%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SCT167+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 14:11:55 EDT 2024 % Result : Theorem 1.58s 1.65s % Output : CNFRefutation 1.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SCT167+1 : TPTP v8.2.0. Released v5.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n020.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Jun 22 09:22:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 1.47/1.58 %------------------------------------------- % 1.47/1.58 % File :CSE---1.7 % 1.47/1.58 % Problem :theBenchmark % 1.47/1.58 % Transform :cnf % 1.47/1.58 % Format :tptp:raw % 1.47/1.58 % Command :java -jar mcs_scs.jar %d %s % 1.47/1.58 % 1.47/1.58 % Result :Theorem 0.460000s % 1.47/1.58 % Output :CNFRefutation 0.460000s % 1.47/1.58 %------------------------------------------- % 1.47/1.59 %------------------------------------------------------------------------------ % 1.47/1.59 % File : SCT167+1 : TPTP v8.2.0. Released v5.2.0. % 1.47/1.59 % Domain : Social Choice Theory % 1.47/1.59 % Problem : Arrow's Impossibility Theorem 433668, 500 axioms selected % 1.47/1.59 % Version : Especial. % 1.47/1.59 % English : % 1.47/1.59 % 1.47/1.59 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.47/1.59 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 1.47/1.59 % Source : [Bla11] % 1.47/1.59 % Names : arrow_433668.500.p [Bla11] % 1.47/1.59 % 1.47/1.59 % Status : ContradictoryAxioms % 1.47/1.59 % Rating : 0.61 v8.2.0, 0.58 v7.5.0, 0.62 v7.4.0, 0.63 v7.3.0, 0.66 v7.1.0, 0.65 v7.0.0, 0.60 v6.4.0, 0.58 v6.3.0, 0.62 v6.2.0, 0.68 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.78 v5.2.0 % 1.47/1.59 % Syntax : Number of formulae : 533 ( 121 unt; 0 def) % 1.47/1.59 % Number of atoms : 1427 ( 332 equ) % 1.47/1.59 % Maximal formula atoms : 17 ( 2 avg) % 1.47/1.59 % Number of connectives : 1056 ( 162 ~; 27 |; 60 &) % 1.47/1.59 % ( 131 <=>; 676 =>; 0 <=; 0 <~>) % 1.47/1.59 % Maximal formula depth : 16 ( 6 avg) % 1.47/1.59 % Maximal term depth : 16 ( 2 avg) % 1.47/1.59 % Number of predicates : 34 ( 33 usr; 0 prp; 1-6 aty) % 1.47/1.59 % Number of functors : 61 ( 61 usr; 24 con; 0-6 aty) % 1.47/1.59 % Number of variables : 1514 (1500 !; 14 ?) % 1.47/1.59 % SPC : FOF_CAX_RFO_SEQ % 1.47/1.59 % 1.47/1.59 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 1.47/1.59 % 2011-03-01 11:30:53 % 1.47/1.59 % : Renamed from SWW169+1 % 1.47/1.59 %------------------------------------------------------------------------------ % 1.47/1.59 %----Relevant facts (491) % 1.47/1.59 fof(fact_ext,axiom, % 1.47/1.59 ! [V_g_2,V_f_2] : % 1.47/1.59 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 1.47/1.59 => V_f_2 = V_g_2 ) ). % 1.47/1.59 % 1.47/1.59 fof(fact_assms_I3_J,axiom, % 1.47/1.59 c_Arrow__Order__Mirabelle_OIIA(v_F) ). % 1.47/1.59 % 1.47/1.59 fof(fact_u,axiom, % 1.47/1.59 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096a_A_126_061_Ab_096,axiom, % 1.47/1.59 v_a____ != v_b____ ). % 1.47/1.59 % 1.47/1.59 fof(fact__096c_A_126_061_Ad_096,axiom, % 1.47/1.59 v_c____ != v_d____ ). % 1.47/1.59 % 1.47/1.59 fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom, % 1.47/1.59 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom, % 1.47/1.59 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom, % 1.47/1.59 ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom, % 1.47/1.59 ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096,axiom, % 1.47/1.59 ! [B_i] : % 1.47/1.59 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) ) % 1.47/1.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.59 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) ) % 1.47/1.59 & ( hAPP(v_h____,B_i) != v_n____ % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) ) % 1.47/1.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ) % 1.47/1.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) ) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096,axiom, % 1.47/1.59 ! [B_i] : % 1.47/1.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,B_i))) % 1.47/1.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) ) % 1.47/1.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.59 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) ) % 1.47/1.59 & ( hAPP(v_h____,B_i) != v_n____ % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) ) ) ). % 1.47/1.59 % 1.47/1.59 fof(fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096,axiom, % 1.47/1.59 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ). % 1.47/1.59 % 1.47/1.59 fof(fact_PW,axiom, % 1.47/1.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____))) % 1.47/1.59 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ) ). % 1.47/1.59 % 1.47/1.59 fof(fact_n_I2_J,axiom, % 1.47/1.59 ! [B_m] : % 1.47/1.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),v_n____)) % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) ) ). % 1.47/1.59 % 1.47/1.59 fof(fact_in__mkbot,axiom, % 1.47/1.59 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.47/1.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_z_2))) % 1.47/1.59 <=> ( V_y_2 != V_z_2 % 1.47/1.59 & ( V_x_2 = V_z_2 % 1.47/1.59 => V_x_2 != V_y_2 ) % 1.47/1.59 & ( V_x_2 != V_z_2 % 1.47/1.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ). % 1.47/1.59 % 1.47/1.59 fof(fact_in__mktop,axiom, % 1.47/1.59 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.47/1.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_z_2))) % 1.47/1.59 <=> ( V_x_2 != V_z_2 % 1.47/1.59 & ( V_y_2 = V_z_2 % 1.47/1.60 => V_x_2 != V_y_2 ) % 1.47/1.60 & ( V_y_2 != V_z_2 % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_PiProf,axiom, % 1.47/1.60 ! [V_na_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),V_na_2))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096_091_124_Ae_A_126_061_Ad_059_Ab_A_126_061_Aa_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_A_058_AProf_059_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_A_058_AProf_059_AALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_124_093_061_061_062_A_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096,axiom, % 1.47/1.60 ( v_e____ != v_d____ % 1.47/1.60 => ( v_b____ != v_a____ % 1.47/1.60 => ( 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% 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( ! [B_i] : % 1.47/1.60 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) ) % 1.47/1.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.60 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) ) % 1.47/1.60 & ( hAPP(v_h____,B_i) != v_n____ % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) ) % 1.47/1.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ) % 1.47/1.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) ) % 1.47/1.60 => ( 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% 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ) ) ) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_n_I3_J,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom, % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom, % 1.47/1.60 ! [B_i] : % 1.47/1.60 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) ) % 1.47/1.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.47/1.60 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) ) % 1.47/1.60 & ( hAPP(v_h____,B_i) != v_n____ % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) ) % 1.47/1.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ) % 1.47/1.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)) ). % 1.47/1.60 % 1.47/1.60 fof(fact_equalityCE,axiom, % 1.47/1.60 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 1.47/1.60 ( V_A_2 = V_B_2 % 1.47/1.60 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.47/1.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 1.47/1.60 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_pred__equals__eq2,axiom, % 1.47/1.60 ! [V_S_2,V_R_2,T_b,T_a] : % 1.47/1.60 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) % 1.47/1.60 <=> V_R_2 = V_S_2 ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_in__rel__def,axiom, % 1.47/1.60 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 1.47/1.60 ( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_same__fstI,axiom, % 1.47/1.60 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] : % 1.47/1.60 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2))) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_pred__equals__eq,axiom, % 1.47/1.60 ! [V_S_2,V_R_2,T_a] : % 1.47/1.60 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) % 1.47/1.60 <=> V_R_2 = V_S_2 ) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096P_A_058_AProf_096,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096Lba_A_058_ALin_096,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ). % 1.47/1.60 % 1.47/1.60 fof(fact__096Lab_A_058_ALin_096,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)) ). % 1.47/1.60 % 1.47/1.60 fof(fact_top1I,axiom, % 1.47/1.60 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 1.47/1.60 % 1.47/1.60 fof(fact_UNIV__I,axiom, % 1.47/1.60 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 1.47/1.60 % 1.47/1.60 fof(fact_n_I1_J,axiom, % 1.47/1.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) ). % 1.47/1.60 % 1.47/1.60 fof(fact_injh,axiom, % 1.47/1.60 c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ). % 1.47/1.60 % 1.47/1.60 fof(fact_termination__basic__simps_I3_J,axiom, % 1.47/1.60 ! [V_z,V_y,V_x] : % 1.47/1.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) % 1.47/1.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_termination__basic__simps_I4_J,axiom, % 1.47/1.60 ! [V_y,V_z,V_x] : % 1.47/1.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) % 1.47/1.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_termination__basic__simps_I2_J,axiom, % 1.47/1.60 ! [V_y,V_z,V_x] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_termination__basic__simps_I1_J,axiom, % 1.47/1.60 ! [V_z,V_y,V_x] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_termination__basic__simps_I5_J,axiom, % 1.47/1.60 ! [V_y,V_x] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.47/1.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_eq__mem__trans,axiom, % 1.47/1.60 ! [V_A_2,T_a,V_ba_2,V_aa_2] : % 1.47/1.60 ( V_aa_2 = V_ba_2 % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) % 1.47/1.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_eqelem__imp__iff,axiom, % 1.47/1.60 ! [V_A_2,T_a,V_y_2,V_x_2] : % 1.47/1.60 ( V_x_2 = V_y_2 % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_eqset__imp__iff,axiom, % 1.47/1.60 ! [V_x_2,T_a,V_B_2,V_A_2] : % 1.47/1.60 ( V_A_2 = V_B_2 % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_eq__mem,axiom, % 1.47/1.60 ! [V_y_2,V_x_2,T_a] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 1.47/1.60 <=> V_x_2 = V_y_2 ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_mem__def,axiom, % 1.47/1.60 ! [V_A_2,V_x_2,T_a] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.47/1.60 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact__C3_C,axiom, % 1.47/1.60 ! [V_P_H_2,V_Pa_2,V_ba_2,V_aa_2] : % 1.47/1.60 ( V_aa_2 != V_ba_2 % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( ! [B_i] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(V_P_H_2,B_i))) ) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact_pairwise__neutrality,axiom, % 1.47/1.60 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.47/1.60 ( V_aa_2 != V_ba_2 % 1.47/1.60 => ( V_a_H_2 != V_b_H_2 % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( ! [B_i] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) ) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact__C4_C,axiom, % 1.47/1.60 ! [V_P_H_2,V_Pa_2,V_ca_2,V_ba_2,V_aa_2] : % 1.47/1.60 ( V_aa_2 != V_ba_2 % 1.47/1.60 => ( V_ba_2 != V_ca_2 % 1.47/1.60 => ( V_aa_2 != V_ca_2 % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.60 => ( ! [B_i] : % 1.47/1.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(V_P_H_2,B_i))) ) % 1.47/1.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) % 1.47/1.60 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ). % 1.47/1.60 % 1.47/1.60 fof(fact__C1_C,axiom, % 1.47/1.60 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.47/1.60 ( V_aa_2 != V_ba_2 % 1.47/1.60 => ( V_a_H_2 != V_b_H_2 % 1.47/1.60 => ( V_aa_2 != V_b_H_2 % 1.47/1.60 => ( V_ba_2 != V_a_H_2 % 1.47/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.61 => ( ! [B_i] : % 1.47/1.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) % 1.47/1.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) ) % 1.47/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) % 1.47/1.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ). % 1.47/1.61 % 1.47/1.61 fof(fact__C2_C,axiom, % 1.47/1.61 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.47/1.61 ( V_aa_2 != V_ba_2 % 1.47/1.61 => ( V_a_H_2 != V_b_H_2 % 1.47/1.61 => ( V_aa_2 != V_b_H_2 % 1.47/1.61 => ( V_ba_2 != V_a_H_2 % 1.47/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf)) % 1.47/1.61 => ( ! [B_i] : % 1.47/1.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i))) % 1.47/1.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) ) % 1.47/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2))) % 1.47/1.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ). % 1.47/1.61 % 1.47/1.61 fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom, % 1.47/1.61 ? [B_n] : % 1.47/1.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) % 1.47/1.61 & ! [B_m] : % 1.47/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 1.47/1.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) ) % 1.47/1.61 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ). % 1.47/1.61 % 1.58/1.61 fof(fact_less__add__one,axiom, % 1.58/1.61 ! [V_a,T_a] : % 1.58/1.61 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_add__less__le__mono,axiom, % 1.58/1.61 ! [V_d,V_c,V_b,V_a,T_a] : % 1.58/1.61 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.58/1.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_add__le__less__mono,axiom, % 1.58/1.61 ! [V_d,V_c,V_b,V_a,T_a] : % 1.58/1.61 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.58/1.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom, % 1.58/1.61 ~ ! [B_n] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) % 1.58/1.61 => ( ! [B_m] : % 1.58/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) ) % 1.58/1.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_order__refl,axiom, % 1.58/1.61 ! [V_x,T_a] : % 1.58/1.61 ( class_Orderings_Opreorder(T_a) % 1.58/1.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_subsetD,axiom, % 1.58/1.61 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 1.58/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_assms_I1_J,axiom, % 1.58/1.61 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ). % 1.58/1.61 % 1.58/1.61 fof(fact_psubsetD,axiom, % 1.58/1.61 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_pred__subset__eq2,axiom, % 1.58/1.61 ! [V_S_2,V_R_2,T_b,T_a] : % 1.58/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))) % 1.58/1.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2),V_S_2)) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_in__mono,axiom, % 1.58/1.61 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.58/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_set__rev__mp,axiom, % 1.58/1.61 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_set__mp,axiom, % 1.58/1.61 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.58/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_subset__UNIV,axiom, % 1.58/1.61 ! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 1.58/1.61 % 1.58/1.61 fof(fact_pred__subset__eq,axiom, % 1.58/1.61 ! [V_S_2,V_R_2,T_a] : % 1.58/1.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) % 1.58/1.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_above__Lin,axiom, % 1.58/1.61 ! [V_L_2,V_y_2,V_x_2] : % 1.58/1.61 ( V_x_2 != V_y_2 % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_mkbot__Lin,axiom, % 1.58/1.61 ! [V_x_2,V_L_2] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_mktop__Lin,axiom, % 1.58/1.61 ! [V_x_2,V_L_2] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.61 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_notin__Lin__iff,axiom, % 1.58/1.61 ! [V_y_2,V_x_2,V_L_2] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.61 => ( V_x_2 != V_y_2 % 1.58/1.61 => ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) % 1.58/1.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)) ) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_Lin__irrefl,axiom, % 1.58/1.61 ! [V_ba_2,V_aa_2,V_L_2] : % 1.58/1.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2)) % 1.58/1.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_linorder__le__cases,axiom, % 1.58/1.61 ! [V_y,V_x,T_a] : % 1.58/1.61 ( class_Orderings_Olinorder(T_a) % 1.58/1.61 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.58/1.61 % 1.58/1.61 fof(fact_le__funE,axiom, % 1.58/1.61 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.58/1.61 ( class_Orderings_Oord(T_b) % 1.58/1.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I6_J,axiom, % 1.58/1.62 ! [V_z,V_x,V_y,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I5_J,axiom, % 1.58/1.62 ! [V_x,V_y,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.62 => V_x = V_y ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__trans,axiom, % 1.58/1.62 ! [V_z,V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__antisym,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.58/1.62 => V_x = V_y ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I4_J,axiom, % 1.58/1.62 ! [V_c,V_a,V_b,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.58/1.62 => ( V_b = V_c % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_ord__le__eq__trans,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Oord(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.62 => ( V_b = V_c % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I3_J,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( V_a = V_b % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_ord__eq__le__trans,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Oord(T_a) % 1.58/1.62 => ( V_a = V_b % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__antisym__conv,axiom, % 1.58/1.62 ! [V_x_2,V_y_2,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.62 <=> V_x_2 = V_y_2 ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_le__funD,axiom, % 1.58/1.62 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.58/1.62 ( class_Orderings_Oord(T_b) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__eq__refl,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( V_x = V_y % 1.58/1.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__eq__iff,axiom, % 1.58/1.62 ! [V_y_2,V_x_2,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( V_x_2 = V_y_2 % 1.58/1.62 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__linear,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.62 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_le__fun__def,axiom, % 1.58/1.62 ! [V_g_2,V_f_2,T_a,T_b] : % 1.58/1.62 ( class_Orderings_Oord(T_b) % 1.58/1.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.58/1.62 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__irrefl,axiom, % 1.58/1.62 ! [V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__neq__iff,axiom, % 1.58/1.62 ! [V_y_2,V_x_2,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( V_x_2 != V_y_2 % 1.58/1.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_not__less__iff__gr__or__eq,axiom, % 1.58/1.62 ! [V_y_2,V_x_2,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.58/1.62 | V_x_2 = V_y_2 ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__less__linear,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 | V_x = V_y % 1.58/1.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__antisym__conv3,axiom, % 1.58/1.62 ! [V_x_2,V_y_2,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.58/1.62 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.62 <=> V_x_2 = V_y_2 ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__neqE,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( V_x != V_y % 1.58/1.62 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__neqE__linordered__idom,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Rings_Olinordered__idom(T_a) % 1.58/1.62 => ( V_x != V_y % 1.58/1.62 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_less__imp__neq,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => V_x != V_y ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__not__sym,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__imp__not__less,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__imp__not__eq,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => V_x != V_y ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__imp__not__eq2,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => V_y != V_x ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__asym_H,axiom, % 1.58/1.62 ! [V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.58/1.62 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I9_J,axiom, % 1.58/1.62 ! [V_a,V_b,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.58/1.62 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_ord__eq__less__trans,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Oord(T_a) % 1.58/1.62 => ( V_a = V_b % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I1_J,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( V_a = V_b % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_ord__less__eq__trans,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Orderings_Oord(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.58/1.62 => ( V_b = V_c % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I2_J,axiom, % 1.58/1.62 ! [V_c,V_a,V_b,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.58/1.62 => ( V_b = V_c % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__trans,axiom, % 1.58/1.62 ! [V_z,V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_xt1_I10_J,axiom, % 1.58/1.62 ! [V_z,V_x,V_y,T_a] : % 1.58/1.62 ( class_Orderings_Oorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_order__less__asym,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Opreorder(T_a) % 1.58/1.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_linorder__cases,axiom, % 1.58/1.62 ! [V_y,V_x,T_a] : % 1.58/1.62 ( class_Orderings_Olinorder(T_a) % 1.58/1.62 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.62 => ( V_x != V_y % 1.58/1.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_add__right__imp__eq,axiom, % 1.58/1.62 ! [V_c,V_a,V_b,T_a] : % 1.58/1.62 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.58/1.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 1.58/1.62 => V_b = V_c ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_add__imp__eq,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 1.58/1.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 1.58/1.62 => V_b = V_c ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_add__left__imp__eq,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.58/1.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 1.58/1.62 => V_b = V_c ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_add__right__cancel,axiom, % 1.58/1.62 ! [V_ca_2,V_aa_2,V_ba_2,T_a] : % 1.58/1.62 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.58/1.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2) % 1.58/1.62 <=> V_ba_2 = V_ca_2 ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_add__left__cancel,axiom, % 1.58/1.62 ! [V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.62 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.58/1.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2) % 1.58/1.62 <=> V_ba_2 = V_ca_2 ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 1.58/1.62 ! [V_c,V_b,V_a,T_a] : % 1.58/1.62 ( class_Groups_Oab__semigroup__add(T_a) % 1.58/1.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_one__reorient,axiom, % 1.58/1.62 ! [V_x_2,T_a] : % 1.58/1.62 ( class_Groups_Oone(T_a) % 1.58/1.62 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 1.58/1.62 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 1.58/1.62 % 1.58/1.62 fof(fact_const__Lin__Prof,axiom, % 1.58/1.62 ! [V_L_2] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),V_L_2)),c_Arrow__Order__Mirabelle_OProf)) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_in__above,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.58/1.63 ( V_aa_2 != V_ba_2 % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_aa_2),V_ba_2))) % 1.58/1.63 <=> ( V_x_2 != V_y_2 % 1.58/1.63 & ( V_x_2 = V_ba_2 % 1.58/1.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2)) ) % 1.58/1.63 & ( V_x_2 != V_ba_2 % 1.58/1.63 => ( ( V_y_2 = V_ba_2 % 1.58/1.63 => ( V_x_2 = V_aa_2 % 1.58/1.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2)) ) ) % 1.58/1.63 & ( V_y_2 != V_ba_2 % 1.58/1.