []). fof(fc26_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k7_comput_1(2,A)) & v1_relat_1(k7_comput_1(2,A)) & v1_funct_1(k7_comput_1(2,A)) & v7_seqm_3(k7_comput_1(2,A)) & v2_comput_1(k7_comput_1(2,A)) & v3_comput_1(k7_comput_1(2,A)) & v4_comput_1(k7_comput_1(2,A)) & v12_comput_1(k7_comput_1(2,A)) ) ) ), file(comput_1,fc26_comput_1), []). fof(fc27_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k7_comput_1(3,A)) & v1_relat_1(k7_comput_1(3,A)) & v1_funct_1(k7_comput_1(3,A)) & v7_seqm_3(k7_comput_1(3,A)) & v2_comput_1(k7_comput_1(3,A)) & v3_comput_1(k7_comput_1(3,A)) & v4_comput_1(k7_comput_1(3,A)) & v13_comput_1(k7_comput_1(3,A)) ) ) ), file(comput_1,fc27_comput_1), []). fof(fc28_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k6_comput_1(A,B)) & v1_relat_1(k6_comput_1(A,B)) & v1_funct_1(k6_comput_1(A,B)) & v7_seqm_3(k6_comput_1(A,B)) & v2_comput_1(k6_comput_1(A,B)) & v3_comput_1(k6_comput_1(A,B)) & v4_comput_1(k6_comput_1(A,B)) & v9_comput_1(k6_comput_1(A,B)) ) ) ), file(comput_1,fc28_comput_1), []). fof(fc2_altcat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_fraenkel(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ) ), file(altcat_1,fc2_altcat_1), []). fof(fc2_comput_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) & 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_funct_7(k1_xboole_0) & v4_comput_1(k1_xboole_0) ), file(comput_1,fc2_comput_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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc32_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) ) => ( v1_relat_1(k16_comput_1(A)) & v1_funct_1(k16_comput_1(A)) & v7_seqm_3(k16_comput_1(A)) & v2_comput_1(k16_comput_1(A)) ) ) ), file(comput_1,fc32_comput_1), []). fof(fc33_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) ) => ( v1_relat_1(k16_comput_1(A)) & v1_funct_1(k16_comput_1(A)) & v4_comput_1(k16_comput_1(A)) ) ) ), file(comput_1,fc33_comput_1), []). fof(fc34_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v12_comput_1(A) ) => ( ~ v1_xboole_0(k16_comput_1(A)) & v1_relat_1(k16_comput_1(A)) & v1_funct_1(k16_comput_1(A)) & v7_seqm_3(k16_comput_1(A)) & v2_comput_1(k16_comput_1(A)) & v3_comput_1(k16_comput_1(A)) & v4_comput_1(k16_comput_1(A)) & v13_comput_1(k16_comput_1(A)) ) ) ), file(comput_1,fc34_comput_1), []). fof(fc3_comput_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ~ v1_xboole_0(k2_funcop_1(k1_tarski(A),B)) & v1_relat_1(k2_funcop_1(k1_tarski(A),B)) & v1_funct_1(k2_funcop_1(k1_tarski(A),B)) & v4_comput_1(k2_funcop_1(k1_tarski(A),B)) ) ) ), file(comput_1,fc3_comput_1), []). 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_funct_7,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) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). fof(fc3_pre_circ,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v2_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) ) ) ), file(pre_circ,fc3_pre_circ), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc4_comput_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) & v4_comput_1(k5_relat_1(A,B)) ) ) ), file(comput_1,fc4_comput_1), []). fof(fc4_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_comput_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) & 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_funct_7(k1_xboole_0) & v4_comput_1(k1_xboole_0) & v5_comput_1(k1_xboole_0) ), file(comput_1,fc5_comput_1), []). fof(fc5_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc5_finseq_1), []). fof(fc5_funct_7,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funcop_1(k10_finseq_1(A,B)) ) ) ), file(funct_7,fc5_funct_7), []). 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_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(fc6_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k6_comput_1(A,B)) & v1_relat_1(k6_comput_1(A,B)) & v1_funct_1(k6_comput_1(A,B)) & v7_seqm_3(k6_comput_1(A,B)) & v2_comput_1(k6_comput_1(A,B)) & v3_comput_1(k6_comput_1(A,B)) & v4_comput_1(k6_comput_1(A,B)) ) ) ), file(comput_1,fc6_comput_1), []). fof(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k7_comput_1(A,B)) & v1_relat_1(k7_comput_1(A,B)) & v1_funct_1(k7_comput_1(A,B)) & v7_seqm_3(k7_comput_1(A,B)) & v2_comput_1(k7_comput_1(A,B)) & v3_comput_1(k7_comput_1(A,B)) & v4_comput_1(k7_comput_1(A,B)) ) ) ), file(comput_1,fc7_comput_1), []). fof(fc7_finseq_1,axiom,( ! [A,B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) ) ), file(finseq_1,fc7_finseq_1), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_funct_7,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finset_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_funcop_1(k2_finseq_2(A,B)) ) ) ), file(funct_7,fc7_funct_7), []). 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(fc8_comput_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k8_comput_1(A,B)) & v1_relat_1(k8_comput_1(A,B)) & v1_funct_1(k8_comput_1(A,B)) & v7_seqm_3(k8_comput_1(A,B)) & v2_comput_1(k8_comput_1(A,B)) & v3_comput_1(k8_comput_1(A,B)) & v4_comput_1(k8_comput_1(A,B)) ) ) ), file(comput_1,fc8_comput_1), []). fof(fc8_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) ) ) ), file(funcop_1,fc8_funcop_1), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_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(fc9_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_comput_1(A)) & v1_fraenkel(k5_comput_1(A)) ) ), file(comput_1,fc9_comput_1), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_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_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fraenkel_a_0_1_comput_1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_comput_1) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_comput_1(k5_numbers))) & A = B & v8_comput_1(B) ) ) ), file(comput_1,a_0_1_comput_1), []). fof(fraenkel_a_1_4_comput_1,axiom,( ! [A,B] : ( r2_hidden(A,a_1_4_comput_1(B)) <=> ? [C] : ( m2_rfunct_3(C,k3_finseq_2(B),B,k4_rfunct_3(k3_finseq_2(B),B)) & A = C & v4_comput_1(C) ) ) ), file(comput_1,a_1_4_comput_1), []). fof(rc10_comput_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v5_comput_1(B) ) ), file(comput_1,rc10_comput_1), []). fof(rc11_comput_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v5_comput_1(B) ) ), file(comput_1,rc11_comput_1), []). fof(rc12_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k5_comput_1(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_unialg_1(B,A) & v4_comput_1(B) ) ) ), file(comput_1,rc12_comput_1), []). fof(rc13_comput_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) & ~ v1_xboole_0(A) & v1_fraenkel(A) & v8_comput_1(A) ) ), file(comput_1,rc13_comput_1), []). fof(rc14_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) ) ), file(comput_1,rc14_comput_1), []). fof(rc15_comput_1,axiom,( ? [A] : ( m1_subset_1(A,k5_comput_1(k5_numbers)) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) ) ), file(comput_1,rc15_comput_1), []). fof(rc16_comput_1,axiom,( ? [A] : ( m1_subset_1(A,k11_comput_1) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_unialg_1(A,k5_numbers) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) ) ), file(comput_1,rc16_comput_1), []). fof(rc17_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) & v10_comput_1(A) ) ), file(comput_1,rc17_comput_1), []). fof(rc18_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) & v11_comput_1(A) ) ), file(comput_1,rc18_comput_1), []). fof(rc19_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) & v12_comput_1(A) ) ), file(comput_1,rc19_comput_1), []). 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_finseq_2,axiom,( ! [A] : ? [B] : ( m1_finseq_2(B,A) & ~ v1_xboole_0(B) ) ), file(finseq_2,rc1_finseq_2), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ), file(funct_7,rc1_funct_7), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc20_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v9_comput_1(A) & v13_comput_1(A) ) ), file(comput_1,rc20_comput_1), []). fof(rc21_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v10_comput_1(A) ) ), file(comput_1,rc21_comput_1), []). fof(rc22_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v11_comput_1(A) ) ), file(comput_1,rc22_comput_1), []). fof(rc23_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v12_comput_1(A) ) ), file(comput_1,rc23_comput_1), []). fof(rc24_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) & v13_comput_1(A) ) ), file(comput_1,rc24_comput_1), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ), file(funct_7,rc2_funct_7), []). 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_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_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_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) ) ), file(comput_1,rc3_comput_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). 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_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_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v4_comput_1(A) ) ), file(comput_1,rc4_comput_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_comput_1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,k3_finseq_2(A),B) & v1_relat_1(C) & v1_funct_1(C) & v4_comput_1(C) ) ), file(comput_1,rc5_comput_1), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc6_comput_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,k3_finseq_2(A),B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v4_comput_1(C) ) ) ), file(comput_1,rc6_comput_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(rc7_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_relset_1(B,k3_finseq_2(A),A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_unialg_1(B,A) & v4_comput_1(B) ) ) ), file(comput_1,rc7_comput_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(rc8_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) & v2_comput_1(A) & v3_comput_1(A) & v4_comput_1(A) ) ), file(comput_1,rc8_comput_1), []). 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(rc9_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v5_comput_1(A) ) ), file(comput_1,rc9_comput_1), []). fof(redefinition_k2_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). 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_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k4_rfunct_3,axiom,( ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ), file(rfunct_3,k4_rfunct_3), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_m1_comput_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(C)) ) => ! [E] : ( m1_comput_1(E,A,B,C,D) <=> m1_subset_1(E,D) ) ) ), file(comput_1,m1_comput_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_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). 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_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(rfunct_3,m2_rfunct_3), []). 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(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(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(t121_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => m2_finseq_2(k10_finseq_1(B,C),A,k4_finseq_2(2,A)) ) ) ) ), file(finseq_2,t121_finseq_2), []). fof(t12_msualg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) ) ), file(msualg_1,t12_msualg_1), []). fof(t147_finseq_2,axiom,( ! [A,B] : k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B) ), file(finseq_2,t147_finseq_2), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). 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(t40_comput_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( k1_relat_1(k8_comput_1(A,B)) = k4_finseq_2(A,k5_numbers) & ( ( r1_xreal_0(1,B) & r1_xreal_0(B,A) ) => k2_relat_1(k8_comput_1(A,B)) = k5_numbers ) ) ) ) ), file(comput_1,t40_comput_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(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_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k10_finseq_1(A,B) <=> ( k3_finseq_1(C) = 2 & k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) ) ) ), file(finseq_1,t61_finseq_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t76_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v8_comput_1(A) & m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) ) => ! [B] : ( m1_comput_1(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers),A) => ! [C] : ( ( v5_comput_1(C) & m2_finseq_1(C,A) ) => ( k3_comput_1(B) = k3_finseq_1(C) => r2_hidden(k5_relat_1(k6_funct_6(C),B),A) ) ) ) ) ), file(comput_1,t76_comput_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).