% Mizar problem: t82_comput_1,comput_1,3737,55 fof(t82_comput_1,conjecture,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) => ( r2_hidden(B,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,A)) => v2_unialg_1(B,k5_numbers) ) ) ) ), 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_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_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k4_subset_1,connectedness_r1_xreal_0,d11_comput_1,d20_comput_1,d21_comput_1,d22_comput_1,d23_comput_1,d2_tarski,d2_xboole_0,d8_comput_1,d9_comput_1,dt_k12_comput_1,dt_k13_comput_1,dt_k13_finseq_1,dt_k14_comput_1,dt_k15_comput_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_prob_1,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_xboole_0,dt_k2_xcmplx_0,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_k4_subset_1,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_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_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_relat_1,fc10_xreal_0,fc11_finseq_1,fc11_xreal_0,fc12_membered,fc12_relat_1,fc12_xreal_0,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc1_finseq_2,fc1_funcop_1,fc1_funct_1,fc1_nat_1,fc1_ordinal2,fc1_partfun1,fc1_subset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_comput_1,fc2_finseq_1,fc2_finset_1,fc2_funcop_1,fc2_membered,fc2_relat_1,fc3_funcop_1,fc3_funct_7,fc3_nat_1,fc3_pre_circ,fc3_subset_1,fc3_xreal_0,fc4_comput_1,fc4_nat_1,fc4_ordinal2,fc4_relat_1,fc4_subset_1,fc5_comput_1,fc5_membered,fc6_comput_1,fc6_funct_1,fc6_membered,fc6_relat_1,fc7_comput_1,fc7_funcop_1,fc7_funct_7,fc7_xreal_0,fc8_comput_1,fc8_funcop_1,fc8_relat_1,fc8_xreal_0,fc9_comput_1,fc9_finseq_1,fc9_finset_1,fc9_funcop_1,fc9_relat_1,fc9_xreal_0,fraenkel_a_0_2_comput_1,fraenkel_a_1_4_comput_1,fraenkel_a_1_6_comput_1,fraenkel_a_1_7_comput_1,fraenkel_a_1_8_comput_1,fraenkel_a_1_9_comput_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc10_comput_1,rc11_comput_1,rc12_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,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_k1_nat_1,redefinition_k1_prob_1,redefinition_k2_pre_circ,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_rfunct_3,redefinition_k4_subset_1,redefinition_k5_numbers,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,s1_nat_1__e3_137__comput_1,spc0_boole,spc1_boole,spc1_numerals,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t2_real,t2_subset,t2_tarski,t32_comput_1,t3_real,t3_subset,t4_real,t4_subset,t50_comput_1,t5_real,t5_subset,t6_boole,t6_real,t72_comput_1,t7_boole,t7_real,t8_boole,t8_real]), [file(comput_1,t82_comput_1)]). 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_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_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_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(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(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(d20_comput_1,axiom,( k12_comput_1 = k2_xboole_0(k2_tarski(k6_comput_1(0,0),k7_comput_1(1,1)),a_0_2_comput_1) ), file(comput_1,d20_comput_1), []). fof(d21_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) => k13_comput_1(A) = k2_xboole_0(A,a_1_6_comput_1(A)) ) ), file(comput_1,d21_comput_1), []). fof(d22_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) => k14_comput_1(A) = k2_xboole_0(A,a_1_7_comput_1(A)) ) ), file(comput_1,d22_comput_1), []). fof(d23_comput_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers))) & m2_relset_1(A,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers))) ) => ( A = k15_comput_1 <=> ( k1_prob_1(k5_comput_1(k5_numbers),A,0) = k12_comput_1 & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k1_prob_1(k5_comput_1(k5_numbers),A,k1_nat_1(B,1)) = k4_subset_1(k5_comput_1(k5_numbers),k13_comput_1(k1_prob_1(k5_comput_1(k5_numbers),A,B)),k14_comput_1(k1_prob_1(k5_comput_1(k5_numbers),A,B))) ) ) ) ) ), file(comput_1,d23_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(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(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_k12_comput_1,axiom,( m1_subset_1(k12_comput_1,k1_zfmisc_1(k5_comput_1(k5_numbers))) ), file(comput_1,k12_comput_1), []). fof(dt_k13_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) => m1_subset_1(k13_comput_1(A),k1_zfmisc_1(k5_comput_1(k5_numbers))) ) ), file(comput_1,k13_comput_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k14_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_comput_1(k5_numbers))) => m1_subset_1(k14_comput_1(A),k1_zfmisc_1(k5_comput_1(k5_numbers))) ) ), file(comput_1,k14_comput_1), []). fof(dt_k15_comput_1,axiom, ( v1_funct_1(k15_comput_1) & v1_funct_2(k15_comput_1,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers))) & m2_relset_1(k15_comput_1,k5_numbers,k1_zfmisc_1(k5_comput_1(k5_numbers))) ), file(comput_1,k15_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_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_prob_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) & m1_subset_1(C,k5_numbers) ) => m1_subset_1(k1_prob_1(A,B,C),k1_zfmisc_1(A)) ) ), file(prob_1,k1_prob_1), []). 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_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_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_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), []). 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_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_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_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(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_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_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_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_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_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_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_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(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_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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_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(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_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_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(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