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_linorder__not__less,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.63 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_linorder__not__le,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_linorder__le__less__linear,axiom, % 1.58/1.63 ! [V_y,V_x,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.63 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__less__le,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.63 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.63 & V_x_2 != V_y_2 ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_less__le__not__le,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Opreorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.63 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.63 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__le__less,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.63 | V_x_2 = V_y_2 ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_leI,axiom, % 1.58/1.63 ! [V_y,V_x,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_not__leE,axiom, % 1.58/1.63 ! [V_x,V_y,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_linorder__antisym__conv1,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.63 <=> V_x_2 = V_y_2 ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__neq__le__trans,axiom, % 1.58/1.63 ! [V_b,V_a,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( V_a != V_b % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_xt1_I12_J,axiom, % 1.58/1.63 ! [V_b,V_a,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( V_a != V_b % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_leD,axiom, % 1.58/1.63 ! [V_x,V_y,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.58/1.63 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__less__imp__le,axiom, % 1.58/1.63 ! [V_y,V_x,T_a] : % 1.58/1.63 ( class_Orderings_Opreorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_linorder__antisym__conv2,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,T_a] : % 1.58/1.63 ( class_Orderings_Olinorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.58/1.63 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.58/1.63 <=> V_x_2 = V_y_2 ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__le__imp__less__or__eq,axiom, % 1.58/1.63 ! [V_y,V_x,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.63 | V_x = V_y ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__le__neq__trans,axiom, % 1.58/1.63 ! [V_b,V_a,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.63 => ( V_a != V_b % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_xt1_I11_J,axiom, % 1.58/1.63 ! [V_a,V_b,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.58/1.63 => ( V_a != V_b % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__less__le__trans,axiom, % 1.58/1.63 ! [V_z,V_y,V_x,T_a] : % 1.58/1.63 ( class_Orderings_Opreorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_xt1_I7_J,axiom, % 1.58/1.63 ! [V_z,V_x,V_y,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_order__le__less__trans,axiom, % 1.58/1.63 ! [V_z,V_y,V_x,T_a] : % 1.58/1.63 ( class_Orderings_Opreorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_xt1_I8_J,axiom, % 1.58/1.63 ! [V_z,V_x,V_y,T_a] : % 1.58/1.63 ( class_Orderings_Oorder(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__le__imp__le__left,axiom, % 1.58/1.63 ! [V_b,V_a,V_c,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__le__imp__le__right,axiom, % 1.58/1.63 ! [V_b,V_c,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__mono,axiom, % 1.58/1.63 ! [V_d,V_c,V_b,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__left__mono,axiom, % 1.58/1.63 ! [V_c,V_b,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__right__mono,axiom, % 1.58/1.63 ! [V_c,V_b,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__le__cancel__left,axiom, % 1.58/1.63 ! [V_ba_2,V_aa_2,V_ca_2,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2))) % 1.58/1.63 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__le__cancel__right,axiom, % 1.58/1.63 ! [V_ba_2,V_ca_2,V_aa_2,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2))) % 1.58/1.63 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__less__cancel__right,axiom, % 1.58/1.63 ! [V_ba_2,V_ca_2,V_aa_2,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2))) % 1.58/1.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__less__cancel__left,axiom, % 1.58/1.63 ! [V_ba_2,V_aa_2,V_ca_2,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2))) % 1.58/1.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__strict__right__mono,axiom, % 1.58/1.63 ! [V_c,V_b,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__strict__left__mono,axiom, % 1.58/1.63 ! [V_c,V_b,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__strict__mono,axiom, % 1.58/1.63 ! [V_d,V_c,V_b,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__less__imp__less__right,axiom, % 1.58/1.63 ! [V_b,V_c,V_a,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_add__less__imp__less__left,axiom, % 1.58/1.63 ! [V_b,V_a,V_c,T_a] : % 1.58/1.63 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_top__greatest,axiom, % 1.58/1.63 ! [V_x,T_a] : % 1.58/1.63 ( class_Orderings_Otop(T_a) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_top__apply,axiom, % 1.58/1.63 ! [V_x_2,T_b,T_a] : % 1.58/1.63 ( class_Orderings_Otop(T_a) % 1.58/1.63 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom, % 1.58/1.63 ~ ! [B_Lab] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),B_Lab)) % 1.58/1.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lab),c_Arrow__Order__Mirabelle_OLin)) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom, % 1.58/1.63 ~ ! [B_Lba] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),B_Lba)) % 1.58/1.63 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lba),c_Arrow__Order__Mirabelle_OLin)) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_in__below,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.58/1.63 ( V_aa_2 != V_ba_2 % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2))) % 1.58/1.63 <=> ( V_x_2 != V_y_2 % 1.58/1.63 & ( V_y_2 = V_aa_2 % 1.58/1.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2)) ) % 1.58/1.63 & ( V_y_2 != V_aa_2 % 1.58/1.63 => ( ( V_x_2 = V_aa_2 % 1.58/1.63 => ( V_y_2 = V_ba_2 % 1.58/1.63 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2)) ) ) % 1.58/1.63 & ( V_x_2 != V_aa_2 % 1.58/1.63 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inv__f__eq,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.63 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.58/1.63 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inv__f__f,axiom, % 1.58/1.63 ! [V_x_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.63 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inv__into__f__eq,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.63 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.58/1.63 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inv__into__f__f,axiom, % 1.58/1.63 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.63 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__fun,axiom, % 1.58/1.63 ! [T_c,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.63 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a,c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_below__Lin,axiom, % 1.58/1.63 ! [V_L_2,V_y_2,V_x_2] : % 1.58/1.63 ( V_x_2 != V_y_2 % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_equalityI,axiom, % 1.58/1.63 ! [V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) % 1.58/1.63 => V_A_2 = V_B_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_subset__refl,axiom, % 1.58/1.63 ! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_A_2)) ). % 1.58/1.63 % 1.58/1.63 fof(fact_psubset__eq,axiom, % 1.58/1.63 ! [V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.63 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 & V_A_2 != V_B_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_less__fun__def,axiom, % 1.58/1.63 ! [V_g_2,V_f_2,T_a,T_b] : % 1.58/1.63 ( class_Orderings_Oord(T_b) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 1.58/1.63 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.58/1.63 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2)) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_set__eq__subset,axiom, % 1.58/1.63 ! [T_a,V_B_2,V_A_2] : % 1.58/1.63 ( V_A_2 = V_B_2 % 1.58/1.63 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_subset__iff__psubset__eq,axiom, % 1.58/1.63 ! [V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.63 | V_A_2 = V_B_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_rev__predicate1D,axiom, % 1.58/1.63 ! [V_Q_2,T_a,V_x_2,V_Pa_2] : % 1.58/1.63 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) % 1.58/1.63 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_equalityD1,axiom, % 1.58/1.63 ! [T_a,V_B_2,V_A_2] : % 1.58/1.63 ( V_A_2 = V_B_2 % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_equalityD2,axiom, % 1.58/1.63 ! [T_a,V_B_2,V_A_2] : % 1.58/1.63 ( V_A_2 = V_B_2 % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_psubset__imp__subset,axiom, % 1.58/1.63 ! [V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_predicate1D,axiom, % 1.58/1.63 ! [V_x_2,V_Q_2,V_Pa_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) % 1.58/1.63 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.58/1.63 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_psubset__trans,axiom, % 1.58/1.63 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_psubset__subset__trans,axiom, % 1.58/1.63 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_subset__psubset__trans,axiom, % 1.58/1.63 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.58/1.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_subset__trans,axiom, % 1.58/1.63 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.58/1.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.58/1.63 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_predicate2D,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_b,T_a] : % 1.58/1.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 1.58/1.63 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_equalityE,axiom, % 1.58/1.63 ! [T_a,V_B_2,V_A_2] : % 1.58/1.63 ( V_A_2 = V_B_2 % 1.58/1.63 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_rev__predicate2D,axiom, % 1.58/1.63 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 1.58/1.63 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__on__def,axiom, % 1.58/1.63 ! [V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.63 <=> ! [B_x] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.58/1.63 => ! [B_xa] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 1.58/1.63 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 1.58/1.63 => B_x = B_xa ) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_subset__inj__on,axiom, % 1.58/1.63 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.58/1.63 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.63 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__on__id2,axiom, % 1.58/1.63 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__onD,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.63 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.58/1.63 => V_x_2 = V_y_2 ) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__on__iff,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.58/1.63 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.58/1.63 <=> V_x_2 = V_y_2 ) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__on__contraD,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.63 => ( V_x_2 != V_y_2 % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.58/1.63 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_inj__eq,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.63 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.58/1.63 <=> V_x_2 = V_y_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_injD,axiom, % 1.58/1.63 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.63 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.58/1.63 => V_x_2 = V_y_2 ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_PiE,axiom, % 1.58/1.63 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) % 1.58/1.63 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) % 1.58/1.63 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 1.58/1.63 % 1.58/1.63 fof(fact_funcset__mem,axiom, % 1.58/1.63 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.63 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 1.58/1.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Pi__mem,axiom, % 1.58/1.64 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Pi__UNIV,axiom, % 1.58/1.64 ! [V_A_2,T_b,T_a] : c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_funcset__id,axiom, % 1.58/1.64 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_dictatorI,axiom, % 1.58/1.64 ! [V_i_2,V_Fa_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) % 1.58/1.64 => ( ! [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) % 1.58/1.64 => ! [B_a,B_b] : % 1.58/1.64 ( B_a != B_b % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) ) % 1.58/1.64 => c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Prof__def,axiom, % 1.58/1.64 c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_dictator__def,axiom, % 1.58/1.64 ! [V_i_2,V_Fa_2] : % 1.58/1.64 ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) % 1.58/1.64 <=> ! [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) % 1.58/1.64 => hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Pi__anti__mono,axiom, % 1.58/1.64 ! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__leE,axiom, % 1.58/1.64 ! [V_n,V_k,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 1.58/1.64 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__leD1,axiom, % 1.58/1.64 ! [V_n,V_k,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__leD2,axiom, % 1.58/1.64 ! [V_n,V_k,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__le__mono,axiom, % 1.58/1.64 ! [V_l,V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__le__mono1,axiom, % 1.58/1.64 ! [V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__less__cases,axiom, % 1.58/1.64 ! [V_Pa_2,V_na_2,V_m_2] : % 1.58/1.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.58/1.64 => ( ( V_m_2 = V_na_2 % 1.58/1.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.58/1.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.58/1.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__not__refl3,axiom, % 1.58/1.64 ! [V_t,V_s] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 1.58/1.64 => V_s != V_t ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__not__refl2,axiom, % 1.58/1.64 ! [V_m,V_n] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.58/1.64 => V_m != V_n ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__irrefl__nat,axiom, % 1.58/1.64 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_linorder__neqE__nat,axiom, % 1.58/1.64 ! [V_y,V_x] : % 1.58/1.64 ( V_x != V_y % 1.58/1.64 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__neq__iff,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( V_m_2 != V_na_2 % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__not__refl,axiom, % 1.58/1.64 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__commute,axiom, % 1.58/1.64 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__left__commute,axiom, % 1.58/1.64 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__assoc,axiom, % 1.58/1.64 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__left__cancel,axiom, % 1.58/1.64 ! [V_na_2,V_m_2,V_k_2] : % 1.58/1.64 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_na_2) % 1.58/1.64 <=> V_m_2 = V_na_2 ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__right__cancel,axiom, % 1.58/1.64 ! [V_na_2,V_k_2,V_m_2] : % 1.58/1.64 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2) % 1.58/1.64 <=> V_m_2 = V_na_2 ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__refl,axiom, % 1.58/1.64 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__le__linear,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_eq__imp__le,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( V_m = V_n % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__trans,axiom, % 1.58/1.64 ! [V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__antisym,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 1.58/1.64 => V_m = V_n ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_inj__on__add__nat,axiom, % 1.58/1.64 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__lessD1,axiom, % 1.58/1.64 ! [V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__add__eq__less,axiom, % 1.58/1.64 ! [V_n,V_m,V_l,V_k] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.58/1.64 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__less__mono,axiom, % 1.58/1.64 ! [V_l,V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__less__mono1,axiom, % 1.58/1.64 ! [V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_trans__less__add2,axiom, % 1.58/1.64 ! [V_m,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_trans__less__add1,axiom, % 1.58/1.64 ! [V_m,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__left__cancel__less,axiom, % 1.58/1.64 ! [V_na_2,V_m_2,V_k_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_na_2))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__add__less2,axiom, % 1.58/1.64 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__add__less1,axiom, % 1.58/1.64 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__or__eq__imp__le,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 | V_m = V_n ) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__neq__implies__less,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 => ( V_m != V_n % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__imp__le__nat,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__eq__less__or__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 | V_m_2 = V_na_2 ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__less__le,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.58/1.64 & V_m_2 != V_na_2 ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__add2,axiom, % 1.58/1.64 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__add1,axiom, % 1.58/1.64 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__iff__add,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.58/1.64 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__add__left__cancel__le,axiom, % 1.58/1.64 ! [V_na_2,V_m_2,V_k_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_na_2))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_trans__le__add1,axiom, % 1.58/1.64 ! [V_m,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_trans__le__add2,axiom, % 1.58/1.64 ! [V_m,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_in__lex__prod,axiom, % 1.58/1.64 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2)) % 1.58/1.64 | ( V_aa_2 = V_a_H_2 % 1.58/1.64 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_IIA__def,axiom, % 1.58/1.64 ! [V_Fa_2] : % 1.58/1.64 ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) % 1.58/1.64 <=> ! [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) % 1.58/1.64 => ! [B_xa] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf)) % 1.58/1.64 => ! [B_a,B_b] : % 1.58/1.64 ( ! [B_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) ) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) ) ) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_unanimity__def,axiom, % 1.58/1.64 ! [V_Fa_2] : % 1.58/1.64 ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) % 1.58/1.64 <=> ! [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf)) % 1.58/1.64 => ! [B_a,B_b] : % 1.58/1.64 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_iso__tuple__UNIV__I,axiom, % 1.58/1.64 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__inj,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 1.58/1.64 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__indi,axiom, % 1.58/1.64 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__bij,axiom, % 1.58/1.64 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 1.58/1.64 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_g_2),c_FuncSet_OPi(T_b,T_a,V_B_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_A_2)))) % 1.58/1.64 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__psubset,axiom, % 1.58/1.64 ! [V_A_2,V_B_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_psubset__card__mono,axiom, % 1.58/1.64 ! [V_A_2,V_B_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__mono,axiom, % 1.58/1.64 ! [V_A_2,V_B_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__seteq,axiom, % 1.58/1.64 ! [V_A_2,V_B_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2)),c_Finite__Set_Ocard(T_a,V_A_2))) % 1.58/1.64 => V_A_2 = V_B_2 ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( class_Finite__Set_Ofinite(T_a) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__code,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( class_Finite__Set_Ofinite(T_a) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__UNIV__unit,axiom, % 1.58/1.64 c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 1.58/1.64 % 1.58/1.64 fof(fact_rev__finite__subset,axiom, % 1.58/1.64 ! [V_A_2,V_B_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__subset,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__option__UNIV,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))) % 1.58/1.64 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__Plus__UNIV__iff,axiom, % 1.58/1.64 ! [T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))) % 1.58/1.64 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__Prod__UNIV,axiom, % 1.58/1.64 ! [T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 1.58/1.64 => c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__UNIV,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Finite__Set_Ofinite(T_a) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__fun__UNIVD2,axiom, % 1.58/1.64 ! [T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) % 1.58/1.64 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_in__measure,axiom, % 1.58/1.64 ! [V_f_2,V_y_2,V_x_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omeasure(T_a,V_f_2))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_mlex__leq,axiom, % 1.58/1.64 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_mlex__less,axiom, % 1.58/1.64 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_in__finite__psubset,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.64 & c_Finite__Set_Ofinite(T_a,V_B_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Pi__mono,axiom, % 1.58/1.64 ! [V_C_2,V_B_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( ! [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),hAPP(V_B_2,B_x)),hAPP(V_C_2,B_x))) ) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_C_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__Plus,axiom, % 1.58/1.64 ! [V_B_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.64 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card_Oinsert,axiom, % 1.58/1.64 ! [V_x_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Pi__I,axiom, % 1.58/1.64 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( ! [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) ) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insertCI,axiom, % 1.58/1.64 ! [V_ba_2,V_B_2,V_aa_2,T_a] : % 1.58/1.64 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) % 1.58/1.64 => V_aa_2 = V_ba_2 ) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insertE,axiom, % 1.58/1.64 ! [V_A_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) % 1.58/1.64 => ( V_aa_2 != V_ba_2 % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite_OinsertI,axiom, % 1.58/1.64 ! [V_aa_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__insert,axiom, % 1.58/1.64 ! [V_A_2,V_aa_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) % 1.58/1.64 <=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__absorb,axiom, % 1.58/1.64 ! [V_A_2,V_aa_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) % 1.58/1.64 => c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insertI2,axiom, % 1.58/1.64 ! [V_ba_2,V_B_2,V_aa_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__ident,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.58/1.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 1.58/1.64 => ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2) % 1.58/1.64 <=> V_A_2 = V_B_2 ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__iff,axiom, % 1.58/1.64 ! [V_A_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) % 1.58/1.64 <=> ( V_aa_2 = V_ba_2 % 1.58/1.64 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insertI1,axiom, % 1.58/1.64 ! [V_B_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__code,axiom, % 1.58/1.64 ! [V_x_2,V_A_2,V_y_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) % 1.58/1.64 <=> ( V_y_2 = V_x_2 % 1.58/1.64 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__commute,axiom, % 1.58/1.64 ! [V_A_2,V_y_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__absorb2,axiom, % 1.58/1.64 ! [V_A_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2) ). % 1.58/1.64 % 1.58/1.64 fof(fact_subset__insertI,axiom, % 1.58/1.64 ! [V_aa_2,V_B_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_subset__insertI2,axiom, % 1.58/1.64 ! [V_ba_2,V_B_2,V_A_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__mono,axiom, % 1.58/1.64 ! [V_aa_2,V_D_2,V_C_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_D_2)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2)),c_Set_Oinsert(T_a,V_aa_2,V_D_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_insert__subset,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2)),V_B_2)) % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 1.58/1.64 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_subset__insert,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.58/1.64 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_x_2,V_B_2))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__insert__le,axiom, % 1.58/1.64 ! [V_x_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__PlusD_I2_J,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.58/1.64 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__PlusD_I1_J,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__Plus,axiom, % 1.58/1.64 ! [V_B_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.64 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__Plus__iff,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.58/1.64 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_UNIV__Plus__UNIV,axiom, % 1.58/1.64 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__Plus__conv__if,axiom, % 1.58/1.64 ! [V_B_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.58/1.64 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2)) ) % 1.58/1.64 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.58/1.64 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_folding__image__simple_Oinsert,axiom, % 1.58/1.64 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.58/1.