%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SCT168+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n025.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 1.45s 1.49s % Output : CNFRefutation 1.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SCT168+1 : TPTP v8.2.0. Released v5.2.0. % 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n025.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sat Jun 22 09:24:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.55 start to proof:theBenchmark % 1.36/1.45 %------------------------------------------- % 1.36/1.45 % File :CSE---1.7 % 1.36/1.45 % Problem :theBenchmark % 1.36/1.45 % Transform :cnf % 1.36/1.45 % Format :tptp:raw % 1.36/1.45 % Command :java -jar mcs_scs.jar %d %s % 1.36/1.45 % 1.36/1.45 % Result :Theorem 0.430000s % 1.36/1.45 % Output :CNFRefutation 0.430000s % 1.36/1.45 %------------------------------------------- % 1.36/1.45 %------------------------------------------------------------------------------ % 1.36/1.45 % File : SCT168+1 : TPTP v8.2.0. Released v5.2.0. % 1.36/1.45 % Domain : Social Choice Theory % 1.36/1.45 % Problem : Arrow's Impossibility Theorem 433680, 500 axioms selected % 1.36/1.45 % Version : Especial. % 1.36/1.45 % English : % 1.36/1.45 % 1.36/1.45 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.36/1.45 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 1.36/1.45 % Source : [Bla11] % 1.36/1.45 % Names : arrow_433680.500.p [Bla11] % 1.36/1.45 % 1.36/1.45 % Status : ContradictoryAxioms % 1.36/1.45 % Rating : 0.61 v8.2.0, 0.58 v8.1.0, 0.61 v7.5.0, 0.62 v7.4.0, 0.63 v7.3.0, 0.69 v7.2.0, 0.66 v7.1.0, 0.61 v7.0.0, 0.57 v6.4.0, 0.62 v6.3.0, 0.58 v6.2.0, 0.68 v6.1.0, 0.77 v6.0.0, 0.65 v5.5.0, 0.81 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0 % 1.36/1.45 % Syntax : Number of formulae : 533 ( 123 unt; 0 def) % 1.36/1.45 % Number of atoms : 1400 ( 324 equ) % 1.36/1.45 % Maximal formula atoms : 12 ( 2 avg) % 1.36/1.45 % Number of connectives : 1024 ( 157 ~; 26 |; 53 &) % 1.36/1.46 % ( 128 <=>; 660 =>; 0 <=; 0 <~>) % 1.36/1.46 % Maximal formula depth : 16 ( 6 avg) % 1.36/1.46 % Maximal term depth : 16 ( 2 avg) % 1.36/1.46 % Number of predicates : 36 ( 35 usr; 0 prp; 1-6 aty) % 1.36/1.46 % Number of functors : 61 ( 61 usr; 24 con; 0-6 aty) % 1.36/1.46 % Number of variables : 1521 (1509 !; 12 ?) % 1.36/1.46 % SPC : FOF_CAX_RFO_SEQ % 1.36/1.46 % 1.36/1.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 1.36/1.46 % 2011-03-01 11:32:08 % 1.36/1.46 % : Renamed from SWW170+1 % 1.36/1.46 %------------------------------------------------------------------------------ % 1.36/1.46 %----Relevant facts (491) % 1.36/1.46 fof(fact_ext,axiom, % 1.36/1.46 ! [V_g_2,V_f_2] : % 1.36/1.46 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 1.36/1.46 => V_f_2 = V_g_2 ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_assms_I3_J,axiom, % 1.36/1.46 c_Arrow__Order__Mirabelle_OIIA(v_F) ). % 1.36/1.46 % 1.36/1.46 fof(fact_u,axiom, % 1.36/1.46 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ). % 1.36/1.46 % 1.36/1.46 fof(fact__096c_A_126_061_Ad_096,axiom, % 1.36/1.46 v_c____ != v_d____ ). % 1.36/1.46 % 1.36/1.46 fof(fact__096e_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_096,axiom, % 1.36/1.46 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____)))))) ). % 1.36/1.46 % 1.36/1.46 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, % 1.36/1.46 ! [B_i] : % 1.36/1.46 ( 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))) % 1.36/1.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.36/1.46 => 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____))) ) % 1.36/1.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.36/1.46 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.36/1.46 => 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____))) ) % 1.36/1.46 & ( hAPP(v_h____,B_i) != v_n____ % 1.36/1.46 => 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____))) ) ) ) ) ) ). % 1.36/1.46 % 1.36/1.46 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, % 1.36/1.46 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____)))))) ). % 1.36/1.46 % 1.36/1.46 fof(fact_PW,axiom, % 1.36/1.46 ( 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____))) % 1.36/1.46 <=> 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____)))))) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_in__mkbot,axiom, % 1.36/1.46 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.36/1.46 ( 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))) % 1.36/1.46 <=> ( V_y_2 != V_z_2 % 1.36/1.46 & ( V_x_2 = V_z_2 % 1.36/1.46 => V_x_2 != V_y_2 ) % 1.36/1.46 & ( V_x_2 != V_z_2 % 1.36/1.46 => 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)) ) ) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_in__mktop,axiom, % 1.36/1.46 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.36/1.46 ( 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))) % 1.36/1.46 <=> ( V_x_2 != V_z_2 % 1.36/1.46 & ( V_y_2 = V_z_2 % 1.36/1.46 => V_x_2 != V_y_2 ) % 1.36/1.46 & ( V_y_2 != V_z_2 % 1.36/1.46 => 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)) ) ) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom, % 1.36/1.46 