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_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(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_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_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_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_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(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_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_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_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_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_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_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_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(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_2_comput_1,axiom,( ! [A] : ( r2_hidden(A,a_0_2_comput_1) <=> ? [B,C] : ( m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & A = k8_comput_1(B,C) & r1_xreal_0(1,C) & r1_xreal_0(C,B) ) ) ), file(comput_1,a_0_2_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(fraenkel_a_1_6_comput_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k5_comput_1(k5_numbers))) => ( r2_hidden(A,a_1_6_comput_1(B)) <=> ? [C] : ( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & A = C & ? [D] : ( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & ? [E] : ( m2_rfunct_3(E,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & r2_hidden(D,B) & r2_hidden(E,B) & r1_comput_1(C,D,E,F) ) ) ) ) ) ) ), file(comput_1,a_1_6_comput_1), []). fof(fraenkel_a_1_7_comput_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k5_comput_1(k5_numbers))) => ( r2_hidden(A,a_1_7_comput_1(B)) <=> ? [C,D] : ( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & v5_comput_1(D) & m2_finseq_2(D,k5_comput_1(k5_numbers),k3_finseq_2(k5_comput_1(k5_numbers))) & A = k5_relat_1(k6_funct_6(D),C) & r2_hidden(C,B) & k3_comput_1(C) = k3_finseq_1(D) & r1_tarski(k2_relat_1(D),B) ) ) ) ), file(comput_1,a_1_7_comput_1), []). fof(fraenkel_a_1_8_comput_1,axiom,( ! [A,B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r2_hidden(A,a_1_8_comput_1(B)) <=> ? [C,D] : ( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & v5_comput_1(D) & m2_finseq_2(D,k5_comput_1(k5_numbers),k3_finseq_2(k5_comput_1(k5_numbers))) & A = k5_relat_1(k6_funct_6(D),C) & r2_hidden(C,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) & k3_comput_1(C) = k3_finseq_1(D) & r1_tarski(k2_relat_1(D),k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) ) ) ) ), file(comput_1,a_1_8_comput_1), []). fof(fraenkel_a_1_9_comput_1,axiom,( ! [A,B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r2_hidden(A,a_1_9_comput_1(B)) <=> ? [C] : ( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & A = C & ? [D] : ( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & ? [E] : ( m2_rfunct_3(E,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) & ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & r2_hidden(D,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) & r2_hidden(E,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) & r1_comput_1(C,D,E,F) ) ) ) ) ) ) ), file(comput_1,a_1_9_comput_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_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(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(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_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_prob_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_zfmisc_1(A)) & m1_relset_1(B,k5_numbers,k1_zfmisc_1(A)) & m1_subset_1(C,k5_numbers) ) => k1_prob_1(A,B,C) = k1_funct_1(B,C) ) ), file(prob_1,k1_prob_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_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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(s1_nat_1__e3_137__comput_1,axiom, ( ( ! [A] : ( m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) => ( r2_hidden(A,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,0)) => v2_unialg_1(A,k5_numbers) ) ) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ! [C] : ( m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) => ( r2_hidden(C,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) => v2_unialg_1(C,k5_numbers) ) ) => ! [D] : ( m2_rfunct_3(D,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) => ( r2_hidden(D,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,k1_nat_1(B,1))) => v2_unialg_1(D,k5_numbers) ) ) ) ) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [E] : ( m2_rfunct_3(E,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) => ( r2_hidden(E,k1_prob_1(k5_comput_1(k5_numbers),k15_comput_1,B)) => v2_unialg_1(E,k5_numbers) ) ) ) ), file(comput_1,s1_nat_1__e3_137__comput_1), []). 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(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_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(t32_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) ) => ( v2_unialg_1(A,k5_numbers) & m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) ) ), file(comput_1,t32_comput_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(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_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v2_unialg_1(B,A) & m2_rfunct_3(B,k3_finseq_2(A),A,k5_comput_1(A)) ) => ! [C] : ( ( v5_comput_1(C) & m2_finseq_1(C,k5_comput_1(A)) ) => ( ( k3_comput_1(B) = k3_finseq_1(C) & ! [D] : ( m2_rfunct_3(D,k3_finseq_2(A),A,k5_comput_1(A)) => ( r2_hidden(D,k2_relat_1(C)) => v2_unialg_1(D,A) ) ) ) => ( v2_unialg_1(k5_relat_1(k6_funct_6(C),B),A) & m2_rfunct_3(k5_relat_1(k6_funct_6(C),B),k3_finseq_2(A),A,k5_comput_1(A)) ) ) ) ) ) ), file(comput_1,t50_comput_1), []). 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(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t72_comput_1,axiom,( ! [A] : ( m2_rfunct_3(A,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) => ! [B] : ( ( v2_unialg_1(B,k5_numbers) & m2_rfunct_3(B,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) => ! [C] : ( ( v2_unialg_1(C,k5_numbers) & m2_rfunct_3(C,k3_finseq_2(k5_numbers),k5_numbers,k5_comput_1(k5_numbers)) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_comput_1(A,B,C,D) => ( v2_unialg_1(A,k5_numbers) & ~ ( ~ v1_xboole_0(B) & v1_xboole_0(A) ) ) ) ) ) ) ) ), file(comput_1,t72_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), []).