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.58/1.64 => hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__zeroE,axiom, % 1.58/1.64 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le0,axiom, % 1.58/1.64 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__0__left,axiom, % 1.58/1.64 ! [V_a,T_a] : % 1.58/1.64 ( class_Groups_Omonoid__add(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__0,axiom, % 1.58/1.64 ! [V_a,T_a] : % 1.58/1.64 ( class_Groups_Ocomm__monoid__add(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_double__zero__sym,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.58/1.64 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) % 1.58/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__0__right,axiom, % 1.58/1.64 ! [V_a,T_a] : % 1.58/1.64 ( class_Groups_Omonoid__add(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add_Ocomm__neutral,axiom, % 1.58/1.64 ! [V_a,T_a] : % 1.58/1.64 ( class_Groups_Ocomm__monoid__add(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_one__neq__zero,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Ozero__neq__one(T_a) % 1.58/1.64 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__neq__one,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Ozero__neq__one(T_a) % 1.58/1.64 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__reorient,axiom, % 1.58/1.64 ! [V_x_2,T_a] : % 1.58/1.64 ( class_Groups_Ozero(T_a) % 1.58/1.64 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 1.58/1.64 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__0__eq,axiom, % 1.58/1.64 ! [V_na_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.58/1.64 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 1.58/1.64 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__eq__self__zero,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 1.58/1.64 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__is__0,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Nat_Oadd__0__right,axiom, % 1.58/1.64 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 1.58/1.64 % 1.58/1.64 fof(fact_plus__nat_Oadd__0,axiom, % 1.58/1.64 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 1.58/1.64 % 1.58/1.64 fof(fact_gr0I,axiom, % 1.58/1.64 ! [V_n] : % 1.58/1.64 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_gr__implies__not0,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__nat__zero__code,axiom, % 1.58/1.64 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_neq0__conv,axiom, % 1.58/1.64 ! [V_na_2] : % 1.58/1.64 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__less0,axiom, % 1.58/1.64 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__nonpos__nonpos,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__increasing2,axiom, % 1.58/1.64 ! [V_a,V_b,V_c,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__increasing,axiom, % 1.58/1.64 ! [V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__nonneg__eq__0__iff,axiom, % 1.58/1.64 ! [V_y_2,V_x_2,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 1.58/1.64 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.58/1.64 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 1.58/1.64 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__nonneg__nonneg,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__neg__neg,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_pos__add__strict,axiom, % 1.58/1.64 ! [V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__pos__pos,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__le__one,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__one__le__zero,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.64 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__less__one,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__one__less__zero,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.64 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__gr__0,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2))) % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 1.58/1.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__infinite,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__nonpos__neg,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__neg__nonpos,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__strict__increasing2,axiom, % 1.58/1.64 ! [V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__strict__increasing,axiom, % 1.58/1.64 ! [V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__nonneg__pos,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__pos__nonneg,axiom, % 1.58/1.64 ! [V_b,V_a,T_a] : % 1.58/1.64 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__less__two,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Olinordered__semidom(T_a) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__ge__0__finite,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2))) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__UNIV__card__ge__0,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_even__less__0__iff,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Rings_Olinordered__idom(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__fun__UNIVD1,axiom, % 1.58/1.64 ! [T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) % 1.58/1.64 => ( c_Finite__Set_Ocard(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.58/1.64 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 1.58/1.64 ! [V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_lessI,axiom, % 1.58/1.64 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__mono,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_zero__less__Suc,axiom, % 1.58/1.64 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Zero__not__Suc,axiom, % 1.58/1.64 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Osimps_I2_J,axiom, % 1.58/1.64 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__not__Zero,axiom, % 1.58/1.64 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Osimps_I3_J,axiom, % 1.58/1.64 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Zero__neq__Suc,axiom, % 1.58/1.64 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__neq__Zero,axiom, % 1.58/1.64 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__Suc__right,axiom, % 1.58/1.64 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__Suc,axiom, % 1.58/1.64 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__Suc__shift,axiom, % 1.58/1.64 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__n__not__le__n,axiom, % 1.58/1.64 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__less__eq__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__Suc__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.58/1.64 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.58/1.64 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__le__mono,axiom, % 1.58/1.64 ! [V_m_2,V_na_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),V_m_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__SucI,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__SucE,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) % 1.58/1.64 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__leD,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__inject,axiom, % 1.58/1.64 ! [V_y,V_x] : % 1.58/1.64 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 1.58/1.64 => V_x = V_y ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Oinject,axiom, % 1.58/1.64 ! [V_nat_H_2,V_nat_2] : % 1.58/1.64 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 1.58/1.64 <=> V_nat_2 = V_nat_H_2 ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__n__not__n,axiom, % 1.58/1.64 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 1.58/1.64 % 1.58/1.64 fof(fact_n__not__Suc__n,axiom, % 1.58/1.64 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__less__SucD,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__lessD,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__SucE,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 1.58/1.64 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => V_m = V_n ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__trans__Suc,axiom, % 1.58/1.64 ! [V_k,V_j,V_i] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__lessI,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__SucI,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__antisym,axiom, % 1.58/1.64 ! [V_m,V_n] : % 1.58/1.64 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 1.58/1.64 => V_m = V_n ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__less__less__Suc__eq,axiom, % 1.58/1.64 ! [V_m_2,V_na_2] : % 1.58/1.64 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.58/1.64 <=> V_na_2 = V_m_2 ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__less__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__Suc__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.58/1.64 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 | V_m_2 = V_na_2 ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_not__less__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_inj__Suc,axiom, % 1.58/1.64 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 1.58/1.64 % 1.58/1.64 fof(fact_gr0__conv__Suc,axiom, % 1.58/1.64 ! [V_na_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 1.58/1.64 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__Suc0,axiom, % 1.58/1.64 ! [V_na_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 1.58/1.64 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__Suc__eq__0__disj,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.58/1.64 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 | ? [B_j] : % 1.58/1.64 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 1.58/1.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__is__1,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.58/1.64 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.58/1.64 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.58/1.64 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_one__is__add,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) % 1.58/1.64 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.58/1.64 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.58/1.64 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.58/1.64 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__add__Suc1,axiom, % 1.58/1.64 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__add__Suc2,axiom, % 1.58/1.64 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__iff__Suc__add,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.58/1.64 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__eq__Suc__le,axiom, % 1.58/1.64 ! [V_m_2,V_na_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__Suc__eq__le,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__le__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__imp__less__Suc,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__leI,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_le__less__Suc__eq,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.58/1.64 <=> V_na_2 = V_m_2 ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__le__lessD,axiom, % 1.58/1.64 ! [V_n,V_m] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_One__nat__def,axiom, % 1.58/1.64 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__eq__Suc__le__raw,axiom, % 1.58/1.64 ! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 1.58/1.64 ! [V_c,V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 1.58/1.64 ! [V_d,V_c,V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 1.58/1.64 ! [V_d,V_c,V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 1.58/1.64 ! [V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 1.58/1.64 ! [V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 1.58/1.64 ! [V_d,V_c,V_b,V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__insert__disjoint,axiom, % 1.58/1.64 ! [V_x_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__insert__if,axiom, % 1.58/1.64 ! [V_x_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) % 1.58/1.64 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_double__eq__0__iff,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.58/1.64 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.58/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_add__0__iff,axiom, % 1.58/1.64 ! [V_aa_2,V_ba_2,T_a] : % 1.58/1.64 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 1.58/1.64 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) % 1.58/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 1.58/1.64 ! [V_a,T_a] : % 1.58/1.64 ( class_Rings_Ocomm__semiring__1(T_a) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__eq__plus1,axiom, % 1.58/1.64 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Suc__eq__plus1__left,axiom, % 1.58/1.64 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Osize_I2_J,axiom, % 1.58/1.64 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Osize_I1_J,axiom, % 1.58/1.64 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Osize_I4_J,axiom, % 1.58/1.64 ! [V_nat] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Ints__odd__less__0,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Rings_Olinordered__idom(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_aa_2)),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__size,axiom, % 1.58/1.64 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ). % 1.58/1.64 % 1.58/1.64 fof(fact_Ints__0,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Oring__1(T_a) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Ints__add,axiom, % 1.58/1.64 ! [V_ba_2,V_aa_2,T_a] : % 1.58/1.64 ( class_Rings_Oring__1(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Int_Oring__1__class_OInts(T_a))) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat_Osize_I3_J,axiom, % 1.58/1.64 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Ints__1,axiom, % 1.58/1.64 ! [T_a] : % 1.58/1.64 ( class_Rings_Oring__1(T_a) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Ints__double__eq__0__iff,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Int_Oring__char__0(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.58/1.64 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.58/1.64 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_Ints__odd__nonzero,axiom, % 1.58/1.64 ! [V_aa_2,T_a] : % 1.58/1.64 ( class_Int_Oring__char__0(T_a) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.58/1.64 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_aa_2)),V_aa_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_ex__least__nat__less,axiom, % 1.58/1.64 ! [V_na_2,V_Pa_2] : % 1.58/1.64 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.58/1.64 => ( hBOOL(hAPP(V_Pa_2,V_na_2)) % 1.58/1.64 => ? [B_k] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2)) % 1.58/1.64 & ! [B_i] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) % 1.58/1.64 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 1.58/1.64 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__def,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_A_2) ) % 1.58/1.64 & ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 1.58/1.64 ! [V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.58/1.64 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.58/1.64 => hAPP(V_Fa_2,V_A_2) = c_Finite__Set_Ofold__image(T_a,T_b,V_f_2,V_g_2,V_z_2,V_A_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card_Oeq__fold__g,axiom, % 1.58/1.64 ! [V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_A_2) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_surjh,axiom, % 1.58/1.64 c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 1.58/1.64 ! [V_na_2,V_m_2] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 1.58/1.64 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_image__eqI,axiom, % 1.58/1.64 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_ba_2] : % 1.58/1.64 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__imageI,axiom, % 1.58/1.64 ! [V_ha_2,T_b,V_Fa_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_Fa_2) % 1.58/1.64 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_inj__image__mem__iff,axiom, % 1.58/1.64 ! [V_A_2,V_aa_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_aa_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.58/1.64 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_range__ex1__eq,axiom, % 1.58/1.64 ! [V_ba_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 1.58/1.64 <=> ? [B_x] : % 1.58/1.64 ( V_ba_2 = hAPP(V_f_2,B_x) % 1.58/1.64 & ! [B_y] : % 1.58/1.64 ( V_ba_2 = hAPP(V_f_2,B_y) % 1.58/1.64 => B_y = B_x ) ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_endo__inj__surj,axiom, % 1.58/1.64 ! [V_f_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)),V_A_2)) % 1.58/1.64 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 1.58/1.64 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__surj__inj,axiom, % 1.58/1.64 ! [V_f_2,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2))) % 1.58/1.64 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__UNIV__inj__surj,axiom, % 1.58/1.64 ! [V_f_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__UNIV__surj__inj,axiom, % 1.58/1.64 ! [V_f_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 1.58/1.64 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_inj__image__subset__iff,axiom, % 1.58/1.64 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.64 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) % 1.58/1.64 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_card__image__le,axiom, % 1.58/1.64 ! [V_f_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_a,V_A_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_inj__on__iff__eq__card,axiom, % 1.58/1.64 ! [V_f_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.64 <=> c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_eq__card__imp__inj__on,axiom, % 1.58/1.64 ! [V_f_2,T_b,V_A_2,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.64 => ( c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) % 1.58/1.64 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_finite__range__imageI,axiom, % 1.58/1.64 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 1.58/1.64 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 1.58/1.64 => c_Finite__Set_Ofinite(T_c,c_Set_Oimage(T_b,T_c,hAPP(c_COMBB(T_a,T_c,T_b,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__case__0,axiom, % 1.58/1.64 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 1.58/1.64 % 1.58/1.64 fof(fact_nat__case__Suc,axiom, % 1.58/1.64 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 1.58/1.64 % 1.58/1.64 fof(fact_image__iff,axiom, % 1.58/1.64 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.58/1.64 <=> ? [B_x] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 1.58/1.64 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_imageI,axiom, % 1.58/1.64 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_rev__image__eqI,axiom, % 1.58/1.64 ! [T_b,V_f_2,V_ba_2,V_A_2,V_x_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.64 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.58/1.64 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_range__composition,axiom, % 1.58/1.64 ! [V_g_2,V_f_2,T_c,T_a,T_b] : c_Set_Oimage(T_b,T_a,hAPP(c_COMBB(T_c,T_a,T_b,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Set_Oimage(T_c,T_a,V_f_2,c_Set_Oimage(T_b,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 1.58/1.64 % 1.58/1.64 fof(fact_image__ident,axiom, % 1.58/1.64 ! [V_Y_2,T_a] : c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2 ). % 1.58/1.64 % 1.58/1.64 fof(fact_image__image,axiom, % 1.58/1.64 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_c,T_b,V_g_2,V_A_2)) = c_Set_Oimage(T_c,T_a,hAPP(c_COMBB(T_b,T_a,T_c,V_f_2),V_g_2),V_A_2) ). % 1.58/1.64 % 1.58/1.64 fof(fact_subset__image__iff,axiom, % 1.58/1.64 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.58/1.64 <=> ? [B_AA] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2)) % 1.58/1.64 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_image__mono,axiom, % 1.58/1.64 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 1.58/1.64 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.58/1.64 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) ) ). % 1.58/1.64 % 1.58/1.64 fof(fact_image__insert,axiom, % 1.58/1.64 ! [V_B_2,V_aa_2,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,hAPP(V_f_2,V_aa_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2)) ). % 1.58/1.64 % 1.58/1.64 fof(fact_inj__on__strict__subset,axiom, % 1.58/1.64 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.58/1.64 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.58/1.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.58/1.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_image__surj__f__inv__f,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_a,T_b] : % 1.58/1.65 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 1.58/1.65 => c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_A_2)) = V_A_2 ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_surj__f__inv__f,axiom, % 1.58/1.65 ! [V_y_2,V_f_2,T_a,T_b] : % 1.58/1.65 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 1.58/1.65 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_surj__iff__all,axiom, % 1.58/1.65 ! [V_f_2,T_a,T_b] : % 1.58/1.65 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 1.58/1.65 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_image__inv__into__cancel,axiom, % 1.58/1.65 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 1.58/1.65 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_A_H_2 % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_H_2),V_A_H_2)) % 1.58/1.65 => c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_H_2)) = V_B_H_2 ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inv__into__injective,axiom, % 1.58/1.65 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_b,T_a] : % 1.58/1.65 ( hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.58/1.65 => V_x_2 = V_y_2 ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inv__into__into,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,V_x_2,T_a] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.58/1.65 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_f__inv__into__f,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,V_y_2,T_a] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.58/1.65 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_card__image,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.65 => c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inj__image__eq__iff,axiom, % 1.58/1.65 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.65 => ( c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) = c_Set_Oimage(T_a,T_b,V_f_2,V_B_2) % 1.58/1.65 <=> V_A_2 = V_B_2 ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_finite__imageD,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) % 1.58/1.65 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 1.58/1.65 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_finite__surj,axiom, % 1.58/1.65 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 1.58/1.65 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.58/1.65 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_range__eqI,axiom, % 1.58/1.65 ! [T_b,T_a,V_x_2,V_f_2,V_ba_2] : % 1.58/1.65 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.58/1.65 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_rangeI,axiom, % 1.58/1.65 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 1.58/1.65 % 1.58/1.65 fof(fact_insert__image,axiom, % 1.58/1.65 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.58/1.65 => c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_pigeonhole,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_b,V_A_2))) % 1.58/1.65 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inj__on__inv__into,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.58/1.65 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.58/1.65 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_2) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inv__into__image__cancel,axiom, % 1.58/1.65 ! [V_S_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_S_2),V_A_2)) % 1.58/1.65 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_S_2)) = V_S_2 ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inj__imp__surj__inv,axiom, % 1.58/1.65 ! [V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.65 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_image__inv__f__f,axiom, % 1.58/1.65 ! [V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.65 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = V_A_2 ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inv__image__comp,axiom, % 1.58/1.65 ! [V_X_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.58/1.65 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_X_2)) = V_X_2 ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_surj__imp__inj__inv,axiom, % 1.58/1.65 ! [V_f_2,T_a,T_b] : % 1.58/1.65 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 1.58/1.65 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_funcset__image,axiom, % 1.58/1.65 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 1.58/1.65 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_card__bij__eq,axiom, % 1.58/1.65 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) % 1.58/1.65 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2)),V_A_2)) % 1.58/1.65 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.65 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.65 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_card__inj__on__le,axiom, % 1.58/1.65 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) % 1.58/1.65 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.65 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom, % 1.58/1.65 ~ ! [B_h] : % 1.58/1.65 ( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) % 1.58/1.65 => c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_inj__on__iff__card__le,axiom, % 1.58/1.65 ! [V_B_2,T_b,V_A_2,T_a] : % 1.58/1.65 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.58/1.65 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.58/1.65 => ( ? [B_f] : % 1.58/1.65 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 1.58/1.65 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2)),V_B_2)) ) % 1.58/1.65 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_finite__atLeastLessThan,axiom, % 1.58/1.65 ! [V_u_2,V_l_2] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)) ). % 1.58/1.65 % 1.58/1.65 fof(fact_image__add__atLeastLessThan,axiom, % 1.58/1.65 ! [V_j_2,V_i_2,V_k_2] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 1.58/1.65 % 1.58/1.65 fof(fact_image__Suc__atLeastLessThan,axiom, % 1.58/1.65 ! [V_j_2,V_i_2] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 1.58/1.65 % 1.58/1.65 fof(fact_finite__nat__set__iff__bounded,axiom, % 1.58/1.65 ! [V_N_2] : % 1.58/1.65 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.58/1.65 <=> ? [B_m] : % 1.58/1.65 ! [B_x] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.58/1.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 1.58/1.65 ! [V_N_2] : % 1.58/1.65 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.58/1.65 <=> ? [B_m] : % 1.58/1.65 ! [B_x] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.58/1.65 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x),B_m)) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_atLeastLessThan__eq__iff,axiom, % 1.58/1.65 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.65 ( class_Orderings_Olinorder(T_a) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2)) % 1.58/1.65 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2) % 1.58/1.65 <=> ( V_aa_2 = V_ca_2 % 1.58/1.65 & V_ba_2 = V_da_2 ) ) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 1.58/1.65 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.65 ( class_Orderings_Olinorder(T_a) % 1.58/1.65 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2)) % 1.58/1.65 => V_aa_2 = V_ca_2 ) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 1.58/1.65 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.65 ( class_Orderings_Olinorder(T_a) % 1.58/1.65 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.58/1.