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____)))) ). % 1.36/1.46 % 1.36/1.46 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, % 1.36/1.46 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)) ). % 1.36/1.46 % 1.36/1.46 fof(fact_equalityCE,axiom, % 1.36/1.46 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 1.36/1.46 ( V_A_2 = V_B_2 % 1.36/1.46 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.36/1.46 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 1.36/1.46 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.36/1.46 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_pred__equals__eq2,axiom, % 1.36/1.46 ! [V_S_2,V_R_2,T_b,T_a] : % 1.36/1.46 ( 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) % 1.36/1.46 <=> V_R_2 = V_S_2 ) ). % 1.36/1.46 % 1.36/1.46 fof(fact__096_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_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, % 1.36/1.46 ( 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____)))))) % 1.36/1.46 <=> 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____)))) ) ). % 1.36/1.46 % 1.36/1.46 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, % 1.36/1.46 ! [B_i] : % 1.36/1.46 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.36/1.46 => 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____))) ) % 1.36/1.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.36/1.46 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.36/1.46 => 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____))) ) % 1.36/1.46 & ( hAPP(v_h____,B_i) != v_n____ % 1.36/1.46 => 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____))) ) ) ) ) % 1.36/1.46 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.36/1.46 => 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____)) ) % 1.36/1.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.36/1.46 => 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____)) ) ) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_in__rel__def,axiom, % 1.36/1.46 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 1.36/1.46 ( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) % 1.36/1.46 <=> 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)) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_same__fstI,axiom, % 1.36/1.46 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] : % 1.36/1.46 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.36/1.46 => ( 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))) % 1.36/1.46 => 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))) ) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_pred__equals__eq,axiom, % 1.36/1.46 ! [V_S_2,V_R_2,T_a] : % 1.36/1.46 ( 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) % 1.36/1.46 <=> V_R_2 = V_S_2 ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_in__measure,axiom, % 1.36/1.46 ! [V_f_2,V_y_2,V_x_2,T_a] : % 1.36/1.46 ( 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))) % 1.36/1.46 <=> 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))) ) ). % 1.36/1.46 % 1.36/1.46 fof(fact_Nitpick_Orefl_H__def,axiom, % 1.36/1.46 ! [V_r_2,T_a] : % 1.36/1.46 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 1.36/1.47 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_mlex__less,axiom, % 1.36/1.47 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.36/1.47 ( 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))) % 1.36/1.47 => 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))) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096a_A_126_061_Ab_096,axiom, % 1.36/1.47 v_a____ != v_b____ ). % 1.36/1.47 % 1.36/1.47 fof(fact__096P_A_058_AProf_096,axiom, % 1.36/1.47 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)) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096Lab_A_058_ALin_096,axiom, % 1.36/1.47 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)) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096Lba_A_058_ALin_096,axiom, % 1.36/1.47 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)) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom, % 1.36/1.47 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____)) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom, % 1.36/1.47 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____)) ). % 1.36/1.47 % 1.36/1.47 fof(fact_top1I,axiom, % 1.36/1.47 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom, % 1.36/1.47 ~ 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____)) ). % 1.36/1.47 % 1.36/1.47 fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom, % 1.36/1.47 ~ 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____)) ). % 1.36/1.47 % 1.36/1.47 fof(fact_UNIV__I,axiom, % 1.36/1.47 ! [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)))) ). % 1.36/1.47 % 1.36/1.47 fof(fact_PiProf,axiom, % 1.36/1.47 ! [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)) ). % 1.36/1.47 % 1.36/1.47 fof(fact_n_I1_J,axiom, % 1.36/1.47 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))))) ). % 1.36/1.47 % 1.36/1.47 fof(fact_n_I2_J,axiom, % 1.36/1.47 ! [B_m] : % 1.36/1.47 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),v_n____)) % 1.36/1.47 => 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____)))) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_injh,axiom, % 1.36/1.47 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))) ). % 1.36/1.47 % 1.36/1.47 fof(fact_eq__mem__trans,axiom, % 1.36/1.47 ! [V_A_2,T_a,V_ba_2,V_aa_2] : % 1.36/1.47 ( V_aa_2 = V_ba_2 % 1.36/1.