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2)) % 1.58/1.65 => V_ba_2 = V_da_2 ) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_subset__card__intvl__is__intvl,axiom, % 1.58/1.65 ! [V_k_2,V_A_2] : % 1.58/1.65 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))))) % 1.58/1.65 => V_A_2 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_atLeastLessThan__subset__iff,axiom, % 1.58/1.65 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.58/1.65 ( class_Orderings_Olinorder(T_a) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2))) % 1.58/1.65 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_aa_2)) % 1.58/1.65 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2),V_aa_2)) % 1.58/1.65 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_da_2)) ) ) ) ) ). % 1.58/1.65 % 1.58/1.65 fof(fact_ex__nat__less__eq,axiom, % 1.58/1.65 ! [V_Pa_2,V_na_2] : % 1.58/1.65 ( ? [B_m] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) % 1.58/1.65 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 1.58/1.65 <=> ? [B_x] : % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2))) % 1.58/1.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 1.58/1.65 % 1.58/1.65 %----Arity declarations (33) % 1.58/1.65 fof(arity_fun__Orderings_Opreorder,axiom, % 1.58/1.65 ! [T_2,T_1] : % 1.58/1.65 ( class_Orderings_Opreorder(T_1) % 1.58/1.65 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_fun__Finite__Set_Ofinite,axiom, % 1.58/1.65 ! [T_1,T_2] : % 1.58/1.65 ( ( class_Finite__Set_Ofinite(T_2) % 1.58/1.65 & class_Finite__Set_Ofinite(T_1) ) % 1.58/1.65 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_fun__Orderings_Oorder,axiom, % 1.58/1.65 ! [T_2,T_1] : % 1.58/1.65 ( class_Orderings_Oorder(T_1) % 1.58/1.65 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_fun__Orderings_Otop,axiom, % 1.58/1.65 ! [T_2,T_1] : % 1.58/1.65 ( class_Orderings_Otop(T_1) % 1.58/1.65 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_fun__Orderings_Oord,axiom, % 1.58/1.65 ! [T_2,T_1] : % 1.58/1.65 ( class_Orderings_Oord(T_1) % 1.58/1.65 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 1.58/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 1.58/1.65 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 1.58/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 1.58/1.65 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 1.58/1.65 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 1.58/1.65 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 1.58/1.65 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 1.58/1.65 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 1.58/1.65 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 1.58/1.65 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 1.58/1.65 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 1.58/1.65 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 1.58/1.65 class_Orderings_Opreorder(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 1.58/1.65 class_Orderings_Olinorder(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 1.58/1.65 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 1.58/1.65 class_Orderings_Oorder(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 1.58/1.65 class_Orderings_Oord(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 1.58/1.65 class_Groups_Ozero(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Nat__Onat__Groups_Oone,axiom, % 1.58/1.65 class_Groups_Oone(tc_Nat_Onat) ). % 1.58/1.65 % 1.58/1.65 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 1.58/1.65 class_Orderings_Opreorder(tc_HOL_Obool) ). % 1.58/1.65 % 1.58/1.65 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 1.58/1.65 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 1.58/1.65 % 1.58/1.65 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 1.58/1.65 class_Orderings_Oorder(tc_HOL_Obool) ). % 1.58/1.65 % 1.58/1.65 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 1.58/1.65 class_Orderings_Otop(tc_HOL_Obool) ). % 1.58/1.65 % 1.58/1.65 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 1.58/1.65 class_Orderings_Oord(tc_HOL_Obool) ). % 1.58/1.65 % 1.58/1.65 fof(arity_sum__Finite__Set_Ofinite,axiom, % 1.58/1.65 ! [T_1,T_2] : % 1.58/1.65 ( ( class_Finite__Set_Ofinite(T_2) % 1.58/1.65 & class_Finite__Set_Ofinite(T_1) ) % 1.58/1.65 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 1.58/1.65 ! [T_1] : % 1.58/1.65 ( class_Finite__Set_Ofinite(T_1) % 1.58/1.65 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_prod__Finite__Set_Ofinite,axiom, % 1.58/1.65 ! [T_1,T_2] : % 1.58/1.65 ( ( class_Finite__Set_Ofinite(T_2) % 1.58/1.65 & class_Finite__Set_Ofinite(T_1) ) % 1.58/1.65 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 1.58/1.65 % 1.58/1.65 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 1.58/1.65 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 1.58/1.65 % 1.58/1.65 %----Helper facts (8) % 1.58/1.65 fof(help_c__COMBI__1,axiom, % 1.58/1.65 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 1.58/1.65 % 1.58/1.65 fof(help_c__COMBK__1,axiom, % 1.58/1.65 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 1.58/1.65 % 1.58/1.65 fof(help_c__COMBB__1,axiom, % 1.58/1.65 ! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ). % 1.58/1.65 % 1.58/1.65 fof(help_c__COMBC__1,axiom, % 1.58/1.65 ! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ). % 1.58/1.65 % 1.58/1.65 fof(help_c__COMBS__1,axiom, % 1.58/1.65 ! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 1.58/1.65 % 1.58/1.65 fof(help_c__fequal__1,axiom, % 1.58/1.65 ! [V_y_2,V_x_2] : % 1.58/1.65 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 1.58/1.65 | V_x_2 = V_y_2 ) ). % 1.58/1.65 % 1.58/1.65 fof(help_c__fequal__2,axiom, % 1.58/1.65 ! [V_y_2,V_x_2] : % 1.58/1.65 ( V_x_2 != V_y_2 % 1.58/1.65 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 1.58/1.65 % 1.58/1.65 fof(help_c__fFalse__1,axiom, % 1.58/1.65 ~ hBOOL(c_fFalse) ). % 1.58/1.65 % 1.58/1.65 %----Conjectures (1) % 1.58/1.65 fof(conj_0,conjecture, % 1.58/1.65 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) % 1.58/1.65 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ) ). % 1.58/1.65 % 1.58/1.65 %------------------------------------------------------------------------------ % 1.58/1.65 %------------------------------------------- % 1.58/1.65 % Proof found % 1.58/1.65 % SZS status Theorem for theBenchmark % 1.58/1.65 % SZS output start Proof % 1.58/1.65 %ClaNum:1092(EqnAxiom:260) % 1.58/1.65 %VarNum:5268(SingletonVarNum:1729) % 1.58/1.65 %MaxLitNum:10 % 1.58/1.65 %MaxfuncDepth:12 % 1.58/1.65 %SharedTerms:304 % 1.58/1.65 %goalClause: 1047 1091 % 1.58/1.65 [261]P1(a1) % 1.58/1.65 [262]P2(a1) % 1.58/1.65 [263]P4(a2) % 1.58/1.65 [264]P5(a2) % 1.58/1.65 [265]P20(a2) % 1.58/1.65 [266]P20(a3) % 1.58/1.65 [267]P21(a2) % 1.58/1.65 [268]P25(a2) % 1.58/1.65 [269]P25(a3) % 1.58/1.65 [270]P26(a2) % 1.58/1.65 [271]P26(a3) % 1.58/1.65 [272]P6(a2) % 1.58/1.65 [273]P7(a2) % 1.58/1.65 [274]P8(a2) % 1.58/1.65 [275]P14(a2) % 1.58/1.65 [276]P18(a2) % 1.58/1.65 [277]P19(a2) % 1.58/1.65 [278]P27(a3) % 1.58/1.65 [279]P9(a3) % 1.58/1.65 [280]P9(a94) % 1.58/1.65 [281]P15(a2) % 1.58/1.65 [282]P16(a2) % 1.58/1.65 [283]P30(a2) % 1.58/1.65 [284]P22(a2) % 1.58/1.65 [285]P23(a2) % 1.58/1.65 [286]P28(a2) % 1.58/1.65 [287]P32(a2) % 1.58/1.65 [371]~E(a104,a102) % 1.58/1.65 [372]~E(a106,a105) % 1.58/1.65 [373]~P33(a40) % 1.58/1.65 [288]E(f21(f4(a2)),f4(a2)) % 1.58/1.65 [290]E(f28(a22,f4(a2)),f5(a2)) % 1.58/1.65 [296]P10(a92,f31(f96(a92,a3))) % 1.58/1.65 [327]P11(a92,a2,a99,f31(f96(a92,a3))) % 1.58/1.65 [328]P11(a92,a2,a45,f31(f96(a92,a3))) % 1.58/1.65 [297]E(f15(a94,f31(f96(a94,a3))),f5(a2)) % 1.58/1.65 [329]P33(f28(f28(f30(a2),a108),f15(a92,f31(f96(a92,a3))))) % 1.58/1.65 [330]P33(f28(f28(f30(a2),a77),f15(a92,f31(f96(a92,a3))))) % 1.58/1.65 [331]P33(f28(f28(f30(a2),a90),f15(a92,f31(f96(a92,a3))))) % 1.58/1.65 [338]E(f32(a2,f4(a2),f15(a92,f31(f96(a92,a3)))),f37(a92,a2,a99,f31(f96(a92,a3)))) % 1.58/1.65 [339]E(f32(a2,f4(a2),f15(a92,f31(f96(a92,a3)))),f37(a92,a2,a45,f31(f96(a92,a3)))) % 1.58/1.65 [343]P33(f28(f28(f35(f96(f98(a93,a93),a3)),a100),a8)) % 1.58/1.65 [344]P33(f28(f28(f35(f96(f98(a93,a93),a3)),a101),a8)) % 1.58/1.65 [345]P33(f28(f28(f35(f96(f98(a93,a93),a3)),a46),a8)) % 1.58/1.65 [346]P33(f28(f28(f35(f96(f98(a93,a93),a3)),a47),a8)) % 1.58/1.65 [349]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a100)) % 1.58/1.65 [350]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a46)) % 1.58/1.65 [351]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101)) % 1.58/1.65 [352]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a47)) % 1.58/1.65 [390]~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.65 [391]~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a100)) % 1.58/1.65 [354]E(f18(a92,f96(f98(a93,a93),a3),f31(f96(a92,a3)),f28(f16(f96(f96(f98(a93,a93),a3),a3),a92),a8)),a9) % 1.58/1.65 [357]P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),a103),a9)) % 1.58/1.65 [363]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,f28(f23(a92,a2,f31(f96(a92,a3)),a99),a108)))) % 1.58/1.65 [364]P33(f28(f28(f35(f96(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3))),a1),f18(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3),a9,f28(f16(f96(f96(f98(a93,a93),a3),a3),f96(a92,f96(f98(a93,a93),a3))),a8)))) % 1.58/1.65 [366]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),f28(f28(f20(a2),a108),f5(a2))))),a100)),a101)))) % 1.58/1.65 [367]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),f28(f28(f20(a2),a77),f5(a2))))),a100)),a101)))) % 1.58/1.65 [368]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),f28(f28(f20(a2),a90),f5(a2))))),a100)),a101)))) % 1.58/1.65 [369]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))))) % 1.58/1.65 [370]P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))),a9)) % 1.58/1.65 [318]P11(a2,a2,a22,x3181) % 1.58/1.65 [289]E(f27(a2,x2891),x2891) % 1.58/1.65 [375]~E(f28(a22,x3751),x3751) % 1.58/1.65 [381]~E(f28(a22,x3811),f4(a2)) % 1.58/1.65 [293]E(f28(f28(f20(a2),x2931),f4(a2)),x2931) % 1.58/1.65 [294]E(f29(a2,f28(a22,x2941)),f28(f30(a2),x2941)) % 1.58/1.65 [298]E(f28(f28(f20(a2),x2981),f5(a2)),f28(a22,x2981)) % 1.58/1.65 [300]P33(f28(f29(a2,x3001),x3001)) % 1.58/1.65 [308]P33(f28(f28(f30(a2),x3081),f28(a22,x3081))) % 1.58/1.65 [309]P33(f28(f28(f30(a2),f4(a2)),f28(a22,x3091))) % 1.58/1.65 [386]~P33(f28(f28(f30(a2),x3861),f4(a2))) % 1.58/1.65 [295]E(f28(f28(f20(a2),f4(a2)),x2951),x2951) % 1.58/1.65 [299]E(f28(f28(f20(a2),f5(a2)),x2991),f28(a22,x2991)) % 1.58/1.65 [302]P33(f28(f29(a2,f4(a2)),x3021)) % 1.58/1.65 [305]E(f28(f28(f20(a2),f21(x3051)),f28(a22,f4(a2))),f21(f28(a22,x3051))) % 1.58/1.65 [310]E(f28(f28(f20(a2),f27(a2,x3101)),f28(a22,f4(a2))),f27(a2,f28(a22,x3101))) % 1.58/1.65 [383]~P33(f28(f28(f30(a2),x3831),x3831)) % 1.58/1.65 [387]~P33(f28(f29(a2,f28(a22,x3871)),x3871)) % 1.58/1.65 [365]P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),x3651))),a100)),a101)),a9)) % 1.58/1.65 [306]P10(a2,f32(a2,x3061,x3062)) % 1.58/1.65 [320]P11(x3201,x3201,f6(x3201),x3202) % 1.58/1.65 [292]E(f28(f6(x2921),x2922),x2922) % 1.58/1.65 [321]E(f37(x3211,x3211,f6(x3211),x3212),x3212) % 1.58/1.65 [337]E(f37(a2,a2,a22,f32(a2,x3371,x3372)),f32(a2,f28(a22,x3371),f28(a22,x3372))) % 1.58/1.65 [303]E(f28(f28(f20(a2),x3031),x3032),f28(f28(f20(a2),x3032),x3031)) % 1.58/1.65 [307]P33(f28(f31(f96(x3071,a3)),x3072)) % 1.58/1.65 [311]E(f28(f28(f20(a2),f28(a22,x3111)),x3112),f28(f28(f20(a2),x3111),f28(a22,x3112))) % 1.58/1.65 [313]P33(f28(f29(f96(x3131,a3),x3132),x3132)) % 1.58/1.65 [316]P33(f28(f28(f35(x3161),x3162),f31(f96(x3161,a3)))) % 1.58/1.65 [325]P33(f28(f29(f96(x3251,a3),x3252),f31(f96(x3251,a3)))) % 1.58/1.65 [336]E(f38(x3361,x3362,f31(f96(x3361,a3)),f31(f96(x3362,a3))),f31(f96(f97(x3361,x3362),a3))) % 1.58/1.65 [348]P11(a2,a2,f28(f28(f7(a2,a2,a2),f20(a2)),x3481),x3482) % 1.58/1.65 [312]E(f28(f28(f20(a2),x3121),f28(a22,x3122)),f28(a22,f28(f28(f20(a2),x3121),x3122))) % 1.58/1.65 [314]E(f28(f28(f20(a2),f28(a22,x3141)),x3142),f28(a22,f28(f28(f20(a2),x3141),x3142))) % 1.58/1.65 [322]P33(f28(f29(a2,x3221),f28(f28(f20(a2),x3222),x3221))) % 1.58/1.65 [323]P33(f28(f29(a2,x3231),f28(f28(f20(a2),x3231),x3232))) % 1.58/1.65 [340]P33(f28(f28(f30(a2),x3401),f28(a22,f28(f28(f20(a2),x3402),x3401)))) % 1.58/1.65 [341]P33(f28(f28(f30(a2),x3411),f28(a22,f28(f28(f20(a2),x3411),x3412)))) % 1.58/1.65 [360]P33(f28(f28(f35(f96(x3601,x3601)),f6(x3601)),f18(x3601,x3601,x3602,f28(f16(f96(x3601,a3),x3601),x3602)))) % 1.58/1.65 [388]~P33(f28(f28(f30(a2),f28(f28(f20(a2),x3881),x3882)),x3882)) % 1.58/1.65 [389]~P33(f28(f28(f30(a2),f28(f28(f20(a2),x3891),x3892)),x3891)) % 1.58/1.65 [317]E(f36(x3171,x3172,f36(x3171,x3172,x3173)),f36(x3171,x3172,x3173)) % 1.58/1.65 [319]E(f26(x3191,x3192,x3193,f4(a2)),x3192) % 1.58/1.65 [332]P33(f28(f28(f35(x3321),x3322),f36(x3321,x3322,x3323))) % 1.58/1.65 [335]P33(f28(f29(f96(x3351,a3),x3352),f36(x3351,x3353,x3352))) % 1.58/1.65 [324]E(f28(f28(f20(a2),x3241),f28(f28(f20(a2),x3242),x3243)),f28(f28(f20(a2),x3242),f28(f28(f20(a2),x3241),x3243))) % 1.58/1.65 [347]E(f18(x3471,x3472,x3473,f28(f16(f96(x3472,a3),x3471),f31(f96(x3472,a3)))),f31(f96(f96(x3471,x3472),a3))) % 1.58/1.65 [355]E(f37(a2,a2,f28(f28(f7(a2,a2,a2),f20(a2)),x3551),f32(a2,x3552,x3553)),f32(a2,f28(f28(f20(a2),x3552),x3551),f28(f28(f20(a2),x3553),x3551))) % 1.58/1.65 [334]E(f28(f28(f20(a2),f28(f28(f20(a2),x3341),x3342)),x3343),f28(f28(f20(a2),x3341),f28(f28(f20(a2),x3342),x3343))) % 1.58/1.65 [326]E(f26(x3261,x3262,x3263,f28(a22,x3264)),f28(x3263,x3264)) % 1.58/1.65 [333]E(f36(x3331,x3332,f36(x3331,x3333,x3334)),f36(x3331,x3333,f36(x3331,x3332,x3334))) % 1.58/1.65 [304]E(f28(f28(f16(x3041,x3042),x3043),x3044),x3043) % 1.58/1.65 [358]P33(f28(f28(f35(x3581),f28(x3582,x3583)),f37(x3584,x3581,x3582,f31(f96(x3584,a3))))) % 1.58/1.65 [353]E(f37(x3531,x3532,x3533,f36(x3531,x3534,x3535)),f36(x3532,f28(x3533,x3534),f37(x3531,x3532,x3533,x3535))) % 1.58/1.65 [361]E(f37(x3611,x3612,f28(f10(x3613,x3612,x3611,x3614),x3615),f31(f96(x3611,a3))),f37(x3613,x3612,x3614,f37(x3611,x3613,x3615,f31(f96(x3611,a3))))) % 1.58/1.65 [362]E(f28(f17(x3621,x3622,x3623,x3624,x3625),x3626),f28(f28(x3624,x3626),f28(x3625,x3626))) % 1.58/1.65 [356]E(f28(f28(f10(x3561,x3562,x3563,x3564),x3565),x3566),f28(x3564,f28(x3565,x3566))) % 1.58/1.65 [359]E(f37(x3591,x3592,x3593,f37(x3594,x3591,x3595,x3596)),f37(x3594,x3592,f28(f10(x3591,x3592,x3594,x3593),x3595),x3596)) % 1.58/1.65 [342]E(f28(f28(f28(f7(x3421,x3422,x3423),x3424),x3425),x3426),f28(f28(x3424,x3426),x3425)) % 1.58/1.65 [1046]~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a1,a103)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))))) % 1.58/1.65 [1048]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a1,a103)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))))) % 1.58/1.65 [1047]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101)))) % 1.58/1.65 [1091]~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101)))) % 1.58/1.65 [392]~P9(x3921)+P9(f95(x3921)) % 1.58/1.65 [394]~P30(x3941)+~E(f5(x3941),f4(x3941)) % 1.58/1.65 [451]~P4(x4511)+P33(f28(f29(x4511,f4(x4511)),f5(x4511))) % 1.58/1.65 [456]E(x4561,f4(a2))+~P33(f28(f29(a2,x4561),f4(a2))) % 1.58/1.65 [465]~P31(x4651)+P33(f28(f28(f35(x4651),f5(x4651)),f25(x4651))) % 1.58/1.65 [466]~P31(x4661)+P33(f28(f28(f35(x4661),f4(x4661)),f25(x4661))) % 1.58/1.65 [467]~P4(x4671)+P33(f28(f28(f30(x4671),f4(x4671)),f5(x4671))) % 1.58/1.65 [506]~P4(x5061)+~P33(f28(f29(x5061,f5(x5061)),f4(x5061))) % 1.58/1.65 [535]~P4(x5351)+~P33(f28(f28(f30(x5351),f5(x5351)),f4(x5351))) % 1.58/1.65 [444]E(x4441,f4(a2))+P33(f28(f28(f30(a2),f4(a2)),x4441)) % 1.58/1.65 [502]E(f28(a22,f57(x5021)),x5021)+~P33(f28(f28(f30(a2),f4(a2)),x5021)) % 1.58/1.65 [514]~P10(x5141,f31(f96(x5141,a3)))+P10(f95(x5141),f31(f96(f95(x5141),a3))) % 1.58/1.65 [521]P10(x5211,f31(f96(x5211,a3)))+~P10(f95(x5211),f31(f96(f95(x5211),a3))) % 1.58/1.65 [542]E(x5421,f4(a2))+~P33(f28(f28(f30(a2),x5421),f28(a22,f4(a2)))) % 1.58/1.65 [649]~P4(x6491)+P33(f28(f28(f30(x6491),f4(x6491)),f28(f28(f20(x6491),f5(x6491)),f5(x6491)))) % 1.58/1.65 [825]P1(x8251)+P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f60(x8251)),a9)) % 1.58/1.65 [826]P1(x8261)+P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f61(x8261)),a9)) % 1.58/1.65 [827]P2(x8271)+P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f59(x8271)),a9)) % 1.58/1.65 [844]P2(x8441)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f58(x8441)),f65(x8441))),f28(x8441,f59(x8441)))) % 1.58/1.65 [670]~P10(x6701,f31(f96(x6701,a3)))+P33(f28(f28(f30(a2),f4(a2)),f15(x6701,f31(f96(x6701,a3))))) % 1.58/1.65 [917]~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9171),a8))+P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f28(f16(f96(f98(a93,a93),a3),a92),x9171)),a9)) % 1.58/1.65 [1043]~P33(f28(f29(a2,x10431),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),x10431))),a100)),a101)))) % 1.58/1.65 [1044]~P33(f28(f29(a2,x10441),a77))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),x10441))),a100)),a101)))) % 1.58/1.65 [1045]~P33(f28(f29(a2,x10451),a90))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),x10451))),a100)),a101)))) % 1.58/1.65 [396]~P9(x3961)+P10(x3961,x3962) % 1.58/1.65 [398]P10(x3981,x3982)+E(f15(x3981,x3982),f4(a2)) % 1.58/1.65 [399]~P20(x3992)+P20(f96(x3991,x3992)) % 1.58/1.65 [400]~P25(x4002)+P25(f96(x4001,x4002)) % 1.58/1.65 [401]~P26(x4012)+P26(f96(x4011,x4012)) % 1.58/1.65 [402]~P27(x4022)+P27(f96(x4021,x4022)) % 1.58/1.65 [404]E(x4041,x4042)+~E(f28(a22,x4041),f28(a22,x4042)) % 1.58/1.65 [409]~P15(x4091)+E(f28(f28(f20(x4091),x4092),f4(x4091)),x4092) % 1.58/1.65 [410]~P16(x4101)+E(f28(f28(f20(x4101),x4102),f4(x4101)),x4102) % 1.58/1.65 [411]~P28(x4111)+E(f28(f28(f20(x4111),x4112),f4(x4111)),x4112) % 1.58/1.65 [420]~E(x4201,x4202)+P33(f28(f28(a39,x4201),x4202)) % 1.58/1.65 [423]~E(x4231,x4232)+P33(f28(f29(a2,x4231),x4232)) % 1.58/1.65 [428]~P20(x4281)+P33(f28(f29(x4281,x4282),x4282)) % 1.58/1.65 [440]~P27(x4401)+P33(f28(f29(x4401,x4402),f31(x4401))) % 1.58/1.65 [450]E(x4501,x4502)+~P33(f28(f28(a39,x4501),x4502)) % 1.58/1.65 [452]E(x4521,x4522)+~E(f28(x4521,f48(x4522,x4521)),f28(x4522,f48(x4522,x4521))) % 1.58/1.65 [457]P3(x4571,x4572)+~E(f28(x4571,f49(x4572,x4571)),f28(f49(x4572,x4571),x4572)) % 1.58/1.65 [459]~E(x4591,x4592)+P33(f28(f28(f30(a2),x4591),f28(a22,x4592))) % 1.58/1.65 [462]~E(x4621,f4(a2))+P33(f28(f28(f30(a2),x4621),f28(a22,x4622))) % 1.58/1.65 [474]P33(f28(f29(a2,x4742),x4741))+P33(f28(f29(a2,x4741),x4742)) % 1.58/1.65 [505]E(f28(f28(f20(a2),x5051),f55(x5052,x5051)),x5052)+~P33(f28(f29(a2,x5051),x5052)) % 1.58/1.65 [539]~P33(f28(f29(a2,x5391),x5392))+P33(f28(f29(a2,x5391),f28(a22,x5392))) % 1.58/1.65 [563]~P33(f28(f29(a2,x5631),x5632))+P33(f28(f28(f30(a2),x5631),f28(a22,x5632))) % 1.58/1.65 [564]P10(x5641,x5642)+~P33(f28(f28(f30(a2),f4(a2)),f15(x5641,x5642))) % 1.58/1.65 [584]P33(f28(f29(a2,x5841),x5842))+~P33(f28(f28(f30(a2),x5841),f28(a22,x5842))) % 1.58/1.65 [609]~P33(f28(f29(a2,x6091),x6092))+P33(f28(f29(a2,f28(a22,x6091)),f28(a22,x6092))) % 1.58/1.65 [648]P33(f28(f29(a2,x6481),x6482))+~P33(f28(f29(a2,f28(a22,x6481)),f28(a22,x6482))) % 1.58/1.65 [987]~P10(x9871,x9872)+E(f19(a2,x9871,f20(a2),f28(f16(a2,x9871),f5(a2)),f4(a2),x9872),f15(x9871,x9872)) % 1.58/1.65 [415]~P15(x4151)+E(f28(f28(f20(x4151),f4(x4151)),x4152),x4152) % 1.58/1.65 [416]~P16(x4161)+E(f28(f28(f20(x4161),f4(x4161)),x4162),x4162) % 1.58/1.65 [417]~P28(x4171)+E(f28(f28(f20(x4171),f4(x4171)),x4172),x4172) % 1.58/1.65 [419]E(x4191,f4(a2))+~E(f28(f28(f20(a2),x4192),x4191),x4192) % 1.58/1.65 [424]E(x4241,f4(a2))+~E(f28(f28(f20(a2),x4242),x4241),f4(a2)) % 1.58/1.65 [425]E(x4251,f4(a2))+~E(f28(f28(f20(a2),x4251),x4252),f4(a2)) % 1.58/1.65 [453]~E(x4531,f28(a22,x4532))+P33(f28(f28(f30(a2),f4(a2)),x4531)) % 1.58/1.65 [473]~E(x4731,x4732)+~P33(f28(f28(f30(a2),x4731),x4732)) % 1.58/1.65 [475]~E(x4751,f4(a2))+~P33(f28(f28(f30(a2),x4752),x4751)) % 1.58/1.65 [487]~P20(x4871)+~P33(f28(f28(f30(x4871),x4872),x4872)) % 1.58/1.65 [516]P10(a2,x5161)+P33(f28(f28(f35(a2),f78(x5161,x5162)),x5161)) % 1.58/1.65 [517]P10(a2,x5171)+P33(f28(f28(f35(a2),f82(x5171,x5172)),x5171)) % 1.58/1.65 [534]P33(f28(f29(a2,x5341),x5342))+~P33(f28(f28(f30(a2),x5341),x5342)) % 1.58/1.65 [536]P33(f28(f28(f30(a2),x5362),f28(a22,x5361)))+P33(f28(f28(f30(a2),x5361),x5362)) % 1.58/1.65 [543]P33(f28(f29(a2,x5431),x5432))+P33(f28(f29(a2,f28(a22,x5432)),x5431)) % 1.58/1.65 [579]P33(f28(f28(f30(a2),x5791),f28(a22,x5792)))+~P33(f28(f28(f30(a2),x5791),x5792)) % 1.58/1.65 [583]P10(a2,x5831)+~P33(f28(f29(a2,f82(x5831,x5832)),x5832)) % 1.58/1.65 [585]E(f28(a22,f28(f28(f20(a2),x5851),f71(x5852,x5851))),x5852)+~P33(f28(f28(f30(a2),x5851),x5852)) % 1.58/1.65 [598]~P33(f28(f28(f30(a2),x5981),x5982))+P33(f28(f29(a2,f28(a22,x5981)),x5982)) % 1.58/1.65 [605]P10(a2,x6051)+~P33(f28(f28(f30(a2),f78(x6051,x6052)),x6052)) % 1.58/1.65 [611]P33(f28(f29(a2,x6111),x6112))+~P33(f28(f29(a2,f28(a22,x6111)),x6112)) % 1.58/1.65 [613]~P4(x6131)+P33(f28(f28(f30(x6131),x6132),f28(f28(f20(x6131),x6132),f5(x6131)))) % 1.58/1.65 [627]P33(f28(f28(f30(a2),x6271),x6272))+~P33(f28(f29(a2,f28(a22,x6271)),x6272)) % 1.58/1.65 [628]~P33(f28(f28(f30(a2),x6282),f28(a22,x6281)))+~P33(f28(f28(f30(a2),x6281),x6282)) % 1.58/1.65 [629]P10(x6291,f31(f96(x6291,a3)))+~P10(f96(x6292,x6291),f31(f96(f96(x6292,x6291),a3))) % 1.58/1.65 [630]P10(x6301,f31(f96(x6301,a3)))+~P10(f97(x6302,x6301),f31(f96(f97(x6302,x6301),a3))) % 1.58/1.65 [631]P10(x6311,f31(f96(x6311,a3)))+~P10(f97(x6311,x6312),f31(f96(f97(x6311,x6312),a3))) % 1.58/1.65 [637]P33(f28(f28(f30(a2),f28(a22,x6371)),f28(a22,x6372)))+~P33(f28(f28(f30(a2),x6371),x6372)) % 1.58/1.65 [638]~P33(f28(f29(a2,x6381),x6382))+~P33(f28(f29(a2,f28(a22,x6382)),x6381)) % 1.58/1.65 [639]P33(f28(f28(f30(a2),x6391),x6392))+~P33(f28(f28(f30(a2),f28(a22,x6391)),x6392)) % 1.58/1.65 [668]~P33(f28(f28(f30(a2),f28(a22,x6681)),f28(a22,x6682)))+P33(f28(f28(f30(a2),x6681),x6682)) % 1.58/1.65 [753]P33(f26(a3,a40,f29(a2,x7531),x7532))+~P33(f28(f29(a2,f28(a22,x7531)),x7532)) % 1.58/1.65 [786]~P33(f26(a3,a40,f29(a2,x7861),x7862))+P33(f28(f29(a2,f28(a22,x7861)),x7862)) % 1.58/1.65 [808]P2(x8081)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f58(x8081)),f65(x8081))),f28(f59(x8081),x8082))) % 1.58/1.65 [831]P3(x8311,x8312)+P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f49(x8312,x8311)),a9)) % 1.58/1.65 [836]E(f32(a2,x8361,f28(f28(f20(a2),x8361),f15(a2,x8362))),x8362)+~P33(f28(f29(f96(a2,a3),x8362),f32(a2,x8361,f28(f28(f20(a2),x8361),f15(a2,x8362))))) % 1.58/1.65 [849]P33(f28(f28(f35(f96(f98(a93,a93),a3)),f28(f28(a11,x8491),x8492)),a8))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8491),a8)) % 1.58/1.65 [850]P33(f28(f28(f35(f96(f98(a93,a93),a3)),f28(f28(a13,x8501),x8502)),a8))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8501),a8)) % 1.58/1.65 [461]~P10(x4611,x4613)+P10(x4611,f36(x4611,x4612,x4613)) % 1.58/1.65 [515]P10(x5151,x5152)+~P10(x5151,f36(x5151,x5153,x5152)) % 1.58/1.65 [477]~E(x4772,x4773)+P33(f28(f28(f35(x4771),x4772),f28(a39,x4773))) % 1.58/1.65 [540]E(x5401,x5402)+~P33(f28(f28(f35(x5403),x5401),f28(a39,x5402))) % 1.58/1.65 [971]P10(x9711,x9712)+~P33(f28(f28(f35(f98(f96(x9711,a3),f96(x9711,a3))),f28(f28(f33(f96(x9711,a3),f96(x9711,a3)),x9713),x9712)),f42(x9711))) % 1.58/1.65 [426]~P27(x4262)+E(f28(f31(f96(x4261,x4262)),x4263),f31(x4262)) % 1.58/1.65 [445]~P28(x4451)+E(f28(f28(f20(x4451),x4452),x4453),f28(f28(f20(x4451),x4453),x4452)) % 1.58/1.65 [463]E(x4631,x4632)+~E(f28(f28(f20(a2),x4633),x4631),f28(f28(f20(a2),x4633),x4632)) % 1.58/1.65 [464]E(x4641,x4642)+~E(f28(f28(f20(a2),x4641),x4643),f28(f28(f20(a2),x4642),x4643)) % 1.58/1.65 [468]~E(x4682,f28(f28(f20(a2),x4681),x4683))+P33(f28(f29(a2,x4681),x4682)) % 1.58/1.65 [476]~P33(f28(x4763,x4762))+P33(f28(f28(f35(x4761),x4762),x4763)) % 1.58/1.65 [488]~E(x4883,x4882)+P33(f28(f29(f96(x4881,a3),x4882),x4883)) % 1.58/1.65 [494]~E(x4942,x4943)+P33(f28(f29(f96(x4941,a3),x4942),x4943)) % 1.58/1.65 [512]P33(f28(x5121,x5122))+~P33(f28(f28(f35(x5123),x5122),x5121)) % 1.58/1.65 [529]E(f36(x5291,x5292,x5293),x5293)+~P33(f28(f28(f35(x5291),x5292),x5293)) % 1.58/1.65 [721]~P10(x7211,x7212)+P33(f28(f29(a2,f15(x7211,x7212)),f15(x7211,f36(x7211,x7213,x7212)))) % 1.58/1.65 [804]E(x8041,x8042)+~E(f28(f28(f7(x8043,f96(x8043,a3),a3),f35(x8043)),x8041),f28(f28(f7(x8043,f96(x8043,a3),a3),f35(x8043)),x8042)) % 1.58/1.65 [830]~P11(x8302,x8301,x8303,f31(f96(x8302,a3)))+E(f37(x8301,x8302,f23(x8302,x8301,f31(f96(x8302,a3)),x8303),f31(f96(x8301,a3))),f31(f96(x8302,a3))) % 1.58/1.65 [832]P11(x8321,x8322,f23(x8322,x8321,f31(f96(x8322,a3)),x8323),f31(f96(x8321,a3)))+~E(f37(x8322,x8321,x8323,f31(f96(x8322,a3))),f31(f96(x8321,a3))) % 1.58/1.65 [877]~E(f28(x8773,f28(f23(x8771,x8772,f31(f96(x8771,a3)),x8773),f75(x8773,x8772,x8771))),f75(x8773,x8772,x8771))+E(f37(x8771,x8772,x8773,f31(f96(x8771,a3))),f31(f96(x8772,a3))) % 1.58/1.65 [559]~E(x5592,f28(a22,f28(f28(f20(a2),x5591),x5593)))+P33(f28(f28(f30(a2),x5591),x5592)) % 1.58/1.65 [633]~P33(f28(f29(a2,x6331),x6333))+P33(f28(f29(a2,x6331),f28(f28(f20(a2),x6332),x6333))) % 1.58/1.65 [635]~P33(f28(f29(a2,x6351),x6352))+P33(f28(f29(a2,x6351),f28(f28(f20(a2),x6352),x6353))) % 1.58/1.65 [657]~P33(f28(f28(f30(a2),x6571),x6573))+P33(f28(f28(f30(a2),x6571),f28(f28(f20(a2),x6572),x6573))) % 1.58/1.65 [659]~P33(f28(f28(f30(a2),x6591),x6592))+P33(f28(f28(f30(a2),x6591),f28(f28(f20(a2),x6592),x6593))) % 1.58/1.65 [669]~E(x6691,x6692)+~P33(f28(f28(f30(f96(x6693,a3)),x6691),x6692)) % 1.58/1.65 [711]P33(f28(f29(f96(x7111,a3),x7112),x7113))+~P33(f28(f28(f30(f96(x7111,a3)),x7112),x7113)) % 1.58/1.65 [734]~P33(f28(f29(a2,x7342),x7343))+P33(f28(f29(a2,f28(f28(f20(a2),x7341),x7342)),f28(f28(f20(a2),x7341),x7343))) % 1.58/1.65 [735]~P33(f28(f29(a2,x7351),x7353))+P33(f28(f29(a2,f28(f28(f20(a2),x7351),x7352)),f28(f28(f20(a2),x7353),x7352))) % 1.58/1.65 [747]~P33(f28(f28(f30(a2),x7472),x7473))+P33(f28(f28(f30(a2),f28(f28(f20(a2),x7471),x7472)),f28(f28(f20(a2),x7471),x7473))) % 1.58/1.65 [748]~P33(f28(f28(f30(a2),x7481),x7483))+P33(f28(f28(f30(a2),f28(f28(f20(a2),x7481),x7482)),f28(f28(f20(a2),x7483),x7482))) % 1.58/1.65 [793]P33(f28(f29(a2,x7931),x7932))+~P33(f28(f29(a2,f28(f28(f20(a2),x7933),x7931)),f28(f28(f20(a2),x7933),x7932))) % 1.58/1.65 [803]P33(f28(f28(f30(a2),x8031),x8032))+~P33(f28(f28(f30(a2),f28(f28(f20(a2),x8033),x8031)),f28(f28(f20(a2),x8033),x8032))) % 1.58/1.65 [958]~P33(f28(f29(f96(x9581,a3),x9582),x9583))+P33(f28(f29(f96(x9581,a3),f28(f28(f7(x9581,f96(x9581,a3),a3),f35(x9581)),x9582)),f28(f28(f7(x9581,f96(x9581,a3),a3),f35(x9581)),x9583))) % 1.58/1.65 [978]~P33(f28(f28(f35(f98(f96(x9781,a3),f96(x9781,a3))),f28(f28(f33(f96(x9781,a3),f96(x9781,a3)),x9782),x9783)),f42(x9781)))+P33(f28(f28(f30(f96(x9781,a3)),x9782),x9783)) % 1.58/1.65 [993]P33(f28(f29(f96(x9931,a3),x9932),x9933))+~P33(f28(f29(f96(x9931,a3),f28(f28(f7(x9931,f96(x9931,a3),a3),f35(x9931)),x9932)),f28(f28(f7(x9931,f96(x9931,a3),a3),f35(x9931)),x9933))) % 1.58/1.65 [740]P33(f28(f29(a2,x7401),x7402))+~P33(f28(f29(a2,f28(f28(f20(a2),x7403),x7401)),x7402)) % 1.58/1.65 [741]P33(f28(f29(a2,x7411),x7412))+~P33(f28(f29(a2,f28(f28(f20(a2),x7411),x7413)),x7412)) % 1.58/1.65 [755]P33(f28(f28(f30(a2),x7551),x7552))+~P33(f28(f28(f30(a2),f28(f28(f20(a2),x7551),x7553)),x7552)) % 1.58/1.65 [685]~P10(x6852,x6854)+P10(x6851,f37(x6852,x6851,x6853,x6854)) % 1.58/1.65 [762]P10(x7621,x7622)+~P10(f97(x7623,x7621),f38(x7623,x7621,x7624,x7622)) % 1.58/1.65 [763]P10(x7631,x7632)+~P10(f97(x7631,x7633),f38(x7631,x7633,x7632,x7634)) % 1.58/1.65 [791]P11(x7911,x7912,x7913,x7914)+~E(f50(x7914,x7913,x7912,x7911),f51(x7914,x7913,x7912,x7911)) % 1.58/1.65 [553]~E(x5532,x5534)+P33(f28(f36(x5531,x5532,x5533),x5534)) % 1.58/1.65 [582]~P33(f28(x5823,x5824))+P33(f28(f36(x5821,x5822,x5823),x5824)) % 1.58/1.65 [604]~E(x6042,x6043)+P33(f28(f28(f35(x6041),x6042),f36(x6041,x6043,x6044))) % 1.58/1.65 [696]P10(x6962,x6964)+E(f15(f97(x6961,x6962),f38(x6961,x6962,x6963,x6964)),f4(a2)) % 1.58/1.65 [697]P10(x6971,x6973)+E(f15(f97(x6971,x6972),f38(x6971,x6972,x6973,x6974)),f4(a2)) % 1.58/1.65 [776]~P11(x7762,x7761,x7763,x7764)+E(f15(x7761,f37(x7762,x7761,x7763,x7764)),f15(x7762,x7764)) % 1.58/1.65 [806]~P11(x8061,x8062,x8063,f31(f96(x8061,a3)))+E(f28(f23(x8061,x8062,f31(f96(x8061,a3)),x8063),f28(x8063,x8064)),x8064) % 1.58/1.65 [821]P11(x8214,x8213,x8211,x8212)+E(f28(x8211,f50(x8212,x8211,x8213,x8214)),f28(x8211,f51(x8212,x8211,x8213,x8214))) % 1.58/1.65 [835]P33(f28(f28(f35(f98(x8351,x8351)),f28(f28(f33(x8351,x8351),x8352),x8353)),f41(x8351,x8354)))+~P33(f28(f28(f30(a2),f28(x8354,x8352)),f28(x8354,x8353))) % 1.58/1.65 [846]~P11(x8462,x8461,x8463,f31(f96(x8462,a3)))+E(f37(x8461,x8462,f23(x8462,x8461,f31(f96(x8462,a3)),x8463),f37(x8462,x8461,x8463,x8464)),x8464) % 1.58/1.65 [853]~P33(f28(f28(f35(f98(x8534,x8534)),f28(f28(f33(x8534,x8534),x8532),x8533)),f41(x8534,x8531)))+P33(f28(f28(f30(a2),f28(x8531,x8532)),f28(x8531,x8533))) % 1.58/1.65 [951]~P10(x9512,x9514)+P33(f28(f29(a2,f15(x9511,f37(x9512,x9511,x9513,x9514))),f15(x9512,x9514))) % 1.58/1.65 [991]~P11(x9911,x9912,x9913,x9914)+~P33(f28(f28(f30(a2),f15(x9912,f37(x9911,x9912,x9913,x9914))),f15(x9911,x9914))) % 1.58/1.65 [675]P33(f28(f28(f35(x6751),x6752),f36(x6751,x6753,x6754)))+~P33(f28(f28(f35(x6751),x6752),x6754)) % 1.58/1.65 [716]P33(f28(f29(f96(x7161,a3),x7162),f36(x7161,x7163,x7164)))+~P33(f28(f29(f96(x7161,a3),x7162),x7164)) % 1.58/1.65 [796]P33(f28(f28(f35(x7961),x7962),x7963))+~P33(f28(f29(f96(x7961,a3),f36(x7961,x7962,x7964)),x7963)) % 1.58/1.65 [798]P33(f28(f29(f96(x7981,a3),f36(x7981,x7982,x7983)),f36(x7981,x7982,x7984)))+~P33(f28(f29(f96(x7981,a3),x7983),x7984)) % 1.58/1.65 [807]~P33(f28(f29(f96(x8071,a3),f36(x8071,x8074,x8072)),x8073))+P33(f28(f29(f96(x8071,a3),x8072),x8073)) % 1.58/1.65 [837]~E(x8371,x8372)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8373),x8371)),f28(f28(a13,x8374),x8372))) % 1.58/1.65 [838]~E(x8381,x8382)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8381),x8383)),f28(f28(a11,x8384),x8382))) % 1.58/1.65 [855]~P11(x8551,x8553,x8554,f31(f96(x8551,a3)))+P11(x8551,f96(x8552,x8553),f28(f10(x8553,f96(x8552,x8553),x8551,f16(x8553,x8552)),x8554),f31(f96(x8551,a3))) % 1.58/1.65 [863]P11(x8631,x8632,x8633,x8634)+P33(f28(f28(f35(x8631),f50(x8634,x8633,x8632,x8631)),x8634)) % 1.58/1.65 [864]P11(x8641,x8642,x8643,x8644)+P33(f28(f28(f35(x8641),f51(x8644,x8643,x8642,x8641)),x8644)) % 1.58/1.65 [595]~P28(x5951)+E(f28(f28(f20(x5951),x5952),f28(f28(f20(x5951),x5953),x5954)),f28(f28(f20(x5951),x5953),f28(f28(f20(x5951),x5952),x5954))) % 1.58/1.65 [653]~P8(x6531)+E(f28(f28(f20(x6531),f28(f28(f20(x6531),x6532),x6533)),x6534),f28(f28(f20(x6531),x6532),f28(f28(f20(x6531),x6533),x6534))) % 1.58/1.65 [654]~P28(x6541)+E(f28(f28(f20(x6541),f28(f28(f20(x6541),x6542),x6543)),x6544),f28(f28(f20(x6541),x6542),f28(f28(f20(x6541),x6543),x6544))) % 1.58/1.65 [683]~P28(x6831)+E(f28(f28(f20(x6831),f28(f28(f20(x6831),x6832),x6833)),x6834),f28(f28(f20(x6831),f28(f28(f20(x6831),x6832),x6834)),x6833)) % 1.58/1.65 [843]~E(f37(x8432,x8433,x8431,f31(f96(x8432,a3))),f31(f96(x8433,a3)))+E(f28(x8431,f28(f23(x8432,x8433,f31(f96(x8432,a3)),x8431),x8434)),x8434) % 1.58/1.65 [870]~E(f37(x8701,x8702,x8703,f31(f96(x8701,a3))),f31(f96(x8702,a3)))+E(f37(x8701,x8702,x8703,f37(x8702,x8701,f23(x8701,x8702,f31(f96(x8701,a3)),x8703),x8704)),x8704) % 1.58/1.65 [1035]E(x10351,x10352)+~E(f28(f28(f7(x10353,f96(f98(x10353,x10354),a3),f96(x10354,a3)),f28(f10(f96(x10354,f96(f96(f98(x10353,x10354),a3),a3)),f96(f96(f98(x10353,x10354),a3),f96(x10354,a3)),x10353,f7(x10354,f96(f98(x10353,x10354),a3),a3)),f28(f10(f96(x10354,f98(x10353,x10354)),f96(x10354,f96(f96(f98(x10353,x10354),a3),a3)),x10353,f10(f98(x10353,x10354),f96(f96(f98(x10353,x10354),a3),a3),x10354,f35(f98(x10353,x10354)))),f33(x10353,x10354)))),x10351),f28(f28(f7(x10353,f96(f98(x10353,x10354),a3),f96(x10354,a3)),f28(f10(f96(x10354,f96(f96(f98(x10353,x10354),a3),a3)),f96(f96(f98(x10353,x10354),a3),f96(x10354,a3)),x10353,f7(x10354,f96(f98(x10353,x10354),a3),a3)),f28(f10(f96(x10354,f98(x10353,x10354)),f96(x10354,f96(f96(f98(x10353,x10354),a3),a3)),x10353,f10(f98(x10353,x10354),f96(f96(f98(x10353,x10354),a3),a3),x10354,f35(f98(x10353,x10354)))),f33(x10353,x10354)))),x10352)) % 1.58/1.65 [1041]~P33(f28(f29(f96(f98(x10411,x10412),a3),x10413),x10414))+P33(f28(f29(f96(x10411,f96(x10412,a3)),f28(f28(f7(x10411,f96(f98(x10411,x10412),a3),f96(x10412,a3)),f28(f10(f96(x10412,f96(f96(f98(x10411,x10412),a3),a3)),f96(f96(f98(x10411,x10412),a3),f96(x10412,a3)),x10411,f7(x10412,f96(f98(x10411,x10412),a3),a3)),f28(f10(f96(x10412,f98(x10411,x10412)),f96(x10412,f96(f96(f98(x10411,x10412),a3),a3)),x10411,f10(f98(x10411,x10412),f96(f96(f98(x10411,x10412),a3),a3),x10412,f35(f98(x10411,x10412)))),f33(x10411,x10412)))),x10413)),f28(f28(f7(x10411,f96(f98(x10411,x10412),a3),f96(x10412,a3)),f28(f10(f96(x10412,f96(f96(f98(x10411,x10412),a3),a3)),f96(f96(f98(x10411,x10412),a3),f96(x10412,a3)),x10411,f7(x10412,f96(f98(x10411,x10412),a3),a3)),f28(f10(f96(x10412,f98(x10411,x10412)),f96(x10412,f96(f96(f98(x10411,x10412),a3),a3)),x10411,f10(f98(x10411,x10412),f96(f96(f98(x10411,x10412),a3),a3),x10412,f35(f98(x10411,x10412)))),f33(x10411,x10412)))),x10414))) % 1.58/1.65 [1042]P33(f28(f29(f96(f98(x10421,x10422),a3),x10423),x10424))+~P33(f28(f29(f96(x10421,f96(x10422,a3)),f28(f28(f7(x10421,f96(f98(x10421,x10422),a3),f96(x10422,a3)),f28(f10(f96(x10422,f96(f96(f98(x10421,x10422),a3),a3)),f96(f96(f98(x10421,x10422),a3),f96(x10422,a3)),x10421,f7(x10422,f96(f98(x10421,x10422),a3),a3)),f28(f10(f96(x10422,f98(x10421,x10422)),f96(x10422,f96(f96(f98(x10421,x10422),a3),a3)),x10421,f10(f98(x10421,x10422),f96(f96(f98(x10421,x10422),a3),a3),x10422,f35(f98(x10421,x10422)))),f33(x10421,x10422)))),x10423)),f28(f28(f7(x10421,f96(f98(x10421,x10422),a3),f96(x10422,a3)),f28(f10(f96(x10422,f96(f96(f98(x10421,x10422),a3),a3)),f96(f96(f98(x10421,x10422),a3),f96(x10422,a3)),x10421,f7(x10422,f96(f98(x10421,x10422),a3),a3)),f28(f10(f96(x10422,f98(x10421,x10422)),f96(x10422,f96(f96(f98(x10421,x10422),a3),a3)),x10421,f10(f98(x10421,x10422),f96(f96(f98(x10421,x10422),a3),a3),x10422,f35(f98(x10421,x10422)))),f33(x10421,x10422)))),x10424))) % 1.58/1.65 [841]P33(f28(f28(f35(f98(x8411,x8411)),f28(f28(f33(x8411,x8411),x8412),x8413)),f44(x8411,x8414,x8415)))+~P33(f28(f28(f30(a2),f28(x8414,x8412)),f28(x8414,x8413))) % 1.58/1.65 [860]E(f28(x8601,f72(x8602,x8601,x8603,x8604)),x8604)+~P33(f28(f28(f35(x8605),x8604),f37(x8603,x8605,x8601,x8602))) % 1.58/1.65 [876]P11(x8761,x8762,f23(x8762,x8761,x8763,x8764),x8765)+~P33(f28(f29(f96(x8761,a3),x8765),f37(x8762,x8761,x8764,x8763))) % 1.58/1.65 [956]E(f37(x9561,x9562,x9563,f76(x9564,x9563,x9561,x9565,x9562)),x9565)+~P33(f28(f29(f96(x9562,a3),x9565),f37(x9561,x9562,x9563,x9564))) % 1.58/1.65 [785]E(f36(x7851,f28(x7852,x7853),f37(x7854,x7851,x7852,x7855)),f37(x7854,x7851,x7852,x7855))+~P33(f28(f28(f35(x7854),x7853),x7855)) % 1.58/1.65 [829]P33(f28(f28(f35(x8291),f28(x8292,x8293)),f37(x8294,x8291,x8292,x8295)))+~P33(f28(f28(f35(x8294),x8293),x8295)) % 1.58/1.65 [881]E(f28(x8811,f28(f23(x8812,x8813,x8814,x8811),x8815)),x8815)+~P33(f28(f28(f35(x8813),x8815),f37(x8812,x8813,x8811,x8814))) % 1.58/1.65 [906]P33(f28(f29(f96(x9061,a3),f37(x9062,x9061,x9063,x9064)),f37(x9062,x9061,x9063,x9065)))+~P33(f28(f29(f96(x9062,a3),x9064),x9065)) % 1.58/1.65 [922]~P10(x9223,f37(x9222,x9223,x9225,f31(f96(x9222,a3))))+P10(x9221,f37(x9222,x9221,f28(f10(x9223,x9221,x9222,x9224),x9225),f31(f96(x9222,a3)))) % 1.58/1.65 [929]P33(f28(f29(f96(f96(x9291,x9292),a3),f18(x9291,x9292,x9293,x9294)),f18(x9291,x9292,x9295,x9294)))+~P33(f28(f29(f96(x9291,a3),x9295),x9293)) % 1.58/1.65 [939]~P33(f28(f28(f35(x9395),x9394),f37(x9391,x9395,x9393,x9392)))+P33(f28(f28(f35(x9391),f72(x9392,x9393,x9391,x9394)),x9392)) % 1.58/1.65 [1006]P33(f28(f28(f35(f96(x10061,x10064)),x10063),f18(x10061,x10064,x10065,x10062)))+P33(f28(f28(f35(x10061),f66(x10062,x10063,x10064,x10065,x10061)),x10065)) % 1.58/1.65 [1007]~P33(f28(f29(f96(x10075,a3),x10074),f37(x10071,x10075,x10073,x10072)))+P33(f28(f29(f96(x10071,a3),f76(x10072,x10073,x10071,x10074,x10075)),x10072)) % 1.58/1.65 [1010]P33(f28(f29(f96(f96(x10101,x10104),a3),f18(x10101,x10104,x10105,x10103)),f18(x10101,x10104,x10105,x10102)))+P33(f28(f28(f35(x10101),f67(x10102,x10103,x10104,x10105,x10101)),x10105)) % 1.58/1.65 [1028]P33(f28(f28(f35(f96(x10281,x10282)),x10283),f18(x10281,x10282,x10284,x10285)))+~P33(f28(f28(f35(x10282),f28(x10283,f66(x10285,x10283,x10282,x10284,x10281))),f28(x10285,f66(x10285,x10283,x10282,x10284,x10281)))) % 1.58/1.65 [1029]P33(f28(f29(f96(f96(x10291,x10292),a3),f18(x10291,x10292,x10293,x10294)),f18(x10291,x10292,x10293,x10295)))+~P33(f28(f29(f96(x10292,a3),f28(x10294,f67(x10295,x10294,x10292,x10293,x10291))),f28(x10295,f67(x10295,x10294,x10292,x10293,x10291)))) % 1.58/1.65 [731]~P28(x7311)+E(f28(f28(f20(x7311),f28(f28(f20(x7311),x7312),x7313)),f28(f28(f20(x7311),x7314),x7315)),f28(f28(f20(x7311),f28(f28(f20(x7311),x7312),x7314)),f28(f28(f20(x7311),x7313),x7315))) % 1.58/1.65 [828]~E(x8282,f28(x8284,x8285))+P33(f28(f28(f35(x8281),x8282),f37(x8283,x8281,x8284,f31(f96(x8283,a3))))) % 1.58/1.65 [984]~P33(f28(f28(f35(x9842),x9845),f37(x9841,x9842,x9844,x9843)))+P33(f28(f28(f35(x9841),f28(f23(x9841,x9842,x9843,x9844),x9845)),x9843)) % 1.58/1.65 [885]P12(x8851,x8852,x8853,x8854,x8855)+~P33(f28(f28(f35(f98(x8851,x8852)),f28(f28(f33(x8851,x8852),x8854),x8855)),x8853)) % 1.58/1.65 [891]~P12(x8911,x8912,x8915,x8913,x8914)+P33(f28(f28(f35(f98(x8911,x8912)),f28(f28(f33(x8911,x8912),x8913),x8914)),x8915)) % 1.58/1.65 [974]P33(f28(f29(f96(x9741,a3),f37(x9742,x9741,x9743,x9744)),x9745))+~P33(f28(f28(f35(f96(x9742,x9741)),x9743),f18(x9742,x9741,x9744,f28(f16(f96(x9741,a3),x9742),x9745)))) % 1.58/1.65 [1003]P33(f28(f28(f35(f98(f98(x10031,x10032),f98(x10031,x10032))),f28(f28(f33(f98(x10031,x10032),f98(x10031,x10032)),f28(f28(f33(x10031,x10032),x10033),x10034)),f28(f28(f33(x10031,x10032),x10035),x10036))),f43(x10031,x10032,x10037,x10038)))+~P33(f28(f28(f35(f98(x10031,x10031)),f28(f28(f33(x10031,x10031),x10033),x10035)),x10037)) % 1.58/1.65 [862]P1(x8621)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x8621)),f63(x8621))),f28(x8621,f61(x8621))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x8621)),f63(x8621))),f28(x8621,f60(x8621)))) % 1.58/1.65 [916]P1(x9161)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x9161)),f63(x9161))),f28(x9161,f61(x9161))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x9161)),f63(x9161))),f28(x9161,f60(x9161)))) % 1.58/1.65 [888]~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x8881)))+~P33(f28(f28(f30(a2),f28(a99,x8881)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a11,f28(a103,x8881)),a107))) % 1.58/1.65 [896]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x8961)))+~P33(f28(f28(f30(a2),f28(a99,x8961)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a11,f28(a103,x8961)),a107))) % 1.58/1.65 [894]~P33(f28(f28(f30(a2),f28(a99,x8941)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a11,f28(a103,x8941)),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a100)) % 1.58/1.65 [405]~P9(x4052)+~P9(x4051)+P9(f98(x4051,x4052)) % 1.58/1.65 [406]~P9(x4062)+~P9(x4061)+P9(f96(x4061,x4062)) % 1.58/1.65 [407]~P9(x4072)+~P9(x4071)+P9(f97(x4071,x4072)) % 1.58/1.65 [541]E(x5411,x5412)+~P33(f28(f29(a2,x5412),x5411))+~P33(f28(f29(a2,x5411),x5412)) % 1.58/1.65 [566]E(x5661,f4(a2))+E(f28(a22,f69(x5662,x5661)),x5661)+~P33(f28(f28(f30(a2),x5661),f28(a22,x5662))) % 1.58/1.65 [575]E(x5751,f28(a22,x5752))+P33(f28(f29(a2,x5751),x5752))+~P33(f28(f29(a2,x5751),f28(a22,x5752))) % 1.58/1.65 [612]E(x6121,x6122)+~P33(f28(f29(a2,x6122),x6121))+~P33(f28(f28(f30(a2),x6121),f28(a22,x6122))) % 1.58/1.65 [715]~P17(x7151)+~P33(f28(f29(x7151,x7152),f4(x7151)))+P33(f28(f29(x7151,f28(f28(f20(x7151),x7152),x7152)),f4(x7151))) % 1.58/1.65 [729]~P29(x7291)+~P33(f28(f28(f30(x7291),x7292),f4(x7291)))+P33(f28(f28(f30(x7291),f28(f28(f20(x7291),x7292),x7292)),f4(x7291))) % 1.58/1.65 [730]~P17(x7301)+~P33(f28(f28(f30(x7301),x7302),f4(x7301)))+P33(f28(f28(f30(x7301),f28(f28(f20(x7301),x7302),x7302)),f4(x7301))) % 1.58/1.65 [768]~P17(x7681)+~P33(f28(f29(x7681,f28(f28(f20(x7681),x7682),x7682)),f4(x7681)))+P33(f28(f29(x7681,x7682),f4(x7681))) % 1.58/1.65 [781]~P29(x7811)+~P33(f28(f28(f30(x7811),f28(f28(f20(x7811),x7812),x7812)),f4(x7811)))+P33(f28(f28(f30(x7811),x7812),f4(x7811))) % 1.58/1.65 [782]~P17(x7821)+~P33(f28(f28(f30(x7821),f28(f28(f20(x7821),x7822),x7822)),f4(x7821)))+P33(f28(f28(f30(x7821),x7822),f4(x7821))) % 1.58/1.65 [408]~E(x4082,f4(a2))+~E(x4081,f4(a2))+E(f28(f28(f20(a2),x4081),x4082),f4(a2)) % 1.58/1.65 [414]~P17(x4141)+~E(x4142,f4(x4141))+E(f28(f28(f20(x4141),x4142),x4142),f4(x4141)) % 1.58/1.65 [435]~E(x4352,f4(a2))+~E(x4351,f28(a22,f4(a2)))+E(f28(f28(f20(a2),x4351),x4352),f28(a22,f4(a2))) % 1.58/1.65 [436]~E(x4361,f4(a2))+~E(x4362,f28(a22,f4(a2)))+E(f28(f28(f20(a2),x4361),x4362),f28(a22,f4(a2))) % 1.58/1.65 [439]~P17(x4392)+E(x4391,f4(x4392))+~E(f28(f28(f20(x4392),x4391),x4391),f4(x4392)) % 1.58/1.65 [442]E(x4421,f4(a2))+E(x4422,f4(a2))+~E(f28(f28(f20(a2),x4422),x4421),f28(a22,f4(a2))) % 1.58/1.65 [448]E(x4481,f4(a2))+E(x4481,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4482),x4481),f28(a22,f4(a2))) % 1.58/1.65 [449]E(x4491,f4(a2))+E(x4491,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4491),x4492),f28(a22,f4(a2))) % 1.58/1.65 [455]E(x4551,f28(a22,f4(a2)))+E(x4552,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4551),x4552),f28(a22,f4(a2))) % 1.58/1.65 [504]E(x5041,x5042)+P33(f28(f28(f30(a2),x5042),x5041))+P33(f28(f28(f30(a2),x5041),x5042)) % 1.58/1.65 [520]E(x5201,x5202)+~P33(f28(f29(a2,x5201),x5202))+P33(f28(f28(f30(a2),x5201),x5202)) % 1.58/1.65 [558]~P10(a2,x5582)+P33(f28(f29(a2,x5581),f83(x5582)))+~P33(f28(f28(f35(a2),x5581),x5582)) % 1.58/1.65 [560]E(x5601,f31(f96(x5602,a3)))+~P10(x5602,f31(f96(x5602,a3)))+~E(f15(x5602,x5601),f15(x5602,f31(f96(x5602,a3)))) % 1.58/1.65 [572]~P10(a2,x5722)+P33(f28(f28(f30(a2),x5721),f79(x5722)))+~P33(f28(f28(f35(a2),x5721),x5722)) % 1.58/1.65 [576]~P33(f28(x5761,x5762))+P33(f28(x5761,f4(a2)))+P33(f28(f28(f30(a2),f70(x5762,x5761)),x5762)) % 1.58/1.65 [602]E(x6021,x6022)+~P33(f28(f28(f30(a2),x6021),f28(a22,x6022)))+P33(f28(f28(f30(a2),x6021),x6022)) % 1.58/1.65 [620]E(f28(a22,x6201),x6202)+~P33(f28(f28(f30(a2),x6201),x6202))+P33(f28(f28(f30(a2),f28(a22,x6201)),x6202)) % 1.58/1.65 [642]~P10(x6422,f31(f96(x6422,a3)))+~P10(x6421,f31(f96(x6421,a3)))+P10(f98(x6421,x6422),f31(f96(f98(x6421,x6422),a3))) % 1.58/1.65 [643]~P10(x6432,f31(f96(x6432,a3)))+~P10(x6431,f31(f96(x6431,a3)))+P10(f97(x6431,x6432),f31(f96(f97(x6431,x6432),a3))) % 1.58/1.65 [655]E(x6551,f4(a2))+~P33(f28(f28(f30(a2),x6551),f28(a22,x6552)))+P33(f28(f28(f30(a2),f69(x6552,x6551)),x6552)) % 1.58/1.65 [666]P10(x6662,f31(f96(x6662,a3)))+E(f15(x6661,f31(f96(x6661,a3))),f28(a22,f4(a2)))+~P10(f96(x6662,x6661),f31(f96(f96(x6662,x6661),a3))) % 1.58/1.65 [676]~P33(f28(x6761,x6762))+P33(f28(x6761,f4(a2)))+P33(f28(x6761,f28(f28(f20(a2),f70(x6762,x6761)),f5(a2)))) % 1.58/1.65 [773]~P11(x7731,x7731,x7732,f31(f96(x7731,a3)))+~P10(x7731,f31(f96(x7731,a3)))+E(f37(x7731,x7731,x7732,f31(f96(x7731,a3))),f31(f96(x7731,a3))) % 1.58/1.65 [778]P11(x7781,x7781,x7782,f31(f96(x7781,a3)))+~P10(x7781,f31(f96(x7781,a3)))+~E(f37(x7781,x7781,x7782,f31(f96(x7781,a3))),f31(f96(x7781,a3))) % 1.58/1.65 [886]P1(x8861)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x8861)),f63(x8861))),f28(f61(x8861),x8862)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x8861)),f63(x8861))),f28(f60(x8861),x8862))) % 1.58/1.65 [887]P1(x8871)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x8871)),f63(x8871))),f28(f60(x8871),x8872)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f62(x8871)),f63(x8871))),f28(f61(x8871),x8872))) % 1.58/1.65 [672]~P17(x6721)+~P33(f28(f29(x6721,f4(x6721)),x6722))+P33(f28(f29(x6721,f4(x6721)),f28(f28(f20(x6721),x6722),x6722))) % 1.58/1.65 [695]~P17(x6951)+~P33(f28(f28(f30(x6951),f4(x6951)),x6952))+P33(f28(f28(f30(x6951),f4(x6951)),f28(f28(f20(x6951),x6952),x6952))) % 1.58/1.65 [704]~P17(x7041)+P33(f28(f29(x7041,f4(x7041)),x7042))+~P33(f28(f29(x7041,f4(x7041)),f28(f28(f20(x7041),x7042),x7042))) % 1.58/1.65 [718]P33(f28(f28(f30(a2),f4(a2)),x7182))+P33(f28(f28(f30(a2),f4(a2)),x7181))+~P33(f28(f28(f30(a2),f4(a2)),f28(f28(f20(a2),x7182),x7181))) % 1.58/1.65 [719]~P17(x7191)+P33(f28(f28(f30(x7191),f4(x7191)),x7192))+~P33(f28(f28(f30(x7191),f4(x7191)),f28(f28(f20(x7191),x7192),x7192))) % 1.58/1.65 [720]~P24(x7201)+~P33(f28(f28(f35(x7201),x7202),f25(x7201)))+~E(f28(f28(f20(x7201),f28(f28(f20(x7201),f5(x7201)),x7202)),x7202),f4(x7201)) % 1.58/1.65 [1016]P3(x10161,x10162)+~E(f52(x10162,x10161),f53(x10162,x10161))+~P33(f28(f28(f35(f96(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3))),x10161),f18(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3),a9,f28(f16(f96(f96(f98(a93,a93),a3),a3),f96(a92,f96(f98(a93,a93),a3))),a8)))) % 1.58/1.65 [1017]P3(x10171,x10172)+P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f54(x10172,x10171)),a9))+~P33(f28(f28(f35(f96(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3))),x10171),f18(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3),a9,f28(f16(f96(f96(f98(a93,a93),a3),a3),f96(a92,f96(f98(a93,a93),a3))),a8)))) % 1.58/1.65 [1018]P3(x10181,x10182)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f53(x10182,x10181)),f52(x10182,x10181))),f28(f54(x10182,x10181),x10182)))+~P33(f28(f28(f35(f96(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3))),x10181),f18(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3),a9,f28(f16(f96(f96(f98(a93,a93),a3),a3),f96(a92,f96(f98(a93,a93),a3))),a8)))) % 1.58/1.65 [1019]P3(x10191,x10192)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),f53(x10192,x10191)),f52(x10192,x10191))),f28(x10191,f54(x10192,x10191))))+~P33(f28(f28(f35(f96(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3))),x10191),f18(f96(a92,f96(f98(a93,a93),a3)),f96(f98(a93,a93),a3),a9,f28(f16(f96(f96(f98(a93,a93),a3),a3),f96(a92,f96(f98(a93,a93),a3))),a8)))) % 1.58/1.65 [430]~E(x4302,x4303)+~P20(x4301)+P33(f28(f29(x4301,x4302),x4303)) % 1.58/1.65 [432]~E(x4322,x4323)+~P26(x4321)+P33(f28(f29(x4321,x4322),x4323)) % 1.58/1.65 [480]~P21(x4801)+P33(f28(f29(x4801,x4803),x4802))+P33(f28(f29(x4801,x4802),x4803)) % 1.58/1.65 [594]~P33(f28(f29(a2,x5941),x5943))+P33(f28(f29(a2,x5941),x5942))+~P33(f28(f29(a2,x5943),x5942)) % 1.58/1.65 [858]~P10(x8581,x8583)+P11(x8581,x8581,x8582,x8583)+~P33(f28(f29(f96(x8581,a3),x8583),f37(x8581,x8581,x8582,x8583))) % 1.58/1.65 [412]~P32(x4121)+~E(x4123,f4(x4121))+E(f28(f28(f20(x4121),x4122),x4123),x4122) % 1.58/1.65 [437]~P32(x4372)+E(x4371,f4(x4372))+~E(f28(f28(f20(x4372),x4373),x4371),x4373) % 1.58/1.65 [500]~E(x5001,x5002)+~P21(x5003)+~P33(f28(f28(f30(x5003),x5001),x5002)) % 1.58/1.65 [501]~E(x5011,x5012)+~P26(x5013)+~P33(f28(f28(f30(x5013),x5011),x5012)) % 1.58/1.65 [511]~P21(x5111)+P33(f28(f29(x5111,x5112),x5113))+P33(f28(f28(f30(x5111),x5113),x5112)) % 1.58/1.65 [555]~P20(x5551)+P33(f28(f29(x5551,x5552),x5553))+~P33(f28(f28(f30(x5551),x5552),x5553)) % 1.58/1.65 [557]~P26(x5571)+P33(f28(f29(x5571,x5572),x5573))+~P33(f28(f28(f30(x5571),x5572),x5573)) % 1.58/1.65 [573]~P33(f28(x5731,x5733))+P33(f28(x5731,f84(x5731,x5732)))+~P33(f28(f28(f30(a2),x5733),x5732)) % 1.58/1.65 [581]~P10(x5811,x5813)+E(f15(x5811,f36(x5811,x5812,x5813)),f28(a22,f15(x5811,x5813)))+P33(f28(f28(f35(x5811),x5812),x5813)) % 1.58/1.65 [586]~P20(x5861)+~P33(f28(f29(x5861,x5862),x5863))+~P33(f28(f28(f30(x5861),x5863),x5862)) % 1.58/1.65 [589]~P21(x5891)+~P33(f28(f29(x5891,x5892),x5893))+~P33(f28(f28(f30(x5891),x5893),x5892)) % 1.58/1.65 [592]P10(x5921,x5922)+~P10(x5921,x5923)+~P33(f28(f29(f96(x5921,a3),x5922),x5923)) % 1.58/1.65 [593]~E(x5931,f28(a22,x5933))+P33(f28(f28(f30(a2),x5931),f28(a22,x5932)))+~P33(f28(f28(f30(a2),x5933),x5932)) % 1.58/1.65 [606]~P10(x6061,x6063)+E(f15(x6061,f36(x6061,x6062,x6063)),f15(x6061,x6063))+~P33(f28(f28(f35(x6061),x6062),x6063)) % 1.58/1.65 [608]~P10(x6081,x6083)+E(f15(x6081,f36(x6081,x6082,x6083)),f28(f28(f20(a2),f5(a2)),f15(x6081,x6083)))+P33(f28(f28(f35(x6081),x6082),x6083)) % 1.58/1.65 [617]~P20(x6171)+~P33(f28(f28(f30(x6171),x6173),x6172))+~P33(f28(f28(f30(x6171),x6172),x6173)) % 1.58/1.65 [618]~P21(x6181)+~P33(f28(f28(f30(x6181),x6183),x6182))+~P33(f28(f28(f30(x6181),x6182),x6183)) % 1.58/1.65 [619]~P26(x6191)+~P33(f28(f28(f30(x6191),x6193),x6192))+~P33(f28(f28(f30(x6191),x6192),x6193)) % 1.58/1.65 [671]~P33(f28(f28(f30(a2),x6711),x6713))+~P33(f28(f28(f30(a2),x6713),x6712))+P33(f28(f28(f30(a2),f28(a22,x6711)),x6712)) % 1.58/1.65 [684]~P10(x6841,x6843)+P33(f28(f29(a2,f15(x6841,x6842)),f15(x6841,x6843)))+~P33(f28(f29(f96(x6841,a3),x6842),x6843)) % 1.58/1.65 [694]E(x6941,x6942)+~P33(f28(f29(f96(x6943,a3),x6941),x6942))+~P33(f28(f29(f96(x6943,a3),x6942),x6941)) % 1.58/1.65 [707]~P33(f28(x7071,x7073))+~P33(f28(f28(f30(a2),x7073),x7072))+P33(f28(f28(f35(a2),f84(x7071,x7072)),f32(a2,f4(a2),x7072))) % 1.58/1.65 [708]~P33(f28(x7081,x7083))+P33(f28(x7081,f85(x7081,x7082)))+~P33(f28(f28(f35(a2),x7083),f32(a2,f4(a2),x7082))) % 1.58/1.65 [736]~P33(f28(x7361,x7363))+P33(f28(f28(f30(a2),f85(x7361,x7362)),x7362))+~P33(f28(f28(f35(a2),x7363),f32(a2,f4(a2),x7362))) % 1.58/1.65 [699]E(x6991,x6992)+~P33(f28(f29(f96(x6993,a3),x6991),x6992))+P33(f28(f28(f30(f96(x6993,a3)),x6991),x6992)) % 1.58/1.65 [732]~P10(x7321,x7323)+P33(f28(f28(f30(a2),f15(x7321,x7322)),f15(x7321,x7323)))+~P33(f28(f28(f30(f96(x7321,a3)),x7322),x7323)) % 1.58/1.65 [932]~P10(x9321,x9323)+P33(f28(f28(f35(f98(f96(x9321,a3),f96(x9321,a3))),f28(f28(f33(f96(x9321,a3),f96(x9321,a3)),x9322),x9323)),f42(x9321)))+~P33(f28(f28(f30(f96(x9321,a3)),x9322),x9323)) % 1.58/1.65 [854]E(x8541,x8542)+P33(f28(f28(f35(f96(f98(a93,a93),a3)),f14(x8543,x8541,x8542)),a8))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8543),a8)) % 1.58/1.65 [861]E(x8611,x8612)+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8613),a8))+P33(f28(f28(f35(f96(f98(a93,a93),a3)),f28(f28(f28(a12,x8613),x8611),x8612)),a8)) % 1.58/1.65 [934]~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9343),x9342)),x9341))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9342),x9343)),x9341))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9341),a8)) % 1.58/1.65 [857]~P3(x8571,x8573)+E(f28(x8571,x8572),f28(x8572,x8573))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x8572),a9)) % 1.58/1.65 [701]~P10(x7012,x7014)+~P10(x7011,x7013)+P10(f97(x7011,x7012),f38(x7011,x7012,x7013,x7014)) % 1.58/1.65 [815]P10(x8151,x8152)+~P11(x8151,x8153,x8154,x8152)+~P10(x8153,f37(x8151,x8153,x8154,x8152)) % 1.58/1.65 [651]E(x6511,x6512)+P33(f28(x6513,x6512))+~P33(f28(f36(x6514,x6511,x6513),x6512)) % 1.58/1.65 [725]~P10(x7252,x7254)+~P10(x7251,x7253)+E(f15(f97(x7251,x7252),f38(x7251,x7252,x7253,x7254)),f28(f28(f20(a2),f15(x7251,x7253)),f15(x7252,x7254))) % 1.58/1.65 [800]~P10(x8001,x8004)+P11(x8001,x8002,x8003,x8004)+~E(f15(x8002,f37(x8001,x8002,x8003,x8004)),f15(x8001,x8004)) % 1.58/1.65 [482]~P6(x4823)+E(x4821,x4822)+~E(f28(f28(f20(x4823),x4824),x4821),f28(f28(f20(x4823),x4824),x4822)) % 1.58/1.65 [483]~P7(x4833)+E(x4831,x4832)+~E(f28(f28(f20(x4833),x4834),x4831),f28(f28(f20(x4833),x4834),x4832)) % 1.58/1.65 [485]~P6(x4853)+E(x4851,x4852)+~E(f28(f28(f20(x4853),x4851),x4854),f28(f28(f20(x4853),x4852),x4854)) % 1.58/1.65 [624]P33(f28(x6241,x6242))+~P33(f28(x6243,x6242))+~P33(f28(f29(f96(x6244,a3),x6243),x6241)) % 1.58/1.65 [641]~E(f28(f28(f20(a2),x6413),x6412),f28(f28(f20(a2),x6411),x6414))+~P33(f28(f28(f30(a2),x6413),x6414))+P33(f28(f28(f30(a2),x6411),x6412)) % 1.58/1.65 [692]P33(f28(f28(f35(x6921),x6922),x6923))+~P33(f28(f28(f35(x6921),x6922),x6924))+~P33(f28(f29(f96(x6921,a3),x6924),x6923)) % 1.58/1.65 [706]E(x7061,x7062)+~P33(f28(f28(f35(x7063),x7061),f36(x7063,x7062,x7064)))+P33(f28(f28(f35(x7063),x7061),x7064)) % 1.58/1.65 [728]~P33(f28(f29(f96(x7281,a3),x7282),x7284))+~P33(f28(f29(f96(x7281,a3),x7284),x7283))+P33(f28(f29(f96(x7281,a3),x7282),x7283)) % 1.58/1.65 [767]~P33(f28(f29(f96(x7671,a3),x7673),f36(x7671,x7672,x7674)))+P33(f28(f28(f35(x7671),x7672),x7673))+P33(f28(f29(f96(x7671,a3),x7673),x7674)) % 1.58/1.65 [792]~P33(f28(f28(f35(x7921),x7922),x7924))+~P33(f28(f29(f96(x7921,a3),x7923),x7924))+P33(f28(f29(f96(x7921,a3),f36(x7921,x7922,x7923)),x7924)) % 1.58/1.65 [839]~E(x8391,x8392)+~E(x8391,x8393)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8392),x8391)),f28(f28(a11,x8394),x8393))) % 1.58/1.65 [840]~E(x8401,x8402)+~E(x8401,x8403)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8401),x8402)),f28(f28(a13,x8404),x8403))) % 1.58/1.65 [1002]~P25(x10022)+~P33(f28(f29(x10022,f28(x10023,f91(x10024,x10023,x10021,x10022))),f28(x10024,f91(x10024,x10023,x10021,x10022))))+P33(f28(f29(f96(x10021,x10022),x10023),x10024)) % 1.58/1.65 [722]~P25(x7222)+P33(f28(f29(f96(x7221,x7222),x7223),x7224))+~P33(f28(f28(f30(f96(x7221,x7222)),x7223),x7224)) % 