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) % 1.36/1.47 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_eqelem__imp__iff,axiom, % 1.36/1.47 ! [V_A_2,T_a,V_y_2,V_x_2] : % 1.36/1.47 ( V_x_2 = V_y_2 % 1.36/1.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.36/1.47 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_eqset__imp__iff,axiom, % 1.36/1.47 ! [V_x_2,T_a,V_B_2,V_A_2] : % 1.36/1.47 ( V_A_2 = V_B_2 % 1.36/1.47 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.36/1.47 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_eq__mem,axiom, % 1.36/1.47 ! [V_y_2,V_x_2,T_a] : % 1.36/1.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 1.36/1.47 <=> V_x_2 = V_y_2 ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_mem__def,axiom, % 1.36/1.47 ! [V_A_2,V_x_2,T_a] : % 1.36/1.47 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.36/1.47 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact__C3_C,axiom, % 1.36/1.47 ! [V_P_H_2,V_Pa_2,V_ba_2,V_aa_2] : % 1.36/1.47 ( V_aa_2 != V_ba_2 % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( ! [B_i] : % 1.36/1.47 ( 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))) % 1.36/1.47 <=> 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))) ) % 1.36/1.47 => ( 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))) % 1.36/1.47 <=> 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))) ) ) ) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact_pairwise__neutrality,axiom, % 1.36/1.47 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.36/1.47 ( V_aa_2 != V_ba_2 % 1.36/1.47 => ( V_a_H_2 != V_b_H_2 % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( ! [B_i] : % 1.36/1.47 ( 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))) % 1.36/1.47 <=> 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))) ) % 1.36/1.47 => ( 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))) % 1.36/1.47 <=> 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))) ) ) ) ) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact__C4_C,axiom, % 1.36/1.47 ! [V_P_H_2,V_Pa_2,V_ca_2,V_ba_2,V_aa_2] : % 1.36/1.47 ( V_aa_2 != V_ba_2 % 1.36/1.47 => ( V_ba_2 != V_ca_2 % 1.36/1.47 => ( V_aa_2 != V_ca_2 % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( ! [B_i] : % 1.36/1.47 ( 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))) % 1.36/1.47 <=> 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))) ) % 1.36/1.47 => ( 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))) % 1.36/1.47 <=> 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))) ) ) ) ) ) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact__C1_C,axiom, % 1.36/1.47 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.36/1.47 ( V_aa_2 != V_ba_2 % 1.36/1.47 => ( V_a_H_2 != V_b_H_2 % 1.36/1.47 => ( V_aa_2 != V_b_H_2 % 1.36/1.47 => ( V_ba_2 != V_a_H_2 % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( 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)) % 1.36/1.47 => ( ! [B_i] : % 1.36/1.47 ( 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))) % 1.36/1.47 <=> 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))) ) % 1.36/1.47 => ( 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))) % 1.36/1.47 => 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))) ) ) ) ) ) ) ) ) ). % 1.36/1.47 % 1.36/1.47 fof(fact__C2_C,axiom, % 1.36/1.47 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.36/1.47 ( V_aa_2 != V_ba_2 % 1.45/1.47 => ( V_a_H_2 != V_b_H_2 % 1.45/1.47 => ( V_aa_2 != V_b_H_2 % 1.45/1.47 => ( V_ba_2 != V_a_H_2 % 1.45/1.47 => ( 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)) % 1.45/1.47 => ( 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)) % 1.45/1.47 => ( ! [B_i] : % 1.45/1.47 ( 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))) % 1.45/1.47 <=> 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))) ) % 1.45/1.47 => ( 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))) % 1.45/1.47 <=> 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))) ) ) ) ) ) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_n_I3_J,axiom, % 1.45/1.47 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____)))) ). % 1.45/1.47 % 1.45/1.47 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, % 1.45/1.47 ( 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____)))))) % 1.45/1.47 <=> 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____)))) ) ). % 1.45/1.47 % 1.45/1.47 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, % 1.45/1.47 ! [B_i] : % 1.45/1.47 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.45/1.47 => 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____))) ) % 1.45/1.47 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.45/1.47 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.45/1.47 => 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____))) ) % 1.45/1.47 & ( hAPP(v_h____,B_i) != v_n____ % 1.45/1.47 => 