1.58/1.65 [733]P33(f28(f28(f35(x7331),x7332),x7333))+~P33(f28(f28(f35(x7331),x7332),x7334))+~P33(f28(f28(f30(f96(x7331,a3)),x7334),x7333)) % 1.58/1.65 [751]~P25(x7511)+~P33(f28(f29(f96(x7512,x7511),x7513),x7514))+~P33(f28(f28(f30(f96(x7512,x7511)),x7514),x7513)) % 1.58/1.65 [756]~P18(x7561)+~P33(f28(f29(x7561,x7563),x7564))+P33(f28(f29(x7561,f28(f28(f20(x7561),x7562),x7563)),f28(f28(f20(x7561),x7562),x7564))) % 1.58/1.65 [757]~P19(x7571)+~P33(f28(f29(x7571,x7573),x7574))+P33(f28(f29(x7571,f28(f28(f20(x7571),x7572),x7573)),f28(f28(f20(x7571),x7572),x7574))) % 1.58/1.65 [758]~P18(x7581)+~P33(f28(f29(x7581,x7582),x7584))+P33(f28(f29(x7581,f28(f28(f20(x7581),x7582),x7583)),f28(f28(f20(x7581),x7584),x7583))) % 1.58/1.65 [759]~P19(x7591)+~P33(f28(f29(x7591,x7592),x7594))+P33(f28(f29(x7591,f28(f28(f20(x7591),x7592),x7593)),f28(f28(f20(x7591),x7594),x7593))) % 1.58/1.65 [764]~P33(f28(f29(a2,x7642),x7644))+~P33(f28(f29(a2,x7641),x7643))+P33(f28(f29(a2,f28(f28(f20(a2),x7641),x7642)),f28(f28(f20(a2),x7643),x7644))) % 1.58/1.65 [769]~P5(x7691)+~P33(f28(f28(f30(x7691),x7693),x7694))+P33(f28(f28(f30(x7691),f28(f28(f20(x7691),x7692),x7693)),f28(f28(f20(x7691),x7692),x7694))) % 1.58/1.65 [770]~P18(x7701)+~P33(f28(f28(f30(x7701),x7703),x7704))+P33(f28(f28(f30(x7701),f28(f28(f20(x7701),x7702),x7703)),f28(f28(f20(x7701),x7702),x7704))) % 1.58/1.65 [771]~P5(x7711)+~P33(f28(f28(f30(x7711),x7712),x7714))+P33(f28(f28(f30(x7711),f28(f28(f20(x7711),x7712),x7713)),f28(f28(f20(x7711),x7714),x7713))) % 1.58/1.65 [772]~P18(x7721)+~P33(f28(f28(f30(x7721),x7722),x7724))+P33(f28(f28(f30(x7721),f28(f28(f20(x7721),x7722),x7723)),f28(f28(f20(x7721),x7724),x7723))) % 1.58/1.65 [779]~P33(f28(f28(f30(a2),x7792),x7794))+~P33(f28(f28(f30(a2),x7791),x7793))+P33(f28(f28(f30(a2),f28(f28(f20(a2),x7791),x7792)),f28(f28(f20(a2),x7793),x7794))) % 1.58/1.65 [787]~P33(f28(f29(f96(x7871,a3),x7874),x7873))+~P33(f28(f28(f30(f96(x7871,a3)),x7872),x7874))+P33(f28(f28(f30(f96(x7871,a3)),x7872),x7873)) % 1.58/1.65 [788]~P33(f28(f29(f96(x7881,a3),x7882),x7884))+~P33(f28(f28(f30(f96(x7881,a3)),x7884),x7883))+P33(f28(f28(f30(f96(x7881,a3)),x7882),x7883)) % 1.58/1.65 [811]~P18(x8111)+P33(f28(f29(x8111,x8112),x8113))+~P33(f28(f29(x8111,f28(f28(f20(x8111),x8114),x8112)),f28(f28(f20(x8111),x8114),x8113))) % 1.58/1.65 [813]~P18(x8131)+P33(f28(f29(x8131,x8132),x8133))+~P33(f28(f29(x8131,f28(f28(f20(x8131),x8132),x8134)),f28(f28(f20(x8131),x8133),x8134))) % 1.58/1.65 [814]~P33(f28(f28(f30(f96(x8141,a3)),x8142),x8144))+P33(f28(f28(f30(f96(x8141,a3)),x8142),x8143))+~P33(f28(f28(f30(f96(x8141,a3)),x8144),x8143)) % 1.58/1.65 [817]~P18(x8171)+P33(f28(f28(f30(x8171),x8172),x8173))+~P33(f28(f28(f30(x8171),f28(f28(f20(x8171),x8174),x8172)),f28(f28(f20(x8171),x8174),x8173))) % 1.58/1.65 [819]~P18(x8191)+P33(f28(f28(f30(x8191),x8192),x8193))+~P33(f28(f28(f30(x8191),f28(f28(f20(x8191),x8192),x8194)),f28(f28(f20(x8191),x8193),x8194))) % 1.58/1.65 [895]~P11(x8954,x8953,x8951,f31(f96(x8954,a3)))+E(f28(x8951,f73(x8952,x8951,x8953,x8954)),x8952)+~P33(f28(f28(f35(x8953),x8952),f37(x8954,x8953,x8951,f31(f96(x8954,a3))))) % 1.58/1.65 [874]E(x8741,x8742)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8743),x8741)),f28(f28(a11,x8744),x8742)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8743),x8741)),x8744)) % 1.58/1.65 [875]E(x8751,x8752)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8751),x8753)),f28(f28(a13,x8754),x8752)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8751),x8753)),x8754)) % 1.58/1.65 [682]E(x6821,x6822)+~E(f28(x6823,x6821),f28(x6823,x6822))+~P11(x6824,x6825,x6823,f31(f96(x6824,a3))) % 1.58/1.66 [820]E(x8201,x8202)+~E(f37(x8203,x8204,x8205,x8201),f37(x8203,x8204,x8205,x8202))+~P11(x8203,x8204,x8205,f31(f96(x8203,a3))) % 1.58/1.66 [851]P10(x8511,x8512)+~P10(x8513,x8514)+~P33(f28(f29(f96(x8511,a3),x8512),f37(x8513,x8511,x8515,x8514))) % 1.58/1.66 [688]~P25(x6881)+P33(f28(f29(x6881,f28(x6882,x6883)),f28(x6884,x6883)))+~P33(f28(f29(f96(x6885,x6881),x6882),x6884)) % 1.58/1.66 [777]P11(x7771,x7772,x7773,x7774)+~P11(x7771,x7772,x7773,x7775)+~P33(f28(f29(f96(x7771,a3),x7774),x7775)) % 1.58/1.66 [802]~P11(x8021,x8022,x8024,x8023)+E(f28(f23(x8021,x8022,x8023,x8024),f28(x8024,x8025)),x8025)+~P33(f28(f28(f35(x8021),x8025),x8023)) % 1.58/1.66 [852]~P11(x8522,x8521,x8524,x8523)+E(f37(x8521,x8522,f23(x8522,x8521,x8523,x8524),f37(x8522,x8521,x8524,x8525)),x8525)+~P33(f28(f29(f96(x8522,a3),x8525),x8523)) % 1.58/1.66 [871]~P11(x8711,x8714,x8715,f31(f96(x8711,a3)))+~P33(f28(f28(f35(x8714),f28(x8715,x8712)),f37(x8711,x8714,x8715,x8713)))+P33(f28(f28(f35(x8711),x8712),x8713)) % 1.58/1.66 [981]~P11(x9811,x9814,x9815,f31(f96(x9811,a3)))+~P33(f28(f29(f96(x9814,a3),f37(x9811,x9814,x9815,x9812)),f37(x9811,x9814,x9815,x9813)))+P33(f28(f29(f96(x9811,a3),x9812),x9813)) % 1.58/1.66 [805]~E(f28(x8053,x8055),x8054)+~P11(x8051,x8052,x8053,f31(f96(x8051,a3)))+E(f28(f23(x8051,x8052,f31(f96(x8051,a3)),x8053),x8054),x8055) % 1.58/1.66 [948]~P11(x9482,x9481,x9483,x9485)+P33(f28(f28(f30(f96(x9481,a3)),f37(x9482,x9481,x9483,x9484)),f37(x9482,x9481,x9483,x9485)))+~P33(f28(f28(f30(f96(x9482,a3)),x9484),x9485)) % 1.58/1.66 [901]P33(f28(f28(f35(f98(x9011,x9011)),f28(f28(f33(x9011,x9011),x9012),x9013)),f44(x9011,x9014,x9015)))+~P33(f28(f29(a2,f28(x9014,x9012)),f28(x9014,x9013)))+~P33(f28(f28(f35(f98(x9011,x9011)),f28(f28(f33(x9011,x9011),x9012),x9013)),x9015)) % 1.58/1.66 [824]~E(x8242,f28(x8244,x8246))+P33(f28(f28(f35(x8241),x8242),f37(x8243,x8241,x8244,x8245)))+~P33(f28(f28(f35(x8243),x8246),x8245)) % 1.58/1.66 [847]~E(x8472,f37(x8473,x8471,x8474,x8476))+P33(f28(f29(f96(x8471,a3),x8472),f37(x8473,x8471,x8474,x8475)))+~P33(f28(f29(f96(x8473,a3),x8476),x8475)) % 1.58/1.66 [865]~E(f37(x8651,x8652,x8653,x8654),x8656)+E(f37(x8651,x8652,x8653,f37(x8652,x8651,f23(x8651,x8652,x8654,x8653),x8655)),x8655)+~P33(f28(f29(f96(x8652,a3),x8655),x8656)) % 1.58/1.66 [873]~P33(f28(f28(f35(f96(x8735,x8731)),x8732),f18(x8735,x8731,x8736,x8734)))+P33(f28(f28(f35(x8731),f28(x8732,x8733)),f28(x8734,x8733)))+~P33(f28(f28(f35(x8735),x8733),x8736)) % 1.58/1.66 [750]P33(f28(f28(x7501,x7502),x7503))+~P33(f28(f28(x7504,x7502),x7503))+~P33(f28(f29(f96(x7505,f96(x7506,a3)),x7504),x7501)) % 1.58/1.66 [915]P33(f28(f28(f35(x9151),f28(x9152,x9153)),x9154))+~P33(f28(f28(f35(x9155),x9153),x9156))+~P33(f28(f28(f35(f96(x9155,x9151)),x9152),f18(x9155,x9151,x9156,f28(f16(f96(x9151,a3),x9155),x9154)))) % 1.58/1.66 [1012]~P10(x10124,x10122)+~P13(x10123,x10124,x10125,x10127,x10126,x10121)+E(f28(x10121,x10122),f19(x10123,x10124,x10125,x10126,x10127,x10122)) % 1.58/1.66 [1005]~P33(f28(x10056,x10053))+~P33(f28(f28(f35(f98(x10052,x10052)),f28(f28(f33(x10052,x10052),x10054),x10055)),f28(x10057,x10053)))+P33(f28(f28(f35(f98(f98(x10051,x10052),f98(x10051,x10052))),f28(f28(f33(f98(x10051,x10052),f98(x10051,x10052)),f28(f28(f33(x10051,x10052),x10053),x10054)),f28(f28(f33(x10051,x10052),x10053),x10055))),f34(x10051,x10052,x10056,x10057))) % 1.58/1.66 [1004]~E(x10043,x10045)+P33(f28(f28(f35(f98(f98(x10041,x10042),f98(x10041,x10042))),f28(f28(f33(f98(x10041,x10042),f98(x10041,x10042)),f28(f28(f33(x10041,x10042),x10043),x10044)),f28(f28(f33(x10041,x10042),x10045),x10046))),f43(x10041,x10042,x10047,x10048)))+~P33(f28(f28(f35(f98(x10042,x10042)),f28(f28(f33(x10042,x10042),x10044),x10046)),x10048)) % 1.58/1.66 [1011]E(x10111,x10112)+~P33(f28(f28(f35(f98(f98(x10113,x10115),f98(x10113,x10115))),f28(f28(f33(f98(x10113,x10115),f98(x10113,x10115)),f28(f28(f33(x10113,x10115),x10111),x10116)),f28(f28(f33(x10113,x10115),x10112),x10117))),f43(x10113,x10115,x10114,x10118)))+P33(f28(f28(f35(f98(x10113,x10113)),f28(f28(f33(x10113,x10113),x10111),x10112)),x10114)) % 1.58/1.66 [1015]~P33(f28(f28(f35(f98(f98(x10151,x10155),f98(x10151,x10155))),f28(f28(f33(f98(x10151,x10155),f98(x10151,x10155)),f28(f28(f33(x10151,x10155),x10152),x10156)),f28(f28(f33(x10151,x10155),x10153),x10157))),f43(x10151,x10155,x10154,x10158)))+P33(f28(f28(f35(f98(x10151,x10151)),f28(f28(f33(x10151,x10151),x10152),x10153)),x10154))+P33(f28(f28(f35(f98(x10155,x10155)),f28(f28(f33(x10155,x10155),x10156),x10157)),x10158)) % 1.58/1.66 [883]E(f28(a99,x8831),a108)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x8831)))+P33(f28(f28(f30(a2),f28(a99,x8831)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a13,f28(a103,x8831)),a107))) % 1.58/1.66 [893]E(f28(a99,x8931),a108)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x8931)))+P33(f28(f28(f30(a2),f28(a99,x8931)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a13,f28(a103,x8931)),a107))) % 1.58/1.66 [957]E(f28(a99,x9571),a108)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x9571)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a13,f28(a103,x9571)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a11,f28(a103,x9571)),a107))) % 1.58/1.66 [879]E(f28(a99,x8791),a108)+P33(f28(f28(f30(a2),f28(a99,x8791)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a13,f28(a103,x8791)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101)) % 1.58/1.66 [898]~E(f28(a99,x8981),a108)+P33(f28(f28(f30(a2),f28(a99,x8981)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(f28(a12,f28(a103,x8981)),a105),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101)) % 1.58/1.66 [899]~E(f28(a99,x8991),a108)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x8991)))+P33(f28(f28(f30(a2),f28(a99,x8991)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(f28(a12,f28(a103,x8991)),a105),a107))) % 1.58/1.66 [905]~P33(f28(f28(f30(a2),f28(a99,x9051)),f28(f28(f20(a2),a108),f5(a2))))+~P33(f28(f28(f30(a2),f28(a99,x9051)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a11,f28(a103,x9051)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a100)) % 1.58/1.66 [918]~E(f28(a99,x9181),a108)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x9181)))+P33(f28(f28(f30(a2),f28(a99,x9181)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(f28(a12,f28(a103,x9181)),a105),a107))) % 1.58/1.66 [973]~E(f28(a99,x9731),a108)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x9731)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a11,f28(a103,x9731)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(f28(a12,f28(a103,x9731)),a105),a107))) % 1.58/1.66 [977]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x9771)))+P33(f28(f28(f30(a2),f28(a99,x9771)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a13,f28(a103,x9771)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(f28(a12,f28(a103,x9771)),a105),a107))) % 1.58/1.66 [992]P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(a103,x9921)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a13,f28(a103,x9921)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(a11,f28(a103,x9921)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a106)),f28(f28(f28(a12,f28(a103,x9921)),a105),a107))) % 1.58/1.66 [892]~P29(x8921)+~P33(f28(f28(f35(x8921),x8922),f25(x8921)))+P33(f28(f28(f30(x8921),f28(f28(f20(x8921),f28(f28(f20(x8921),f5(x8921)),x8922)),x8922)),f4(x8921)))+~P33(f28(f28(f30(x8921),x8922),f4(x8921))) % 1.58/1.66 [953]~P29(x9531)+~P33(f28(f28(f35(x9531),x9532),f25(x9531)))+~P33(f28(f28(f30(x9531),f28(f28(f20(x9531),f28(f28(f20(x9531),f5(x9531)),x9532)),x9532)),f4(x9531)))+P33(f28(f28(f30(x9531),x9532),f4(x9531))) % 1.58/1.66 [561]~P24(x5611)+~E(x5612,f4(x5611))+E(f28(f28(f20(x5611),x5612),x5612),f4(x5611))+~P33(f28(f28(f35(x5611),x5612),f25(x5611))) % 1.58/1.66 [577]~P24(x5772)+E(x5771,f4(x5772))+~E(f28(f28(f20(x5772),x5771),x5771),f4(x5772))+~P33(f28(f28(f35(x5772),x5771),f25(x5772))) % 1.58/1.66 [570]E(x5701,x5702)+~P26(x5703)+~P33(f28(f29(x5703,x5702),x5701))+~P33(f28(f29(x5703,x5701),x5702)) % 1.58/1.66 [610]~P33(f28(x6101,x6102))+~P33(f28(x6101,x6103))+~P33(f28(f29(a2,x6103),f70(x6102,x6101)))+P33(f28(x6101,f4(a2))) % 1.58/1.66 [754]~P23(x7541)+~P33(f28(f29(x7541,x7543),f4(x7541)))+~P33(f28(f29(x7541,x7542),f4(x7541)))+P33(f28(f29(x7541,f28(f28(f20(x7541),x7542),x7543)),f4(x7541))) % 1.58/1.66 [765]~P23(x7651)+~P33(f28(f29(x7651,x7653),f4(x7651)))+~P33(f28(f28(f30(x7651),x7652),f4(x7651)))+P33(f28(f28(f30(x7651),f28(f28(f20(x7651),x7652),x7653)),f4(x7651))) % 1.58/1.66 [766]~P23(x7661)+~P33(f28(f29(x7661,x7662),f4(x7661)))+~P33(f28(f28(f30(x7661),x7663),f4(x7661)))+P33(f28(f28(f30(x7661),f28(f28(f20(x7661),x7662),x7663)),f4(x7661))) % 1.58/1.66 [774]~P31(x7741)+~P33(f28(f28(f35(x7741),x7743),f25(x7741)))+~P33(f28(f28(f35(x7741),x7742),f25(x7741)))+P33(f28(f28(f35(x7741),f28(f28(f20(x7741),x7742),x7743)),f25(x7741))) % 1.58/1.66 [775]~P23(x7751)+~P33(f28(f28(f30(x7751),x7753),f4(x7751)))+~P33(f28(f28(f30(x7751),x7752),f4(x7751)))+P33(f28(f28(f30(x7751),f28(f28(f20(x7751),x7752),x7753)),f4(x7751))) % 1.58/1.66 [513]~E(x5132,x5133)+~P21(x5131)+P33(f28(f29(x5131,x5132),x5133))+P33(f28(f28(f30(x5131),x5132),x5133)) % 1.58/1.66 [527]~P29(x5273)+E(x5271,x5272)+P33(f28(f28(f30(x5273),x5272),x5271))+P33(f28(f28(f30(x5273),x5271),x5272)) % 1.58/1.66 [528]~P21(x5283)+E(x5281,x5282)+P33(f28(f28(f30(x5283),x5282),x5281))+P33(f28(f28(f30(x5283),x5281),x5282)) % 1.58/1.66 [544]~P26(x5443)+E(x5441,x5442)+~P33(f28(f29(x5443,x5442),x5441))+P33(f28(f28(f30(x5443),x5442),x5441)) % 1.58/1.66 [546]~P21(x5463)+E(x5461,x5462)+~P33(f28(f29(x5463,x5461),x5462))+P33(f28(f28(f30(x5463),x5461),x5462)) % 1.58/1.66 [552]~P26(x5523)+E(x5521,x5522)+~P33(f28(f29(x5523,x5521),x5522))+P33(f28(f28(f30(x5523),x5521),x5522)) % 1.58/1.66 [607]~P20(x6071)+~P33(f28(f29(x6071,x6073),x6072))+P33(f28(f29(x6071,x6072),x6073))+P33(f28(f28(f30(x6071),x6073),x6072)) % 1.58/1.66 [717]E(x7171,x7172)+~P10(x7173,x7171)+~P33(f28(f29(a2,f15(x7173,x7171)),f15(x7173,x7172)))+~P33(f28(f29(f96(x7173,a3),x7172),x7171)) % 1.58/1.66 [943]~P10(x9431,x9433)+~P11(x9431,x9431,x9432,x9433)+E(f37(x9431,x9431,x9432,x9433),x9433)+~P33(f28(f29(f96(x9431,a3),f37(x9431,x9431,x9432,x9433)),x9433)) % 1.58/1.66 [737]~P23(x7371)+~P33(f28(f28(f30(x7371),f4(x7371)),x7373))+~P33(f28(f28(f30(x7371),f4(x7371)),x7372))+P33(f28(f28(f30(x7371),f4(x7371)),f28(f28(f20(x7371),x7372),x7373))) % 1.58/1.66 [784]~P10(x7841,x7843)+~P33(f28(f28(f30(a2),f15(x7841,x7842)),f15(x7841,x7843)))+~P33(f28(f29(f96(x7841,a3),x7842),x7843))+P33(f28(f28(f30(f96(x7841,a3)),x7842),x7843)) % 1.58/1.66 [880]E(x8801,x8802)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8801),x8802)),x8803))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8802),x8801)),x8803))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8803),a8)) % 1.58/1.66 [621]~P26(x6211)+~P33(f28(f29(x6211,x6214),x6213))+P33(f28(f29(x6211,x6212),x6213))+~P33(f28(f29(x6211,x6212),x6214)) % 1.58/1.66 [622]~P20(x6221)+~P33(f28(f29(x6221,x6222),x6224))+P33(f28(f29(x6221,x6222),x6223))+~P33(f28(f29(x6221,x6224),x6223)) % 1.58/1.66 [809]~P10(x8092,x8093)+~P10(x8091,x8094)+P11(x8091,x8092,f80(x8093,x8092,x8094,x8091),x8094)+~P33(f28(f29(a2,f15(x8091,x8094)),f15(x8092,x8093))) % 1.58/1.66 [640]E(x6401,x6402)+~E(f36(x6403,x6404,x6401),f36(x6403,x6404,x6402))+P33(f28(f28(f35(x6403),x6404),x6402))+P33(f28(f28(f35(x6403),x6404),x6401)) % 1.58/1.66 [644]~P26(x6441)+~P33(f28(f29(x6441,x6442),x6444))+~P33(f28(f28(f30(x6441),x6444),x6443))+P33(f28(f28(f30(x6441),x6442),x6443)) % 1.58/1.66 [645]~P26(x6451)+~P33(f28(f29(x6451,x6454),x6453))+~P33(f28(f28(f30(x6451),x6452),x6454))+P33(f28(f28(f30(x6451),x6452),x6453)) % 1.58/1.66 [646]~P20(x6461)+~P33(f28(f29(x6461,x6464),x6463))+~P33(f28(f28(f30(x6461),x6462),x6464))+P33(f28(f28(f30(x6461),x6462),x6463)) % 1.58/1.66 [647]~P20(x6471)+~P33(f28(f29(x6471,x6472),x6474))+~P33(f28(f28(f30(x6471),x6474),x6473))+P33(f28(f28(f30(x6471),x6472),x6473)) % 1.58/1.66 [662]~P26(x6621)+~P33(f28(f28(f30(x6621),x6624),x6623))+P33(f28(f28(f30(x6621),x6622),x6623))+~P33(f28(f28(f30(x6621),x6622),x6624)) % 1.58/1.66 [663]~P20(x6631)+~P33(f28(f28(f30(x6631),x6632),x6634))+P33(f28(f28(f30(x6631),x6632),x6633))+~P33(f28(f28(f30(x6631),x6634),x6633)) % 1.58/1.66 [794]~E(x7943,x7941)+E(x7941,x7942)+E(x7943,x7942)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x7942),x7943)),f28(f28(a11,x7944),x7941))) % 1.58/1.66 [795]~E(x7953,x7951)+E(x7951,x7952)+E(x7953,x7952)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x7953),x7952)),f28(f28(a13,x7954),x7951))) % 1.58/1.66 [702]~P23(x7021)+~P33(f28(f29(x7021,x7022),x7023))+~P33(f28(f29(x7021,f4(x7021)),x7024))+P33(f28(f29(x7021,x7022),f28(f28(f20(x7021),x7023),x7024))) % 1.58/1.66 [703]~P23(x7031)+~P33(f28(f29(x7031,x7032),x7034))+~P33(f28(f29(x7031,f4(x7031)),x7033))+P33(f28(f29(x7031,x7032),f28(f28(f20(x7031),x7033),x7034))) % 1.58/1.66 [713]~P23(x7131)+~P33(f28(f29(x7131,x7132),x7134))+~P33(f28(f28(f30(x7131),f4(x7131)),x7133))+P33(f28(f28(f30(x7131),x7132),f28(f28(f20(x7131),x7133),x7134))) % 1.58/1.66 [714]~P23(x7141)+~P33(f28(f29(x7141,f4(x7141)),x7143))+~P33(f28(f28(f30(x7141),x7142),x7144))+P33(f28(f28(f30(x7141),x7142),f28(f28(f20(x7141),x7143),x7144))) % 1.58/1.66 [723]~P4(x7231)+~P33(f28(f28(f30(x7231),f4(x7231)),x7233))+~P33(f28(f28(f30(x7231),x7232),x7234))+P33(f28(f28(f30(x7231),x7232),f28(f28(f20(x7231),x7233),x7234))) % 1.58/1.66 [752]~P25(x7522)+~P33(f28(f29(f96(x7521,x7522),x7524),x7523))+P33(f28(f29(f96(x7521,x7522),x7523),x7524))+P33(f28(f28(f30(f96(x7521,x7522)),x7524),x7523)) % 1.58/1.66 [990]~P10(x9902,x9904)+~P10(x9901,x9903)+~P33(f28(f29(a2,f15(x9902,x9904)),f15(x9901,x9903)))+P33(f28(f29(f96(x9901,a3),f37(x9902,x9901,f80(x9903,x9901,x9904,x9902),x9904)),x9903)) % 1.58/1.66 [866]E(x8661,x8662)+E(x8663,x8662)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8663),x8661)),f28(f28(a11,x8664),x8662)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8663),x8661)),x8664)) % 1.58/1.66 [867]E(x8671,x8672)+E(x8673,x8672)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8673),x8671)),f28(f28(a13,x8674),x8672)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8673),x8671)),x8674)) % 1.58/1.66 [868]E(x8681,x8682)+E(x8683,x8681)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8683),x8681)),f28(f28(a13,x8684),x8682)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8683),x8681)),x8684)) % 1.58/1.66 [869]E(x8691,x8692)+E(x8691,x8693)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8691),x8693)),f28(f28(a11,x8694),x8692)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8691),x8693)),x8694)) % 1.58/1.66 [999]~P2(x9993)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9991),x9992)),f28(x9993,x9994)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9991),x9992)),f28(x9994,f64(x9993,x9994,x9991,x9992))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x9994),a9)) % 1.58/1.66 [833]~P21(x8331)+P33(f28(f29(x8331,x8332),x8333))+P33(f28(f29(x8331,x8334),x8333))+~P33(f28(f29(f96(x8331,a3),f32(x8331,x8333,x8332)),f32(x8331,x8334,x8335))) % 1.58/1.66 [834]~P21(x8341)+P33(f28(f29(x8341,x8342),x8343))+P33(f28(f29(x8341,x8342),x8344))+~P33(f28(f29(f96(x8341,a3),f32(x8341,x8343,x8342)),f32(x8341,x8345,x8344))) % 1.58/1.66 [942]~P10(x9423,x9424)+~P11(x9421,x9423,x9425,x9422)+P33(f28(f29(a2,f15(x9421,x9422)),f15(x9423,x9424)))+~P33(f28(f29(f96(x9423,a3),f37(x9421,x9423,x9425,x9422)),x9424)) % 1.58/1.66 [783]~P19(x7831)+~P33(f28(f29(x7831,x7833),x7835))+~P33(f28(f29(x7831,x7832),x7834))+P33(f28(f29(x7831,f28(f28(f20(x7831),x7832),x7833)),f28(f28(f20(x7831),x7834),x7835))) % 1.58/1.66 [789]~P5(x7891)+~P33(f28(f29(x7891,x7893),x7895))+~P33(f28(f28(f30(x7891),x7892),x7894))+P33(f28(f28(f30(x7891),f28(f28(f20(x7891),x7892),x7893)),f28(f28(f20(x7891),x7894),x7895))) % 1.58/1.66 [790]~P5(x7901)+~P33(f28(f29(x7901,x7902),x7904))+~P33(f28(f28(f30(x7901),x7903),x7905))+P33(f28(f28(f30(x7901),f28(f28(f20(x7901),x7902),x7903)),f28(f28(f20(x7901),x7904),x7905))) % 1.58/1.66 [797]~P5(x7971)+~P33(f28(f28(f30(x7971),x7973),x7975))+~P33(f28(f28(f30(x7971),x7972),x7974))+P33(f28(f28(f30(x7971),f28(f28(f20(x7971),x7972),x7973)),f28(f28(f20(x7971),x7974),x7975))) % 1.58/1.66 [882]~E(x8822,f28(x8823,x8821))+E(x8821,f73(x8822,x8823,x8824,x8825))+~P11(x8825,x8824,x8823,f31(f96(x8825,a3)))+~P33(f28(f28(f35(x8824),x8822),f37(x8825,x8824,x8823,f31(f96(x8825,a3))))) % 1.58/1.66 [878]E(x8781,x8782)+~E(x8783,x8784)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8783),x8784)),f14(x8785,x8781,x8782)))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8785),a8)) % 1.58/1.66 [889]E(x8891,x8892)+~E(x8893,x8894)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8893),x8894)),f28(f28(f28(a12,x8895),x8891),x8892)))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8895),a8)) % 1.58/1.66 [933]~P10(x9333,x9334)+~P11(x9331,x9333,x9335,x9332)+P33(f28(f29(a2,f15(x9331,x9332)),f15(x9333,x9334)))+~P33(f28(f28(f35(f96(x9331,x9333)),x9335),f18(x9331,x9333,x9332,f28(f16(f96(x9333,a3),x9331),x9334)))) % 1.58/1.66 [970]E(x9701,x9702)+~E(f28(f23(x9703,x9704,x9705,x9706),x9701),f28(f23(x9703,x9704,x9705,x9706),x9702))+~P33(f28(f28(f35(x9704),x9702),f37(x9703,x9704,x9706,x9705)))+~P33(f28(f28(f35(x9704),x9701),f37(x9703,x9704,x9706,x9705))) % 1.58/1.66 [801]~P11(x8011,x8012,x8014,x8013)+~E(f28(x8014,x8016),x8015)+E(f28(f23(x8011,x8012,x8013,x8014),x8015),x8016)+~P33(f28(f28(f35(x8011),x8016),x8013)) % 1.58/1.66 [1001]~P10(x10012,x10014)+~P13(x10017,x10012,x10015,x10018,x10016,x10011)+E(f28(x10011,f36(x10012,x10013,x10014)),f28(f28(x10015,f28(x10016,x10013)),f28(x10011,x10014)))+P33(f28(f28(f35(x10012),x10013),x10014)) % 1.58/1.66 [1092]E(a104,a102)+E(a107,a106)+P34(a5000)+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101)),a9)) % 1.58/1.66 [902]E(f28(a99,x9021),a108)+P33(f28(f28(f30(a2),f28(a99,x9021)),f28(f28(f20(a2),a108),f5(a2))))+P33(f28(f28(f30(a2),f28(a99,x9021)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a13,f28(a103,x9021)),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.66 [903]E(f28(a99,x9031),a108)+~P33(f28(f28(f30(a2),f28(a99,x9031)),f28(f28(f20(a2),a108),f5(a2))))+P33(f28(f28(f30(a2),f28(a99,x9031)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a13,f28(a103,x9031)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a100)) % 1.58/1.66 [930]~E(f28(a99,x9301),a108)+~P33(f28(f28(f30(a2),f28(a99,x9301)),f28(f28(f20(a2),a108),f5(a2))))+P33(f28(f28(f30(a2),f28(a99,x9301)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(f28(a12,f28(a103,x9301)),a105),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a100)) % 1.58/1.66 [940]~E(f28(a99,x9401),a108)+P33(f28(f28(f30(a2),f28(a99,x9401)),f28(f28(f20(a2),a108),f5(a2))))+P33(f28(f28(f30(a2),f28(a99,x9401)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(f28(a12,f28(a103,x9401)),a105),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.66 [965]E(f28(a99,x9651),a108)+P33(f28(f28(f30(a2),f28(a99,x9651)),f28(f28(f20(a2),a108),f5(a2))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a13,f28(a103,x9651)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a11,f28(a103,x9651)),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.66 [980]~E(f28(a99,x9801),a108)+P33(f28(f28(f30(a2),f28(a99,x9801)),f28(f28(f20(a2),a108),f5(a2))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a11,f28(a103,x9801)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(f28(a12,f28(a103,x9801)),a105),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.66 [982]P33(f28(f28(f30(a2),f28(a99,x9821)),f28(f28(f20(a2),a108),f5(a2))))+P33(f28(f28(f30(a2),f28(a99,x9821)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a13,f28(a103,x9821)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(f28(a12,f28(a103,x9821)),a105),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.66 [997]P33(f28(f28(f30(a2),f28(a99,x9971)),f28(f28(f20(a2),a108),f5(a2))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a13,f28(a103,x9971)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(a11,f28(a103,x9971)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a105),a107)),f28(f28(f28(a12,f28(a103,x9971)),a105),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a102),a104)),a101)) % 1.58/1.66 [660]~P23(x6602)+E(x6601,f4(x6602))+~E(f28(f28(f20(x6602),x6603),x6601),f4(x6602))+~P33(f28(f29(x6602,f4(x6602)),x6603))+~P33(f28(f29(x6602,f4(x6602)),x6601)) % 1.58/1.66 [661]~P23(x6612)+E(x6611,f4(x6612))+~E(f28(f28(f20(x6612),x6611),x6613),f4(x6612))+~P33(f28(f29(x6612,f4(x6612)),x6613))+~P33(f28(f29(x6612,f4(x6612)),x6611)) % 1.58/1.66 [679]~P21(x6793)+E(x6791,x6792)+~E(f32(x6793,x6794,x6791),f32(x6793,x6795,x6792))+~P33(f28(f28(f30(x6793),x6795),x6792))+~P33(f28(f28(f30(x6793),x6794),x6791)) % 1.58/1.66 [680]~P21(x6803)+E(x6801,x6802)+~E(f32(x6803,x6801,x6804),f32(x6803,x6802,x6805))+~P33(f28(f28(f30(x6803),x6802),x6805))+~P33(f28(f28(f30(x6803),x6801),x6804)) % 1.58/1.66 [920]E(x9201,x9202)+~E(x9205,x9201)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9203),x9205)),f14(x9204,x9201,x9202)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9203),x9202)),x9204))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9204),a8)) % 1.58/1.66 [936]E(x9361,x9362)+~E(x9365,x9361)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9365),x9363)),f28(f28(f28(a12,x9364),x9362),x9361)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9362),x9363)),x9364))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9364),a8)) % 1.58/1.66 [746]E(x7461,x7462)+~P11(x7464,x7465,x7463,x7466)+~E(f28(x7463,x7461),f28(x7463,x7462))+~P33(f28(f28(f35(x7464),x7462),x7466))+~P33(f28(f28(f35(x7464),x7461),x7466)) % 1.58/1.66 [1050]~P34(a5000)+~P33(f28(f28(f30(a2),f28(a99,a87)),a108))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a11,f28(a103,a87)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a100))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))))) % 1.58/1.66 [1071]~P34(a5000)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a11,f28(a103,a87)),a107)))+~P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a100))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101)))) % 1.58/1.66 [650]~P23(x6501)+~E(x6503,f4(x6501))+~E(x6502,f4(x6501))+E(f28(f28(f20(x6501),x6502),x6503),f4(x6501))+~P33(f28(f29(x6501,f4(x6501)),x6503))+~P33(f28(f29(x6501,f4(x6501)),x6502)) % 1.58/1.66 [908]~E(x9083,x9081)+E(x9081,x9082)+E(x9083,x9084)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9084),x9083)),f14(x9085,x9081,x9082)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9084),x9082)),x9085))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9085),a8)) % 1.58/1.66 [921]E(x9211,x9212)+E(x9211,x9213)+E(x9214,x9211)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9214),x9213)),f14(x9215,x9211,x9212)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9214),x9213)),x9215))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9215),a8)) % 1.58/1.66 [924]~E(x9243,x9241)+E(x9241,x9242)+E(x9243,x9244)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9243),x9244)),f28(f28(f28(a12,x9245),x9242),x9241)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9242),x9244)),x9245))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9245),a8)) % 1.58/1.66 [937]E(x9371,x9372)+E(x9371,x9373)+E(x9374,x9371)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9373),x9374)),f28(f28(f28(a12,x9375),x9372),x9371)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9373),x9374)),x9375))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9375),a8)) % 1.58/1.66 [1052]~P34(a5000)+E(f28(a99,a87),a108)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a13,f28(a103,a87)),a107)))+P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))))) % 1.58/1.66 [1054]~P34(a5000)+~E(f28(a99,a87),a108)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(f28(a12,f28(a103,a87)),a105),a107)))+P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107)))))) % 1.58/1.66 [1060]~P34(a5000)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(f28(a12,f28(a103,a87)),a105),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a13,f28(a103,a87)),a107)))+P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101)))) % 1.58/1.66 [1073]~P34(a5000)+E(f28(a99,a87),a108)+P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a13,f28(a103,a87)),a107)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101)) % 1.58/1.66 [1075]~P34(a5000)+~E(f28(a99,a87),a108)+P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(f28(a12,f28(a103,a87)),a105),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101)) % 1.58/1.66 [1081]~P34(a5000)+P33(f28(f28(f30(a2),f28(a99,a87)),a108))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(a13,f28(a103,a87)),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(f28(f28(a12,f28(a103,a87)),a105),a107)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),a101))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a107),a106)),f28(a1,f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a11),a103)),a107)),f17(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3),f17(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,a39),a99)),a108)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f28(f7(a92,a93,f96(a93,f96(f98(a93,a93),a3))),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(a93,f96(f98(a93,a93),a3))),a92,a12),a103)),a105)),a107)),f28(f28(f7(a92,a93,f96(f98(a93,a93),a3)),f28(f10(f96(f98(a93,a93),a3),f96(a93,f96(f98(a93,a93),a3)),a92,a13),a103)),a107))))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),a104),a102)),f28(a1,f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f98(a93,a93),a3)),f28(f28(f7(a92,f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),f28(f10(a3,f96(f96(f98(a93,a93),a3),f96(f96(f98(a93,a93),a3),f96(f98(a93,a93),a3))),a92,f24(f96(f98(a93,a93),a3))),f28(f28(f7(a92,a2,a3),f28(f10(a2,f96(a2,a3),a92,f30(a2)),a99)),a108))),a100)),a101)))) % 1.58/1.66 [1008]E(x10081,x10082)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10081),x10082)),f28(a1,x10084)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10082),x10081)),f28(a1,x10083)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10082),x10081)),f28(x10083,f68(x10083,x10084,x10082,x10081))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10081),x10082)),f28(x10084,f68(x10083,x10084,x10082,x10081))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10083),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10084),a9)) % 1.58/1.66 [1009]E(x10091,x10092)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10091),x10092)),f28(a1,x10094)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10092),x10091)),f28(a1,x10093)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10092),x10091)),f28(x10093,f68(x10094,x10093,x10091,x10092))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10091),x10092)),f28(x10094,f68(x10094,x10093,x10091,x10092))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10093),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10094),a9)) % 1.58/1.66 [1013]E(x10131,x10132)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10131),x10132)),f28(a1,x10134)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10132),x10131)),f28(a1,x10133)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10132),x10131)),f28(x10133,f68(x10133,x10134,x10132,x10131))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10131),x10132)),f28(x10134,f68(x10133,x10134,x10132,x10131))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10133),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10134),a9)) % 1.58/1.66 [1014]E(x10141,x10142)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10141),x10142)),f28(a1,x10144)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10142),x10141)),f28(a1,x10143)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10142),x10141)),f28(x10143,f68(x10144,x10143,x10141,x10142))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10141),x10142)),f28(x10144,f68(x10144,x10143,x10141,x10142))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10143),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10144),a9)) % 1.58/1.66 [856]~E(x8563,x8562)+~E(x8564,x8561)+E(x8561,x8562)+E(x8561,x8563)+E(x8564,x8563)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8564),x8563)),f14(x8565,x8561,x8562)))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8565),a8)) % 1.58/1.66 [859]~E(x8593,x8592)+~E(x8594,x8591)+E(x8591,x8592)+E(x8591,x8593)+E(x8594,x8593)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x8593),x8594)),f28(f28(f28(a12,x8595),x8592),x8591)))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x8595),a8)) % 1.58/1.66 [909]E(x9094,x9093)+E(x9091,x9092)+E(x9093,x9091)+E(x9094,x9091)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9094),x9093)),f14(x9095,x9091,x9092)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9094),x9093)),x9095))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9095),a8)) % 1.58/1.66 [910]~E(x9103,x9101)+E(x9101,x9102)+E(x9103,x9102)+E(x9104,x9103)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9104),x9103)),f14(x9105,x9102,x9101)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9104),x9103)),x9105))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9105),a8)) % 1.58/1.66 [911]~E(x9114,x9111)+E(x9111,x9112)+E(x9111,x9113)+E(x9114,x9112)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9114),x9112)),f14(x9115,x9111,x9113)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9113),x9112)),x9115))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9115),a8)) % 1.58/1.66 [912]~E(x9124,x9122)+~E(x9123,x9121)+E(x9121,x9122)+E(x9123,x9124)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9123),x9124)),f14(x9125,x9121,x9122)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9123),x9122)),x9125))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9125),a8)) % 1.58/1.66 [923]E(x9233,x9231)+E(x9231,x9232)+E(x9233,x9232)+~E(x9235,x9233)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9235),x9231)),f14(x9234,x9233,x9232)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9232),x9231)),x9234))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9234),a8)) % 1.58/1.66 [925]E(x9254,x9253)+E(x9251,x9252)+E(x9253,x9251)+E(x9254,x9251)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9254),x9253)),f28(f28(f28(a12,x9255),x9252),x9251)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9254),x9253)),x9255))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9255),a8)) % 1.58/1.66 [926]~E(x9263,x9261)+E(x9261,x9262)+E(x9263,x9262)+E(x9263,x9264)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9263),x9264)),f28(f28(f28(a12,x9265),x9261),x9262)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9263),x9264)),x9265))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9265),a8)) % 1.58/1.66 [927]~E(x9274,x9271)+E(x9271,x9272)+E(x9271,x9273)+E(x9274,x9273)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9273),x9274)),f28(f28(f28(a12,x9275),x9272),x9271)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9273),x9272)),x9275))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9275),a8)) % 1.58/1.66 [928]~E(x9284,x9282)+~E(x9283,x9281)+E(x9281,x9282)+E(x9283,x9284)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9284),x9283)),f28(f28(f28(a12,x9285),x9282),x9281)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9282),x9283)),x9285))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9285),a8)) % 1.58/1.66 [938]E(x9383,x9381)+E(x9381,x9382)+E(x9383,x9382)+~E(x9385,x9383)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9381),x9385)),f28(f28(f28(a12,x9384),x9382),x9383)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9381),x9382)),x9384))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9384),a8)) % 1.58/1.66 [961]E(x9611,x9612)+E(x9613,x9612)+E(x9614,x9613)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9614),x9613)),f14(x9615,x9612,x9611)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9614),x9613)),x9615))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9611),x9613)),x9615))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9615),a8)) % 1.58/1.66 [962]E(x9621,x9622)+E(x9623,x9621)+E(x9623,x9624)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9623),x9624)),f14(x9625,x9621,x9622)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9623),x9624)),x9625))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9623),x9622)),x9625))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9625),a8)) % 1.58/1.66 [963]~E(x9634,x9631)+E(x9631,x9632)+E(x9633,x9634)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9633),x9634)),f14(x9635,x9632,x9631)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9633),x9634)),x9635))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9633),x9631)),x9635))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9635),a8)) % 1.58/1.66 [964]~E(x9643,x9641)+E(x9641,x9642)+E(x9643,x9644)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9643),x9644)),f14(x9645,x9641,x9642)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9642),x9644)),x9645))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9643),x9642)),x9645))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9645),a8)) % 1.58/1.66 [966]E(x9661,x9662)+E(x9663,x9661)+E(x9664,x9663)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9664),x9663)),f28(f28(f28(a12,x9665),x9662),x9661)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9664),x9663)),x9665))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9662),x9663)),x9665))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9665),a8)) % 1.58/1.66 [967]E(x9671,x9672)+E(x9673,x9672)+E(x9673,x9674)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9673),x9674)),f28(f28(f28(a12,x9675),x9671),x9672)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9673),x9674)),x9675))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9673),x9671)),x9675))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9675),a8)) % 1.58/1.66 [968]~E(x9683,x9681)+E(x9681,x9682)+E(x9683,x9684)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9683),x9684)),f28(f28(f28(a12,x9685),x9681),x9682)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9683),x9684)),x9685))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9681),x9684)),x9685))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9685),a8)) % 1.58/1.66 [969]~E(x9693,x9691)+E(x9691,x9692)+E(x9693,x9694)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9694),x9693)),f28(f28(f28(a12,x9695),x9692),x9691)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9692),x9693)),x9695))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9694),x9692)),x9695))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9695),a8)) % 1.58/1.66 [988]E(x9881,x9882)+E(x9883,x9884)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9883),x9884)),f14(x9885,x9882,x9881)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9883),x9884)),x9885))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9881),x9884)),x9885))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9883),x9881)),x9885))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9885),a8)) % 1.58/1.66 [989]E(x9891,x9892)+E(x9893,x9894)+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9893),x9894)),f28(f28(f28(a12,x9895),x9891),x9892)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9893),x9894)),x9895))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9891),x9894)),x9895))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x9893),x9891)),x9895))+~P33(f28(f28(f35(f96(f98(a93,a93),a3)),x9895),a8)) % 1.58/1.66 [1022]~P1(x10223)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10221),x10222)),f28(x10223,x10225)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10221),x10222)),f28(x10223,x10224)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10221),x10222)),f28(x10225,f56(x10223,x10224,x10225,x10221,x10222))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10221),x10222)),f28(x10224,f56(x10223,x10224,x10225,x10221,x10222))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10224),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10225),a9)) % 1.58/1.66 [1023]~P1(x10233)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10231),x10232)),f28(x10233,x10235)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10231),x10232)),f28(x10233,x10234)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10231),x10232)),f28(x10235,f56(x10233,x10235,x10234,x10231,x10232))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10231),x10232)),f28(x10234,f56(x10233,x10235,x10234,x10231,x10232))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10234),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10235),a9)) % 1.58/1.66 [1026]~P1(x10263)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10261),x10262)),f28(x10263,x10265)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10261),x10262)),f28(x10263,x10264)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10261),x10262)),f28(x10265,f56(x10263,x10264,x10265,x10261,x10262))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10261),x10262)),f28(x10264,f56(x10263,x10264,x10265,x10261,x10262))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10264),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10265),a9)) % 1.58/1.66 [1027]~P1(x10273)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10271),x10272)),f28(x10273,x10275)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10271),x10272)),f28(x10273,x10274)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10271),x10272)),f28(x10275,f56(x10273,x10275,x10274,x10271,x10272))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10271),x10272)),f28(x10274,f56(x10273,x10275,x10274,x10271,x10272))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10274),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10275),a9)) % 1.58/1.66 [1000]~P10(x10003,x10004)+~P10(x10001,x10002)+~P11(x10003,x10001,x10005,x10004)+~P11(x10001,x10003,x10006,x10002)+E(f15(x10001,x10002),f15(x10003,x10004))+~P33(f28(f29(f96(x10003,a3),f37(x10001,x10003,x10006,x10002)),x10004))+~P33(f28(f29(f96(x10001,a3),f37(x10003,x10001,x10005,x10004)),x10002)) % 1.58/1.66 [994]~P10(x9943,x9944)+~P10(x9941,x9942)+~P11(x9943,x9941,x9945,x9944)+~P11(x9941,x9943,x9946,x9942)+E(f15(x9941,x9942),f15(x9943,x9944))+~P33(f28(f28(f35(f96(x9943,x9941)),x9945),f18(x9943,x9941,x9944,f28(f16(f96(x9941,a3),x9943),x9942))))+~P33(f28(f28(f35(f96(x9941,x9943)),x9946),f18(x9941,x9943,x9942,f28(f16(f96(x9943,a3),x9941),x9944)))) % 1.58/1.66 [1030]E(x10301,x10302)+E(x10303,x10304)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10303),x10304)),f28(a1,x10306)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10301),x10302)),f28(a1,x10305)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10301),x10302)),f28(x10305,f81(x10305,x10306,x10302,x10301,x10304,x10303))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10303),x10304)),f28(x10306,f81(x10305,x10306,x10302,x10301,x10304,x10303))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10305),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10306),a9)) % 1.58/1.66 [1031]E(x10311,x10312)+E(x10313,x10314)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10313),x10314)),f28(a1,x10316)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10311),x10312)),f28(a1,x10315)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10311),x10312)),f28(x10315,f81(x10316,x10315,x10314,x10313,x10312,x10311))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10313),x10314)),f28(x10316,f81(x10316,x10315,x10314,x10313,x10312,x10311))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10315),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10316),a9)) % 1.58/1.66 [1036]E(x10361,x10362)+E(x10363,x10364)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10363),x10364)),f28(a1,x10366)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10361),x10362)),f28(a1,x10365)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10361),x10362)),f28(x10365,f81(x10365,x10366,x10362,x10361,x10364,x10363))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10363),x10364)),f28(x10366,f81(x10365,x10366,x10362,x10361,x10364,x10363))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10365),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10366),a9)) % 1.58/1.66 [1037]E(x10371,x10372)+E(x10373,x10374)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10373),x10374)),f28(a1,x10376)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10371),x10372)),f28(a1,x10375)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10371),x10372)),f28(x10375,f81(x10376,x10375,x10374,x10373,x10372,x10371))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10373),x10374)),f28(x10376,f81(x10376,x10375,x10374,x10373,x10372,x10371))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10375),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10376),a9)) % 1.58/1.66 [1020]E(x10203,x10201)+E(x10201,x10202)+E(x10203,x10202)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10203),x10201)),f28(a1,x10205)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10202),x10203)),f28(a1,x10204)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10202),x10203)),f28(x10204,f86(x10205,x10204,x10201,x10203,x10202))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10203),x10201)),f28(x10205,f86(x10205,x10204,x10201,x10203,x10202))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10204),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10205),a9)) % 1.58/1.66 [1021]E(x10213,x10211)+E(x10211,x10212)+E(x10213,x10212)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10213),x10211)),f28(a1,x10215)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10211),x10212)),f28(a1,x10214)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10211),x10212)),f28(x10214,f86(x10214,x10215,x10212,x10211,x10213))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10213),x10211)),f28(x10215,f86(x10214,x10215,x10212,x10211,x10213))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10214),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10215),a9)) % 1.58/1.66 [1024]E(x10243,x10241)+E(x10241,x10242)+E(x10243,x10242)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10243),x10241)),f28(a1,x10245)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10242),x10243)),f28(a1,x10244)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10242),x10243)),f28(x10244,f86(x10245,x10244,x10241,x10243,x10242))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10243),x10241)),f28(x10245,f86(x10245,x10244,x10241,x10243,x10242))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10244),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10245),a9)) % 1.58/1.66 [1025]E(x10253,x10251)+E(x10251,x10252)+E(x10253,x10252)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10253),x10251)),f28(a1,x10255)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10251),x10252)),f28(a1,x10254)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10251),x10252)),f28(x10254,f86(x10254,x10255,x10252,x10251,x10253))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10253),x10251)),f28(x10255,f86(x10254,x10255,x10252,x10251,x10253))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10254),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10255),a9)) % 1.58/1.66 [1032]E(x10324,x10323)+E(x10321,x10322)+E(x10323,x10322)+E(x10324,x10321)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10324),x10323)),f28(a1,x10326)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10322),x10321)),f28(a1,x10325)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10322),x10321)),f28(x10325,f88(x10325,x10326,x10321,x10322,x10323,x10324))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10324),x10323)),f28(x10326,f88(x10325,x10326,x10321,x10322,x10323,x10324))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10325),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10326),a9)) % 1.58/1.66 [1033]E(x10334,x10333)+E(x10331,x10332)+E(x10333,x10331)+E(x10334,x10332)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10334),x10333)),f28(a1,x10336)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10331),x10332)),f28(a1,x10335)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10331),x10332)),f28(x10335,f89(x10335,x10336,x10332,x10331,x10333,x10334))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10334),x10333)),f28(x10336,f89(x10335,x10336,x10332,x10331,x10333,x10334))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10335),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10336),a9)) % 1.58/1.66 [1034]E(x10344,x10343)+E(x10341,x10342)+E(x10343,x10341)+E(x10344,x10342)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10344),x10343)),f28(a1,x10346)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10341),x10342)),f28(a1,x10345)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10341),x10342)),f28(x10345,f89(x10346,x10345,x10343,x10344,x10342,x10341))))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10344),x10343)),f28(x10346,f89(x10346,x10345,x10343,x10344,x10342,x10341))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10345),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10346),a9)) % 1.58/1.66 [1038]E(x10384,x10383)+E(x10381,x10382)+E(x10383,x10382)+E(x10384,x10381)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10384),x10383)),f28(a1,x10386)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10382),x10381)),f28(a1,x10385)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10382),x10381)),f28(x10385,f88(x10385,x10386,x10381,x10382,x10383,x10384))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10384),x10383)),f28(x10386,f88(x10385,x10386,x10381,x10382,x10383,x10384))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10385),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10386),a9)) % 1.58/1.66 [1039]E(x10394,x10393)+E(x10391,x10392)+E(x10393,x10391)+E(x10394,x10392)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10394),x10393)),f28(a1,x10396)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10391),x10392)),f28(a1,x10395)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10391),x10392)),f28(x10395,f89(x10395,x10396,x10392,x10391,x10393,x10394))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10394),x10393)),f28(x10396,f89(x10395,x10396,x10392,x10391,x10393,x10394))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10395),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10396),a9)) % 1.58/1.66 [1040]E(x10404,x10403)+E(x10401,x10402)+E(x10403,x10401)+E(x10404,x10402)+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10404),x10403)),f28(a1,x10406)))+P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10401),x10402)),f28(a1,x10405)))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10401),x10402)),f28(x10405,f89(x10406,x10405,x10403,x10404,x10402,x10401))))+~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x10404),x10403)),f28(x10406,f89(x10406,x10405,x10403,x10404,x10402,x10401))))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10405),a9))+~P33(f28(f28(f35(f96(a92,f96(f98(a93,a93),a3))),x10406),a9)) % 1.58/1.66 %EqnAxiom % 1.58/1.66 [1]E(x11,x11) % 1.58/1.66 [2]E(x22,x21)+~E(x21,x22) % 1.58/1.