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____))) ) ) ) ) % 1.45/1.47 <=> ( ( 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)))) % 1.45/1.47 => 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____)) ) % 1.45/1.47 & ( ~ 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)))) % 1.45/1.47 => 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____)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_in__lex__prod,axiom, % 1.45/1.47 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] : % 1.45/1.47 ( 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))) % 1.45/1.47 <=> ( 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)) % 1.45/1.47 | ( V_aa_2 = V_a_H_2 % 1.45/1.47 & 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)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_top__apply,axiom, % 1.45/1.47 ! [V_x_2,T_b,T_a] : % 1.45/1.47 ( class_Orderings_Otop(T_a) % 1.45/1.47 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_IIA__def,axiom, % 1.45/1.47 ! [V_Fa_2] : % 1.45/1.47 ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) % 1.45/1.47 <=> ! [B_x] : % 1.45/1.47 ( 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)) % 1.45/1.47 => ! [B_xa] : % 1.45/1.47 ( 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)) % 1.45/1.47 => ! [B_a,B_b] : % 1.45/1.47 ( ! [B_i] : % 1.45/1.47 ( 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))) % 1.45/1.47 <=> 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))) ) % 1.45/1.47 => ( 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))) % 1.45/1.47 <=> 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))) ) ) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__refl,axiom, % 1.45/1.47 ! [V_x,T_a] : % 1.45/1.47 ( class_Orderings_Opreorder(T_a) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_assms_I1_J,axiom, % 1.45/1.47 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)))) ). % 1.45/1.47 % 1.45/1.47 fof(fact_termination__basic__simps_I3_J,axiom, % 1.45/1.47 ! [V_z,V_y,V_x] : % 1.45/1.47 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) % 1.45/1.47 => 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))) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_termination__basic__simps_I4_J,axiom, % 1.45/1.47 ! [V_y,V_z,V_x] : % 1.45/1.47 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) % 1.45/1.47 => 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))) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__le__cases,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_le__funE,axiom, % 1.45/1.47 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.45/1.47 ( class_Orderings_Oord(T_b) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I6_J,axiom, % 1.45/1.47 ! [V_z,V_x,V_y,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I5_J,axiom, % 1.45/1.47 ! [V_x,V_y,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 => V_x = V_y ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__trans,axiom, % 1.45/1.47 ! [V_z,V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Opreorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__antisym,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.45/1.47 => V_x = V_y ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I4_J,axiom, % 1.45/1.47 ! [V_c,V_a,V_b,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.45/1.47 => ( V_b = V_c % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_ord__le__eq__trans,axiom, % 1.45/1.47 ! [V_c,V_b,V_a,T_a] : % 1.45/1.47 ( class_Orderings_Oord(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.47 => ( V_b = V_c % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I3_J,axiom, % 1.45/1.47 ! [V_c,V_b,V_a,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( V_a = V_b % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_ord__eq__le__trans,axiom, % 1.45/1.47 ! [V_c,V_b,V_a,T_a] : % 1.45/1.47 ( class_Orderings_Oord(T_a) % 1.45/1.47 => ( V_a = V_b % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__antisym__conv,axiom, % 1.45/1.47 ! [V_x_2,V_y_2,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 <=> V_x_2 = V_y_2 ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_le__funD,axiom, % 1.45/1.47 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.45/1.47 ( class_Orderings_Oord(T_b) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__eq__refl,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Opreorder(T_a) % 1.45/1.47 => ( V_x = V_y % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__eq__iff,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( V_x_2 = V_y_2 % 1.45/1.47 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__linear,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_le__fun__def,axiom, % 1.45/1.47 ! [V_g_2,V_f_2,T_a,T_b] : % 1.45/1.47 ( class_Orderings_Oord(T_b) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.45/1.47 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__not__less,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.47 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__not__le,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__le__less__linear,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__less__le,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.47 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 & V_x_2 != V_y_2 ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_less__le__not__le,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Opreorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.47 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__le__less,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.47 | V_x_2 = V_y_2 ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_leI,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_not__leE,axiom, % 1.45/1.47 ! [V_x,V_y,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__antisym__conv1,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 <=> V_x_2 = V_y_2 ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__neq__le__trans,axiom, % 1.45/1.47 ! [V_b,V_a,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( V_a != V_b % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I12_J,axiom, % 1.45/1.47 ! [V_b,V_a,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( V_a != V_b % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_leD,axiom, % 1.45/1.47 ! [V_x,V_y,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.45/1.47 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__less__imp__le,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Opreorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_linorder__antisym__conv2,axiom, % 1.45/1.47 ! [V_y_2,V_x_2,T_a] : % 1.45/1.47 ( class_Orderings_Olinorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.45/1.47 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.47 <=> V_x_2 = V_y_2 ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__le__imp__less__or__eq,axiom, % 1.45/1.47 ! [V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.47 | V_x = V_y ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__le__neq__trans,axiom, % 1.45/1.47 ! [V_b,V_a,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.47 => ( V_a != V_b % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I11_J,axiom, % 1.45/1.47 ! [V_a,V_b,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.45/1.47 => ( V_a != V_b % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_order__less__le__trans,axiom, % 1.45/1.47 ! [V_z,V_y,V_x,T_a] : % 1.45/1.47 ( class_Orderings_Opreorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.45/1.47 % 1.45/1.47 fof(fact_xt1_I7_J,axiom, % 1.45/1.47 ! [V_z,V_x,V_y,T_a] : % 1.45/1.47 ( class_Orderings_Oorder(T_a) % 1.45/1.47 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.45/1.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.45/1.47 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.45/1.47 % 1.45/1.48 fof(fact_order__le__less__trans,axiom, % 1.45/1.48 ! [V_z,V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_xt1_I8_J,axiom, % 1.45/1.48 ! [V_z,V_x,V_y,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_top__greatest,axiom, % 1.45/1.48 ! [V_x,T_a] : % 1.45/1.48 ( class_Orderings_Otop(T_a) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_termination__basic__simps_I1_J,axiom, % 1.45/1.48 ! [V_z,V_y,V_x] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_termination__basic__simps_I2_J,axiom, % 1.45/1.48 ! [V_y,V_z,V_x] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_termination__basic__simps_I5_J,axiom, % 1.45/1.48 ! [V_y,V_x] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_above__Lin,axiom, % 1.45/1.48 ! [V_L_2,V_y_2,V_x_2] : % 1.45/1.48 ( V_x_2 != V_y_2 % 1.45/1.48 => ( 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)) % 1.45/1.48 => 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)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_mkbot__Lin,axiom, % 1.45/1.48 ! [V_x_2,V_L_2] : % 1.45/1.48 ( 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)) % 1.45/1.48 => 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)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_mktop__Lin,axiom, % 1.45/1.48 ! [V_x_2,V_L_2] : % 1.45/1.48 ( 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)) % 1.45/1.48 => 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)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_notin__Lin__iff,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_L_2] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ( V_x_2 != V_y_2 % 1.45/1.48 => ( ~ 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)) % 1.45/1.48 <=> 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)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Lin__irrefl,axiom, % 1.45/1.48 ! [V_ba_2,V_aa_2,V_L_2] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ( 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)) % 1.45/1.48 => ~ 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)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__irrefl,axiom, % 1.45/1.48 ! [V_x,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__neq__iff,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,T_a] : % 1.45/1.48 ( class_Orderings_Olinorder(T_a) % 1.45/1.48 => ( V_x_2 != V_y_2 % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_not__less__iff__gr__or__eq,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,T_a] : % 1.45/1.48 ( class_Orderings_Olinorder(T_a) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.45/1.48 | V_x_2 = V_y_2 ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__less__linear,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Olinorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 | V_x = V_y % 1.45/1.