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.58/1.66 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 1.58/1.66 [5]~E(x51,x52)+E(f21(x51),f21(x52)) % 1.58/1.66 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63)) % 1.58/1.66 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72)) % 1.58/1.66 [8]~E(x81,x82)+E(f27(x81,x83),f27(x82,x83)) % 1.58/1.66 [9]~E(x91,x92)+E(f27(x93,x91),f27(x93,x92)) % 1.58/1.66 [10]~E(x101,x102)+E(f96(x101,x103),f96(x102,x103)) % 1.58/1.66 [11]~E(x111,x112)+E(f96(x113,x111),f96(x113,x112)) % 1.58/1.66 [12]~E(x121,x122)+E(f98(x121,x123),f98(x122,x123)) % 1.58/1.66 [13]~E(x131,x132)+E(f98(x133,x131),f98(x133,x132)) % 1.58/1.66 [14]~E(x141,x142)+E(f5(x141),f5(x142)) % 1.58/1.66 [15]~E(x151,x152)+E(f17(x151,x153,x154,x155,x156),f17(x152,x153,x154,x155,x156)) % 1.58/1.66 [16]~E(x161,x162)+E(f17(x163,x161,x164,x165,x166),f17(x163,x162,x164,x165,x166)) % 1.58/1.66 [17]~E(x171,x172)+E(f17(x173,x174,x171,x175,x176),f17(x173,x174,x172,x175,x176)) % 1.58/1.66 [18]~E(x181,x182)+E(f17(x183,x184,x185,x181,x186),f17(x183,x184,x185,x182,x186)) % 1.58/1.66 [19]~E(x191,x192)+E(f17(x193,x194,x195,x196,x191),f17(x193,x194,x195,x196,x192)) % 1.58/1.66 [20]~E(x201,x202)+E(f35(x201),f35(x202)) % 1.58/1.66 [21]~E(x211,x212)+E(f33(x211,x213),f33(x212,x213)) % 1.58/1.66 [22]~E(x221,x222)+E(f33(x223,x221),f33(x223,x222)) % 1.58/1.66 [23]~E(x231,x232)+E(f6(x231),f6(x232)) % 1.58/1.66 [24]~E(x241,x242)+E(f10(x241,x243,x244,x245),f10(x242,x243,x244,x245)) % 1.58/1.66 [25]~E(x251,x252)+E(f10(x253,x251,x254,x255),f10(x253,x252,x254,x255)) % 1.58/1.66 [26]~E(x261,x262)+E(f10(x263,x264,x261,x265),f10(x263,x264,x262,x265)) % 1.58/1.66 [27]~E(x271,x272)+E(f10(x273,x274,x275,x271),f10(x273,x274,x275,x272)) % 1.58/1.66 [28]~E(x281,x282)+E(f20(x281),f20(x282)) % 1.58/1.66 [29]~E(x291,x292)+E(f91(x291,x293,x294,x295),f91(x292,x293,x294,x295)) % 1.58/1.66 [30]~E(x301,x302)+E(f91(x303,x301,x304,x305),f91(x303,x302,x304,x305)) % 1.58/1.66 [31]~E(x311,x312)+E(f91(x313,x314,x311,x315),f91(x313,x314,x312,x315)) % 1.58/1.66 [32]~E(x321,x322)+E(f91(x323,x324,x325,x321),f91(x323,x324,x325,x322)) % 1.58/1.66 [33]~E(x331,x332)+E(f7(x331,x333,x334),f7(x332,x333,x334)) % 1.58/1.66 [34]~E(x341,x342)+E(f7(x343,x341,x344),f7(x343,x342,x344)) % 1.58/1.66 [35]~E(x351,x352)+E(f7(x353,x354,x351),f7(x353,x354,x352)) % 1.58/1.66 [36]~E(x361,x362)+E(f29(x361,x363),f29(x362,x363)) % 1.58/1.66 [37]~E(x371,x372)+E(f29(x373,x371),f29(x373,x372)) % 1.58/1.66 [38]~E(x381,x382)+E(f30(x381),f30(x382)) % 1.58/1.66 [39]~E(x391,x392)+E(f16(x391,x393),f16(x392,x393)) % 1.58/1.66 [40]~E(x401,x402)+E(f16(x403,x401),f16(x403,x402)) % 1.58/1.66 [41]~E(x411,x412)+E(f88(x411,x413,x414,x415,x416,x417),f88(x412,x413,x414,x415,x416,x417)) % 1.58/1.66 [42]~E(x421,x422)+E(f88(x423,x421,x424,x425,x426,x427),f88(x423,x422,x424,x425,x426,x427)) % 1.58/1.66 [43]~E(x431,x432)+E(f88(x433,x434,x431,x435,x436,x437),f88(x433,x434,x432,x435,x436,x437)) % 1.58/1.66 [44]~E(x441,x442)+E(f88(x443,x444,x445,x441,x446,x447),f88(x443,x444,x445,x442,x446,x447)) % 1.58/1.66 [45]~E(x451,x452)+E(f88(x453,x454,x455,x456,x451,x457),f88(x453,x454,x455,x456,x452,x457)) % 1.58/1.66 [46]~E(x461,x462)+E(f88(x463,x464,x465,x466,x467,x461),f88(x463,x464,x465,x466,x467,x462)) % 1.58/1.66 [47]~E(x471,x472)+E(f24(x471),f24(x472)) % 1.58/1.66 [48]~E(x481,x482)+E(f31(x481),f31(x482)) % 1.58/1.66 [49]~E(x491,x492)+E(f65(x491),f65(x492)) % 1.58/1.66 [50]~E(x501,x502)+E(f38(x501,x503,x504,x505),f38(x502,x503,x504,x505)) % 1.58/1.66 [51]~E(x511,x512)+E(f38(x513,x511,x514,x515),f38(x513,x512,x514,x515)) % 1.58/1.66 [52]~E(x521,x522)+E(f38(x523,x524,x521,x525),f38(x523,x524,x522,x525)) % 1.58/1.66 [53]~E(x531,x532)+E(f38(x533,x534,x535,x531),f38(x533,x534,x535,x532)) % 1.58/1.66 [54]~E(x541,x542)+E(f32(x541,x543,x544),f32(x542,x543,x544)) % 1.58/1.66 [55]~E(x551,x552)+E(f32(x553,x551,x554),f32(x553,x552,x554)) % 1.58/1.66 [56]~E(x561,x562)+E(f32(x563,x564,x561),f32(x563,x564,x562)) % 1.58/1.66 [57]~E(x571,x572)+E(f37(x571,x573,x574,x575),f37(x572,x573,x574,x575)) % 1.58/1.66 [58]~E(x581,x582)+E(f37(x583,x581,x584,x585),f37(x583,x582,x584,x585)) % 1.58/1.66 [59]~E(x591,x592)+E(f37(x593,x594,x591,x595),f37(x593,x594,x592,x595)) % 1.58/1.66 [60]~E(x601,x602)+E(f37(x603,x604,x605,x601),f37(x603,x604,x605,x602)) % 1.58/1.66 [61]~E(x611,x612)+E(f15(x611,x613),f15(x612,x613)) % 1.58/1.66 [62]~E(x621,x622)+E(f15(x623,x621),f15(x623,x622)) % 1.58/1.66 [63]~E(x631,x632)+E(f54(x631,x633),f54(x632,x633)) % 1.58/1.66 [64]~E(x641,x642)+E(f54(x643,x641),f54(x643,x642)) % 1.58/1.66 [65]~E(x651,x652)+E(f18(x651,x653,x654,x655),f18(x652,x653,x654,x655)) % 1.58/1.66 [66]~E(x661,x662)+E(f18(x663,x661,x664,x665),f18(x663,x662,x664,x665)) % 1.58/1.66 [67]~E(x671,x672)+E(f18(x673,x674,x671,x675),f18(x673,x674,x672,x675)) % 1.58/1.66 [68]~E(x681,x682)+E(f18(x683,x684,x685,x681),f18(x683,x684,x685,x682)) % 1.58/1.66 [69]~E(x691,x692)+E(f76(x691,x693,x694,x695,x696),f76(x692,x693,x694,x695,x696)) % 1.58/1.66 [70]~E(x701,x702)+E(f76(x703,x701,x704,x705,x706),f76(x703,x702,x704,x705,x706)) % 1.58/1.66 [71]~E(x711,x712)+E(f76(x713,x714,x711,x715,x716),f76(x713,x714,x712,x715,x716)) % 1.58/1.66 [72]~E(x721,x722)+E(f76(x723,x724,x725,x721,x726),f76(x723,x724,x725,x722,x726)) % 1.58/1.66 [73]~E(x731,x732)+E(f76(x733,x734,x735,x736,x731),f76(x733,x734,x735,x736,x732)) % 1.58/1.66 [74]~E(x741,x742)+E(f36(x741,x743,x744),f36(x742,x743,x744)) % 1.58/1.66 [75]~E(x751,x752)+E(f36(x753,x751,x754),f36(x753,x752,x754)) % 1.58/1.66 [76]~E(x761,x762)+E(f36(x763,x764,x761),f36(x763,x764,x762)) % 1.58/1.66 [77]~E(x771,x772)+E(f49(x771,x773),f49(x772,x773)) % 1.58/1.66 [78]~E(x781,x782)+E(f49(x783,x781),f49(x783,x782)) % 1.58/1.66 [79]~E(x791,x792)+E(f86(x791,x793,x794,x795,x796),f86(x792,x793,x794,x795,x796)) % 1.58/1.66 [80]~E(x801,x802)+E(f86(x803,x801,x804,x805,x806),f86(x803,x802,x804,x805,x806)) % 1.58/1.66 [81]~E(x811,x812)+E(f86(x813,x814,x811,x815,x816),f86(x813,x814,x812,x815,x816)) % 1.58/1.66 [82]~E(x821,x822)+E(f86(x823,x824,x825,x821,x826),f86(x823,x824,x825,x822,x826)) % 1.58/1.66 [83]~E(x831,x832)+E(f86(x833,x834,x835,x836,x831),f86(x833,x834,x835,x836,x832)) % 1.58/1.66 [84]~E(x841,x842)+E(f97(x841,x843),f97(x842,x843)) % 1.58/1.66 [85]~E(x851,x852)+E(f97(x853,x851),f97(x853,x852)) % 1.58/1.66 [86]~E(x861,x862)+E(f56(x861,x863,x864,x865,x866),f56(x862,x863,x864,x865,x866)) % 1.58/1.66 [87]~E(x871,x872)+E(f56(x873,x871,x874,x875,x876),f56(x873,x872,x874,x875,x876)) % 1.58/1.66 [88]~E(x881,x882)+E(f56(x883,x884,x881,x885,x886),f56(x883,x884,x882,x885,x886)) % 1.58/1.66 [89]~E(x891,x892)+E(f56(x893,x894,x895,x891,x896),f56(x893,x894,x895,x892,x896)) % 1.58/1.66 [90]~E(x901,x902)+E(f56(x903,x904,x905,x906,x901),f56(x903,x904,x905,x906,x902)) % 1.58/1.66 [91]~E(x911,x912)+E(f14(x911,x913,x914),f14(x912,x913,x914)) % 1.58/1.66 [92]~E(x921,x922)+E(f14(x923,x921,x924),f14(x923,x922,x924)) % 1.58/1.66 [93]~E(x931,x932)+E(f14(x933,x934,x931),f14(x933,x934,x932)) % 1.58/1.66 [94]~E(x941,x942)+E(f23(x941,x943,x944,x945),f23(x942,x943,x944,x945)) % 1.58/1.66 [95]~E(x951,x952)+E(f23(x953,x951,x954,x955),f23(x953,x952,x954,x955)) % 1.58/1.66 [96]~E(x961,x962)+E(f23(x963,x964,x961,x965),f23(x963,x964,x962,x965)) % 1.58/1.66 [97]~E(x971,x972)+E(f23(x973,x974,x975,x971),f23(x973,x974,x975,x972)) % 1.58/1.66 [98]~E(x981,x982)+E(f19(x981,x983,x984,x985,x986,x987),f19(x982,x983,x984,x985,x986,x987)) % 1.58/1.66 [99]~E(x991,x992)+E(f19(x993,x991,x994,x995,x996,x997),f19(x993,x992,x994,x995,x996,x997)) % 1.58/1.66 [100]~E(x1001,x1002)+E(f19(x1003,x1004,x1001,x1005,x1006,x1007),f19(x1003,x1004,x1002,x1005,x1006,x1007)) % 1.58/1.66 [101]~E(x1011,x1012)+E(f19(x1013,x1014,x1015,x1011,x1016,x1017),f19(x1013,x1014,x1015,x1012,x1016,x1017)) % 1.58/1.66 [102]~E(x1021,x1022)+E(f19(x1023,x1024,x1025,x1026,x1021,x1027),f19(x1023,x1024,x1025,x1026,x1022,x1027)) % 1.58/1.66 [103]~E(x1031,x1032)+E(f19(x1033,x1034,x1035,x1036,x1037,x1031),f19(x1033,x1034,x1035,x1036,x1037,x1032)) % 1.58/1.66 [104]~E(x1041,x1042)+E(f42(x1041),f42(x1042)) % 1.58/1.66 [105]~E(x1051,x1052)+E(f50(x1051,x1053,x1054,x1055),f50(x1052,x1053,x1054,x1055)) % 1.58/1.66 [106]~E(x1061,x1062)+E(f50(x1063,x1061,x1064,x1065),f50(x1063,x1062,x1064,x1065)) % 1.58/1.66 [107]~E(x1071,x1072)+E(f50(x1073,x1074,x1071,x1075),f50(x1073,x1074,x1072,x1075)) % 1.58/1.66 [108]~E(x1081,x1082)+E(f50(x1083,x1084,x1085,x1081),f50(x1083,x1084,x1085,x1082)) % 1.58/1.66 [109]~E(x1091,x1092)+E(f59(x1091),f59(x1092)) % 1.58/1.66 [110]~E(x1101,x1102)+E(f80(x1101,x1103,x1104,x1105),f80(x1102,x1103,x1104,x1105)) % 1.58/1.66 [111]~E(x1111,x1112)+E(f80(x1113,x1111,x1114,x1115),f80(x1113,x1112,x1114,x1115)) % 1.58/1.66 [112]~E(x1121,x1122)+E(f80(x1123,x1124,x1121,x1125),f80(x1123,x1124,x1122,x1125)) % 1.58/1.66 [113]~E(x1131,x1132)+E(f80(x1133,x1134,x1135,x1131),f80(x1133,x1134,x1135,x1132)) % 1.58/1.66 [114]~E(x1141,x1142)+E(f51(x1141,x1143,x1144,x1145),f51(x1142,x1143,x1144,x1145)) % 1.58/1.66 [115]~E(x1151,x1152)+E(f51(x1153,x1151,x1154,x1155),f51(x1153,x1152,x1154,x1155)) % 1.58/1.66 [116]~E(x1161,x1162)+E(f51(x1163,x1164,x1161,x1165),f51(x1163,x1164,x1162,x1165)) % 1.58/1.66 [117]~E(x1171,x1172)+E(f51(x1173,x1174,x1175,x1171),f51(x1173,x1174,x1175,x1172)) % 1.58/1.66 [118]~E(x1181,x1182)+E(f25(x1181),f25(x1182)) % 1.58/1.66 [119]~E(x1191,x1192)+E(f89(x1191,x1193,x1194,x1195,x1196,x1197),f89(x1192,x1193,x1194,x1195,x1196,x1197)) % 1.58/1.66 [120]~E(x1201,x1202)+E(f89(x1203,x1201,x1204,x1205,x1206,x1207),f89(x1203,x1202,x1204,x1205,x1206,x1207)) % 1.58/1.66 [121]~E(x1211,x1212)+E(f89(x1213,x1214,x1211,x1215,x1216,x1217),f89(x1213,x1214,x1212,x1215,x1216,x1217)) % 1.58/1.66 [122]~E(x1221,x1222)+E(f89(x1223,x1224,x1225,x1221,x1226,x1227),f89(x1223,x1224,x1225,x1222,x1226,x1227)) % 1.58/1.66 [123]~E(x1231,x1232)+E(f89(x1233,x1234,x1235,x1236,x1231,x1237),f89(x1233,x1234,x1235,x1236,x1232,x1237)) % 1.58/1.66 [124]~E(x1241,x1242)+E(f89(x1243,x1244,x1245,x1246,x1247,x1241),f89(x1243,x1244,x1245,x1246,x1247,x1242)) % 1.58/1.66 [125]~E(x1251,x1252)+E(f53(x1251,x1253),f53(x1252,x1253)) % 1.58/1.66 [126]~E(x1261,x1262)+E(f53(x1263,x1261),f53(x1263,x1262)) % 1.58/1.66 [127]~E(x1271,x1272)+E(f81(x1271,x1273,x1274,x1275,x1276,x1277),f81(x1272,x1273,x1274,x1275,x1276,x1277)) % 1.58/1.66 [128]~E(x1281,x1282)+E(f81(x1283,x1281,x1284,x1285,x1286,x1287),f81(x1283,x1282,x1284,x1285,x1286,x1287)) % 1.58/1.66 [129]~E(x1291,x1292)+E(f81(x1293,x1294,x1291,x1295,x1296,x1297),f81(x1293,x1294,x1292,x1295,x1296,x1297)) % 1.58/1.66 [130]~E(x1301,x1302)+E(f81(x1303,x1304,x1305,x1301,x1306,x1307),f81(x1303,x1304,x1305,x1302,x1306,x1307)) % 1.58/1.66 [131]~E(x1311,x1312)+E(f81(x1313,x1314,x1315,x1316,x1311,x1317),f81(x1313,x1314,x1315,x1316,x1312,x1317)) % 1.58/1.66 [132]~E(x1321,x1322)+E(f81(x1323,x1324,x1325,x1326,x1327,x1321),f81(x1323,x1324,x1325,x1326,x1327,x1322)) % 1.58/1.66 [133]~E(x1331,x1332)+E(f82(x1331,x1333),f82(x1332,x1333)) % 1.58/1.66 [134]~E(x1341,x1342)+E(f82(x1343,x1341),f82(x1343,x1342)) % 1.58/1.66 [135]~E(x1351,x1352)+E(f61(x1351),f61(x1352)) % 1.58/1.66 [136]~E(x1361,x1362)+E(f67(x1361,x1363,x1364,x1365,x1366),f67(x1362,x1363,x1364,x1365,x1366)) % 1.58/1.66 [137]~E(x1371,x1372)+E(f67(x1373,x1371,x1374,x1375,x1376),f67(x1373,x1372,x1374,x1375,x1376)) % 1.58/1.66 [138]~E(x1381,x1382)+E(f67(x1383,x1384,x1381,x1385,x1386),f67(x1383,x1384,x1382,x1385,x1386)) % 1.58/1.66 [139]~E(x1391,x1392)+E(f67(x1393,x1394,x1395,x1391,x1396),f67(x1393,x1394,x1395,x1392,x1396)) % 1.58/1.66 [140]~E(x1401,x1402)+E(f67(x1403,x1404,x1405,x1406,x1401),f67(x1403,x1404,x1405,x1406,x1402)) % 1.58/1.66 [141]~E(x1411,x1412)+E(f73(x1411,x1413,x1414,x1415),f73(x1412,x1413,x1414,x1415)) % 1.58/1.66 [142]~E(x1421,x1422)+E(f73(x1423,x1421,x1424,x1425),f73(x1423,x1422,x1424,x1425)) % 1.58/1.66 [143]~E(x1431,x1432)+E(f73(x1433,x1434,x1431,x1435),f73(x1433,x1434,x1432,x1435)) % 1.58/1.66 [144]~E(x1441,x1442)+E(f73(x1443,x1444,x1445,x1441),f73(x1443,x1444,x1445,x1442)) % 1.58/1.66 [145]~E(x1451,x1452)+E(f95(x1451),f95(x1452)) % 1.58/1.66 [146]~E(x1461,x1462)+E(f43(x1461,x1463,x1464,x1465),f43(x1462,x1463,x1464,x1465)) % 1.58/1.66 [147]~E(x1471,x1472)+E(f43(x1473,x1471,x1474,x1475),f43(x1473,x1472,x1474,x1475)) % 1.58/1.66 [148]~E(x1481,x1482)+E(f43(x1483,x1484,x1481,x1485),f43(x1483,x1484,x1482,x1485)) % 1.58/1.66 [149]~E(x1491,x1492)+E(f43(x1493,x1494,x1495,x1491),f43(x1493,x1494,x1495,x1492)) % 1.58/1.66 [150]~E(x1501,x1502)+E(f62(x1501),f62(x1502)) % 1.58/1.66 [151]~E(x1511,x1512)+E(f72(x1511,x1513,x1514,x1515),f72(x1512,x1513,x1514,x1515)) % 1.58/1.66 [152]~E(x1521,x1522)+E(f72(x1523,x1521,x1524,x1525),f72(x1523,x1522,x1524,x1525)) % 1.58/1.66 [153]~E(x1531,x1532)+E(f72(x1533,x1534,x1531,x1535),f72(x1533,x1534,x1532,x1535)) % 1.58/1.66 [154]~E(x1541,x1542)+E(f72(x1543,x1544,x1545,x1541),f72(x1543,x1544,x1545,x1542)) % 1.58/1.66 [155]~E(x1551,x1552)+E(f63(x1551),f63(x1552)) % 1.58/1.66 [156]~E(x1561,x1562)+E(f60(x1561),f60(x1562)) % 1.58/1.66 [157]~E(x1571,x1572)+E(f68(x1571,x1573,x1574,x1575),f68(x1572,x1573,x1574,x1575)) % 1.58/1.66 [158]~E(x1581,x1582)+E(f68(x1583,x1581,x1584,x1585),f68(x1583,x1582,x1584,x1585)) % 1.58/1.66 [159]~E(x1591,x1592)+E(f68(x1593,x1594,x1591,x1595),f68(x1593,x1594,x1592,x1595)) % 1.58/1.66 [160]~E(x1601,x1602)+E(f68(x1603,x1604,x1605,x1601),f68(x1603,x1604,x1605,x1602)) % 1.58/1.66 [161]~E(x1611,x1612)+E(f75(x1611,x1613,x1614),f75(x1612,x1613,x1614)) % 1.58/1.66 [162]~E(x1621,x1622)+E(f75(x1623,x1621,x1624),f75(x1623,x1622,x1624)) % 1.58/1.66 [163]~E(x1631,x1632)+E(f75(x1633,x1634,x1631),f75(x1633,x1634,x1632)) % 1.58/1.66 [164]~E(x1641,x1642)+E(f55(x1641,x1643),f55(x1642,x1643)) % 1.58/1.66 [165]~E(x1651,x1652)+E(f55(x1653,x1651),f55(x1653,x1652)) % 1.58/1.66 [166]~E(x1661,x1662)+E(f34(x1661,x1663,x1664,x1665),f34(x1662,x1663,x1664,x1665)) % 1.58/1.66 [167]~E(x1671,x1672)+E(f34(x1673,x1671,x1674,x1675),f34(x1673,x1672,x1674,x1675)) % 1.58/1.66 [168]~E(x1681,x1682)+E(f34(x1683,x1684,x1681,x1685),f34(x1683,x1684,x1682,x1685)) % 1.58/1.66 [169]~E(x1691,x1692)+E(f34(x1693,x1694,x1695,x1691),f34(x1693,x1694,x1695,x1692)) % 1.58/1.66 [170]~E(x1701,x1702)+E(f85(x1701,x1703),f85(x1702,x1703)) % 1.58/1.66 [171]~E(x1711,x1712)+E(f85(x1713,x1711),f85(x1713,x1712)) % 1.58/1.66 [172]~E(x1721,x1722)+E(f41(x1721,x1723),f41(x1722,x1723)) % 1.58/1.66 [173]~E(x1731,x1732)+E(f41(x1733,x1731),f41(x1733,x1732)) % 1.58/1.66 [174]~E(x1741,x1742)+E(f70(x1741,x1743),f70(x1742,x1743)) % 1.58/1.66 [175]~E(x1751,x1752)+E(f70(x1753,x1751),f70(x1753,x1752)) % 1.58/1.66 [176]~E(x1761,x1762)+E(f66(x1761,x1763,x1764,x1765,x1766),f66(x1762,x1763,x1764,x1765,x1766)) % 1.58/1.66 [177]~E(x1771,x1772)+E(f66(x1773,x1771,x1774,x1775,x1776),f66(x1773,x1772,x1774,x1775,x1776)) % 1.58/1.66 [178]~E(x1781,x1782)+E(f66(x1783,x1784,x1781,x1785,x1786),f66(x1783,x1784,x1782,x1785,x1786)) % 1.58/1.66 [179]~E(x1791,x1792)+E(f66(x1793,x1794,x1795,x1791,x1796),f66(x1793,x1794,x1795,x1792,x1796)) % 1.58/1.66 [180]~E(x1801,x1802)+E(f66(x1803,x1804,x1805,x1806,x1801),f66(x1803,x1804,x1805,x1806,x1802)) % 1.58/1.66 [181]~E(x1811,x1812)+E(f52(x1811,x1813),f52(x1812,x1813)) % 1.58/1.66 [182]~E(x1821,x1822)+E(f52(x1823,x1821),f52(x1823,x1822)) % 1.58/1.66 [183]~E(x1831,x1832)+E(f74(x1831,x1833,x1834,x1835,x1836),f74(x1832,x1833,x1834,x1835,x1836)) % 1.58/1.66 [184]~E(x1841,x1842)+E(f74(x1843,x1841,x1844,x1845,x1846),f74(x1843,x1842,x1844,x1845,x1846)) % 1.58/1.66 [185]~E(x1851,x1852)+E(f74(x1853,x1854,x1851,x1855,x1856),f74(x1853,x1854,x1852,x1855,x1856)) % 1.58/1.66 [186]~E(x1861,x1862)+E(f74(x1863,x1864,x1865,x1861,x1866),f74(x1863,x1864,x1865,x1862,x1866)) % 1.58/1.66 [187]~E(x1871,x1872)+E(f74(x1873,x1874,x1875,x1876,x1871),f74(x1873,x1874,x1875,x1876,x1872)) % 1.58/1.66 [188]~E(x1881,x1882)+E(f44(x1881,x1883,x1884),f44(x1882,x1883,x1884)) % 1.58/1.66 [189]~E(x1891,x1892)+E(f44(x1893,x1891,x1894),f44(x1893,x1892,x1894)) % 1.58/1.66 [190]~E(x1901,x1902)+E(f44(x1903,x1904,x1901),f44(x1903,x1904,x1902)) % 1.58/1.66 [191]~E(x1911,x1912)+E(f79(x1911),f79(x1912)) % 1.58/1.66 [192]~E(x1921,x1922)+E(f26(x1921,x1923,x1924,x1925),f26(x1922,x1923,x1924,x1925)) % 1.58/1.66 [193]~E(x1931,x1932)+E(f26(x1933,x1931,x1934,x1935),f26(x1933,x1932,x1934,x1935)) % 1.58/1.66 [194]~E(x1941,x1942)+E(f26(x1943,x1944,x1941,x1945),f26(x1943,x1944,x1942,x1945)) % 1.58/1.66 [195]~E(x1951,x1952)+E(f26(x1953,x1954,x1955,x1951),f26(x1953,x1954,x1955,x1952)) % 1.58/1.66 [196]~E(x1961,x1962)+E(f58(x1961),f58(x1962)) % 1.58/1.66 [197]~E(x1971,x1972)+E(f78(x1971,x1973),f78(x1972,x1973)) % 1.58/1.66 [198]~E(x1981,x1982)+E(f78(x1983,x1981),f78(x1983,x1982)) % 1.58/1.66 [199]~E(x1991,x1992)+E(f64(x1991,x1993,x1994,x1995),f64(x1992,x1993,x1994,x1995)) % 1.58/1.66 [200]~E(x2001,x2002)+E(f64(x2003,x2001,x2004,x2005),f64(x2003,x2002,x2004,x2005)) % 1.58/1.66 [201]~E(x2011,x2012)+E(f64(x2013,x2014,x2011,x2015),f64(x2013,x2014,x2012,x2015)) % 1.58/1.66 [202]~E(x2021,x2022)+E(f64(x2023,x2024,x2025,x2021),f64(x2023,x2024,x2025,x2022)) % 1.58/1.66 [203]~E(x2031,x2032)+E(f57(x2031),f57(x2032)) % 1.58/1.66 [204]~E(x2041,x2042)+E(f71(x2041,x2043),f71(x2042,x2043)) % 1.58/1.66 [205]~E(x2051,x2052)+E(f71(x2053,x2051),f71(x2053,x2052)) % 1.58/1.66 [206]~E(x2061,x2062)+E(f69(x2061,x2063),f69(x2062,x2063)) % 1.58/1.66 [207]~E(x2071,x2072)+E(f69(x2073,x2071),f69(x2073,x2072)) % 1.58/1.66 [208]~E(x2081,x2082)+E(f48(x2081,x2083),f48(x2082,x2083)) % 1.58/1.66 [209]~E(x2091,x2092)+E(f48(x2093,x2091),f48(x2093,x2092)) % 1.58/1.66 [210]~E(x2101,x2102)+E(f84(x2101,x2103),f84(x2102,x2103)) % 1.58/1.66 [211]~E(x2111,x2112)+E(f84(x2113,x2111),f84(x2113,x2112)) % 1.58/1.66 [212]~E(x2121,x2122)+E(f83(x2121),f83(x2122)) % 1.58/1.66 [213]~P1(x2131)+P1(x2132)+~E(x2131,x2132) % 1.58/1.66 [214]~P2(x2141)+P2(x2142)+~E(x2141,x2142) % 1.58/1.66 [215]~P4(x2151)+P4(x2152)+~E(x2151,x2152) % 1.58/1.66 [216]~P5(x2161)+P5(x2162)+~E(x2161,x2162) % 1.58/1.66 [217]~P20(x2171)+P20(x2172)+~E(x2171,x2172) % 1.58/1.66 [218]~P33(x2181)+P33(x2182)+~E(x2181,x2182) % 1.58/1.66 [219]~P21(x2191)+P21(x2192)+~E(x2191,x2192) % 1.58/1.66 [220]~P25(x2201)+P25(x2202)+~E(x2201,x2202) % 1.58/1.66 [221]P10(x2212,x2213)+~E(x2211,x2212)+~P10(x2211,x2213) % 1.58/1.66 [222]P10(x2223,x2222)+~E(x2221,x2222)+~P10(x2223,x2221) % 1.58/1.66 [223]~P26(x2231)+P26(x2232)+~E(x2231,x2232) % 1.58/1.66 [224]~P23(x2241)+P23(x2242)+~E(x2241,x2242) % 1.58/1.66 [225]~P6(x2251)+P6(x2252)+~E(x2251,x2252) % 1.58/1.66 [226]~P7(x2261)+P7(x2262)+~E(x2261,x2262) % 1.58/1.66 [227]~P8(x2271)+P8(x2272)+~E(x2271,x2272) % 1.58/1.66 [228]~P14(x2281)+P14(x2282)+~E(x2281,x2282) % 1.58/1.66 [229]~P18(x2291)+P18(x2292)+~E(x2291,x2292) % 1.58/1.66 [230]~P19(x2301)+P19(x2302)+~E(x2301,x2302) % 1.58/1.66 [231]~P27(x2311)+P27(x2312)+~E(x2311,x2312) % 1.58/1.66 [232]~P9(x2321)+P9(x2322)+~E(x2321,x2322) % 1.58/1.66 [233]P11(x2332,x2333,x2334,x2335)+~E(x2331,x2332)+~P11(x2331,x2333,x2334,x2335) % 1.58/1.66 [234]P11(x2343,x2342,x2344,x2345)+~E(x2341,x2342)+~P11(x2343,x2341,x2344,x2345) % 1.58/1.66 [235]P11(x2353,x2354,x2352,x2355)+~E(x2351,x2352)+~P11(x2353,x2354,x2351,x2355) % 1.58/1.66 [236]P11(x2363,x2364,x2365,x2362)+~E(x2361,x2362)+~P11(x2363,x2364,x2365,x2361) % 1.58/1.66 [237]~P15(x2371)+P15(x2372)+~E(x2371,x2372) % 1.58/1.66 [238]~P16(x2381)+P16(x2382)+~E(x2381,x2382) % 1.58/1.66 [239]~P30(x2391)+P30(x2392)+~E(x2391,x2392) % 1.58/1.66 [240]~P22(x2401)+P22(x2402)+~E(x2401,x2402) % 1.58/1.66 [241]P12(x2412,x2413,x2414,x2415,x2416)+~E(x2411,x2412)+~P12(x2411,x2413,x2414,x2415,x2416) % 1.58/1.66 [242]P12(x2423,x2422,x2424,x2425,x2426)+~E(x2421,x2422)+~P12(x2423,x2421,x2424,x2425,x2426) % 1.58/1.66 [243]P12(x2433,x2434,x2432,x2435,x2436)+~E(x2431,x2432)+~P12(x2433,x2434,x2431,x2435,x2436) % 1.58/1.66 [244]P12(x2443,x2444,x2445,x2442,x2446)+~E(x2441,x2442)+~P12(x2443,x2444,x2445,x2441,x2446) % 1.58/1.66 [245]P12(x2453,x2454,x2455,x2456,x2452)+~E(x2451,x2452)+~P12(x2453,x2454,x2455,x2456,x2451) % 1.58/1.66 [246]~P28(x2461)+P28(x2462)+~E(x2461,x2462) % 1.58/1.66 [247]~P32(x2471)+P32(x2472)+~E(x2471,x2472) % 1.58/1.66 [248]~P17(x2481)+P17(x2482)+~E(x2481,x2482) % 1.58/1.66 [249]~P34(x2491)+P34(x2492)+~E(x2491,x2492) % 1.58/1.66 [250]~P24(x2501)+P24(x2502)+~E(x2501,x2502) % 1.58/1.66 [251]~P29(x2511)+P29(x2512)+~E(x2511,x2512) % 1.58/1.66 [252]~P31(x2521)+P31(x2522)+~E(x2521,x2522) % 1.58/1.66 [253]P3(x2532,x2533)+~E(x2531,x2532)+~P3(x2531,x2533) % 1.58/1.66 [254]P3(x2543,x2542)+~E(x2541,x2542)+~P3(x2543,x2541) % 1.58/1.66 [255]P13(x2552,x2553,x2554,x2555,x2556,x2557)+~E(x2551,x2552)+~P13(x2551,x2553,x2554,x2555,x2556,x2557) % 1.58/1.66 [256]P13(x2563,x2562,x2564,x2565,x2566,x2567)+~E(x2561,x2562)+~P13(x2563,x2561,x2564,x2565,x2566,x2567) % 1.58/1.66 [257]P13(x2573,x2574,x2572,x2575,x2576,x2577)+~E(x2571,x2572)+~P13(x2573,x2574,x2571,x2575,x2576,x2577) % 1.58/1.66 [258]P13(x2583,x2584,x2585,x2582,x2586,x2587)+~E(x2581,x2582)+~P13(x2583,x2584,x2585,x2581,x2586,x2587) % 1.58/1.66 [259]P13(x2593,x2594,x2595,x2596,x2592,x2597)+~E(x2591,x2592)+~P13(x2593,x2594,x2595,x2596,x2591,x2597) % 1.58/1.66 [260]P13(x2603,x2604,x2605,x2606,x2607,x2602)+~E(x2601,x2602)+~P13(x2603,x2604,x2605,x2606,x2607,x2601) % 1.58/1.66 % 1.58/1.66 %------------------------------------------- % 1.58/1.67 cnf(1109,plain, % 1.58/1.67 (P33(f28(f28(f35(x11092),x11091),f28(a39,x11091)))), % 1.58/1.67 inference(equality_inference,[],[477])). % 1.58/1.67 cnf(1118,plain, % 1.58/1.67 (P33(f28(f36(x11182,x11181,x11183),x11181))), % 1.58/1.67 inference(equality_inference,[],[553])). % 1.58/1.67 cnf(1126,plain, % 1.58/1.67 (~P33(f28(f28(f30(f96(x11262,a3)),x11261),x11261))), % 1.58/1.67 inference(equality_inference,[],[669])). % 1.58/1.67 cnf(1139,plain, % 1.58/1.67 (~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x11392),x11391)),f28(f28(a13,x11393),x11391)))), % 1.58/1.67 inference(equality_inference,[],[837])). % 1.58/1.67 cnf(1142,plain, % 1.58/1.67 (E(f37(x11421,x11422,x11423,f37(x11422,x11421,f23(x11421,x11422,x11424,x11423),x11425)),x11425)+~P33(f28(f29(f96(x11422,a3),x11425),f37(x11421,x11422,x11423,x11424)))), % 1.58/1.67 inference(equality_inference,[],[865])). % 1.58/1.67 cnf(1174,plain, % 1.58/1.67 (P33(f28(f29(f96(x11741,a3),x11742),f36(x11741,x11743,x11742)))), % 1.58/1.67 inference(rename_variables,[],[335])). % 1.58/1.67 cnf(1179,plain, % 1.58/1.67 (P33(f28(f28(f35(x11791),x11792),f28(a39,x11792)))), % 1.58/1.67 inference(rename_variables,[],[1109])). % 1.58/1.67 cnf(1184,plain, % 1.58/1.67 (~P33(f28(f29(a2,f28(a22,x11841)),x11841))), % 1.58/1.67 inference(rename_variables,[],[387])). % 1.58/1.67 cnf(1187,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),x11871),f4(a2)))), % 1.58/1.67 inference(rename_variables,[],[386])). % 1.58/1.67 cnf(1190,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),f28(f28(f20(a2),x11901),x11902)),x11902))), % 1.58/1.67 inference(rename_variables,[],[388])). % 1.58/1.67 cnf(1193,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),f28(f28(f20(a2),x11931),x11932)),x11932))), % 1.58/1.67 inference(rename_variables,[],[388])). % 1.58/1.67 cnf(1204,plain, % 1.58/1.67 (P33(f28(f28(f30(a2),x12041),f28(a22,x12041)))), % 1.58/1.67 inference(rename_variables,[],[308])). % 1.58/1.67 cnf(1211,plain, % 1.58/1.67 (~P33(f28(f29(a2,f28(a22,x12111)),x12111))), % 1.58/1.67 inference(rename_variables,[],[387])). % 1.58/1.67 cnf(1216,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),f28(f28(f20(a2),x12161),x12162)),x12162))), % 1.58/1.67 inference(rename_variables,[],[388])). % 1.58/1.67 cnf(1225,plain, % 1.58/1.67 (P33(f28(f29(a2,x12251),f28(f28(f20(a2),x12252),x12251)))), % 1.58/1.67 inference(rename_variables,[],[322])). % 1.58/1.67 cnf(1228,plain, % 1.58/1.67 (P33(f28(f29(a2,x12281),f28(f28(f20(a2),x12282),x12281)))), % 1.58/1.67 inference(rename_variables,[],[322])). % 1.58/1.67 cnf(1233,plain, % 1.58/1.67 (~P33(f28(f29(a2,f28(a22,x12331)),x12331))), % 1.58/1.67 inference(rename_variables,[],[387])). % 1.58/1.67 cnf(1236,plain, % 1.58/1.67 (~P33(f28(f29(a2,f28(a22,x12361)),x12361))), % 1.58/1.67 inference(rename_variables,[],[387])). % 1.58/1.67 cnf(1244,plain, % 1.58/1.67 (P33(f28(f28(f30(a2),x12441),f28(a22,x12441)))), % 1.58/1.67 inference(rename_variables,[],[308])). % 1.58/1.67 cnf(1247,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),f28(f28(f20(a2),x12471),x12472)),x12472))), % 1.58/1.67 inference(rename_variables,[],[388])). % 1.58/1.67 cnf(1250,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),f28(f28(f20(a2),x12501),x12502)),x12502))), % 1.58/1.67 inference(rename_variables,[],[388])). % 1.58/1.67 cnf(1257,plain, % 1.58/1.67 (P33(f28(f29(a2,x12571),f28(f28(f20(a2),x12572),x12571)))), % 1.58/1.67 inference(rename_variables,[],[322])). % 1.58/1.67 cnf(1263,plain, % 1.58/1.67 (P33(f28(f29(a2,x12631),x12631))), % 1.58/1.67 inference(rename_variables,[],[300])). % 1.58/1.67 cnf(1277,plain, % 1.58/1.67 (P33(f28(f28(f30(a2),x12771),f28(a22,x12771)))), % 1.58/1.67 inference(rename_variables,[],[308])). % 1.58/1.67 cnf(1280,plain, % 1.58/1.67 (P33(f28(f28(f30(a2),x12801),f28(a22,x12801)))), % 1.58/1.67 inference(rename_variables,[],[308])). % 1.58/1.67 cnf(1287,plain, % 1.58/1.67 (~P33(f28(f28(f30(a2),x12871),x12871))), % 1.58/1.67 inference(rename_variables,[],[383])). % 1.58/1.67 cnf(1292,plain, % 1.58/1.68 (P33(f28(f29(f96(x12921,a3),x12922),x12922))), % 1.58/1.68 inference(rename_variables,[],[313])). % 1.58/1.68 cnf(1297,plain, % 1.58/1.68 (P33(f28(f29(f96(x12971,a3),x12972),f36(x12971,x12973,x12972)))), % 1.58/1.68 inference(rename_variables,[],[335])). % 1.58/1.68 cnf(1302,plain, % 1.58/1.68 (P33(f28(f29(f96(x13021,a3),x13022),x13022))), % 1.58/1.68 inference(rename_variables,[],[313])). % 1.58/1.68 cnf(1309,plain, % 1.58/1.68 (P33(f28(f29(f96(x13091,a3),x13092),x13092))), % 1.58/1.68 inference(rename_variables,[],[313])). % 1.58/1.68 cnf(1329,plain, % 1.58/1.68 (~E(f28(a22,x13291),f4(a2))), % 1.58/1.68 inference(rename_variables,[],[381])). % 1.58/1.68 cnf(1337,plain, % 1.58/1.68 (P33(f28(f28(f35(x13371),x13372),f28(a39,x13372)))), % 1.58/1.68 inference(rename_variables,[],[1109])). % 1.58/1.68 cnf(1340,plain, % 1.58/1.68 (P33(f28(f29(f96(x13401,a3),x13402),f36(x13401,x13403,x13402)))), % 1.58/1.68 inference(rename_variables,[],[335])). % 1.58/1.68 cnf(1345,plain, % 1.58/1.68 (P33(f28(f29(f96(x13451,a3),x13452),x13452))), % 1.58/1.68 inference(rename_variables,[],[313])). % 1.58/1.68 cnf(1348,plain, % 1.58/1.68 (P33(f28(f28(f35(x13481),x13482),f28(a39,x13482)))), % 1.58/1.68 inference(rename_variables,[],[1109])). % 1.58/1.68 cnf(1349,plain, % 1.58/1.68 (P11(x13491,x13491,f6(x13491),x13492)), % 1.58/1.68 inference(rename_variables,[],[320])). % 1.58/1.68 cnf(1352,plain, % 1.58/1.68 (E(f27(a2,x13521),x13521)), % 1.58/1.68 inference(rename_variables,[],[289])). % 1.58/1.68 cnf(1358,plain, % 1.58/1.68 (P33(f28(f28(f35(x13581),x13582),f28(a39,x13582)))), % 1.58/1.68 inference(rename_variables,[],[1109])). % 1.58/1.68 cnf(1362,plain, % 1.58/1.68 (~P33(f28(f28(f35(f98(a93,a93)),f28(f28(f33(a93,a93),x13621),x13622)),f28(f28(a13,x13623),x13622)))), % 1.58/1.68 inference(rename_variables,[],[1139])). % 1.58/1.68 cnf(1376,plain, % 1.58/1.68 (E(f27(a2,x13761),x13761)), % 1.58/1.68 inference(rename_variables,[],[289])). % 1.58/1.68 cnf(1390,plain, % 1.58/1.68 (~P33(f28(f28(f30(a2),f28(f28(f20(a2),x13901),x13902)),x13901))), % 1.58/1.68 inference(rename_variables,[],[389])). % 1.58/1.68 cnf(1412,plain, % 1.58/1.68 (P33(f28(f29(f96(x14121,a3),x14122),f36(x14121,x14123,x14122)))), % 1.58/1.68 inference(rename_variables,[],[335])). % 1.58/1.68 cnf(1431,plain, % 1.58/1.68 (P33(f28(f29(f96(x14311,a3),x14312),f31(f96(x14311,a3))))), % 1.58/1.68 inference(rename_variables,[],[325])). % 1.58/1.68 cnf(1436,plain, % 1.58/1.68 (P33(f28(f29(f96(x14361,a3),x14362),f36(x14361,x14363,x14362)))), % 1.58/1.68 inference(rename_variables,[],[335])). % 1.58/1.68 cnf(1437,plain, % 1.58/1.68 (P33(f28(f29(f96(x14371,a3),x14372),f31(f96(x14371,a3))))), % 1.58/1.68 inference(rename_variables,[],[325])). % 1.58/1.68 cnf(1441,plain, % 1.58/1.68 (P33(f28(f29(f96(x14411,a3),x14412),f36(x14411,x14413,x14412)))), % 1.58/1.68 inference(rename_variables,[],[335])). % 1.58/1.68 cnf(1451,plain, % 1.58/1.68 ($false), % 1.58/1.68 inference(scs_inference,[],[329,1118,1126,1139,1362,1109,1179,1337,1348,1358,332,335,1174,1297,1340,1412,1436,1441,300,1263,308,1204,1244,1277,1280,309,386,1187,313,1292,1302,1309,1345,383,1287,316,325,1431,1437,387,1184,1211,1233,1236,358,322,1225,1228,1257,323,331,330,360,388,1190,1193,1216,1247,1250,389,1390,340,350,343,345,357,364,320,1349,289,1352,1376,375,381,1329,265,267,269,270,276,279,321,296,299,476,512,529,675,785,796,829,885,891,440,453,459,462,468,473,474,475,502,505,534,539,559,563,579,585,598,611,627,628,633,635,637,638,639,657,659,668,716,740,741,753,755,786,793,798,807,835,841,849,850,853,860,876,881,906,929,956,974,978,1142,2,6,7,396,404,419,452,463,832,843,877,573,606,624,692,792,802,824,871,873,874,875,901,915,934,218,430,432,480,500,501,511,520,555,557,558,566,572,586,589,592,593,602,617,618,619,641,671,684,688,694,728,788,811,847,851]), % 1.58/1.68 ['proof']). % 1.58/1.68 % SZS output end Proof % 1.58/1.68 % Total time :0.460000s %------------------------------------------------------------------------------