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__antisym__conv3,axiom, % 1.45/1.48 ! [V_x_2,V_y_2,T_a] : % 1.45/1.48 ( class_Orderings_Olinorder(T_a) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.45/1.48 <=> V_x_2 = V_y_2 ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__neqE,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Olinorder(T_a) % 1.45/1.48 => ( V_x != V_y % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__imp__neq,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => V_x != V_y ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__not__sym,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__imp__not__less,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__imp__not__eq,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => V_x != V_y ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__imp__not__eq2,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => V_y != V_x ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__asym_H,axiom, % 1.45/1.48 ! [V_b,V_a,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_xt1_I9_J,axiom, % 1.45/1.48 ! [V_a,V_b,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_ord__eq__less__trans,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Orderings_Oord(T_a) % 1.45/1.48 => ( V_a = V_b % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_xt1_I1_J,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( V_a = V_b % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_ord__less__eq__trans,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Orderings_Oord(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.45/1.48 => ( V_b = V_c % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_xt1_I2_J,axiom, % 1.45/1.48 ! [V_c,V_a,V_b,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.45/1.48 => ( V_b = V_c % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__trans,axiom, % 1.45/1.48 ! [V_z,V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_xt1_I10_J,axiom, % 1.45/1.48 ! [V_z,V_x,V_y,T_a] : % 1.45/1.48 ( class_Orderings_Oorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_order__less__asym,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Opreorder(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__cases,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Orderings_Olinorder(T_a) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => ( V_x != V_y % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_mlex__leq,axiom, % 1.45/1.48 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.45/1.48 ( 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))) % 1.45/1.48 => ( 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)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_const__Lin__Prof,axiom, % 1.45/1.48 ! [V_L_2] : % 1.45/1.48 ( 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)) % 1.45/1.48 => 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)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_in__above,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.45/1.48 ( V_aa_2 != V_ba_2 % 1.45/1.48 => ( 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)) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> ( V_x_2 != V_y_2 % 1.45/1.48 & ( V_x_2 = V_ba_2 % 1.45/1.48 => 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)) ) % 1.45/1.48 & ( V_x_2 != V_ba_2 % 1.45/1.48 => ( ( V_y_2 = V_ba_2 % 1.45/1.48 => ( V_x_2 = V_aa_2 % 1.45/1.48 | 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)) ) ) % 1.45/1.48 & ( V_y_2 != V_ba_2 % 1.45/1.48 => 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)) ) ) ) ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 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, % 1.45/1.48 ? [B_n] : % 1.45/1.48 ( 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))))) % 1.45/1.48 & ! [B_m] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 1.45/1.48 => 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____)))) ) % 1.45/1.48 & 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____)))) ) ). % 1.45/1.48 % 1.45/1.48 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, % 1.45/1.48 ~ ! [B_Lab] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ~ 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)) ) ). % 1.45/1.48 % 1.45/1.48 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, % 1.45/1.48 ~ ! [B_Lba] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ~ 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)) ) ). % 1.45/1.48 % 1.45/1.48 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, % 1.45/1.48 ~ ! [B_n] : % 1.45/1.48 ( 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))))) % 1.45/1.48 => ( ! [B_m] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 1.45/1.48 => 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____)))) ) % 1.45/1.48 => ~ 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____)))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_in__below,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.45/1.48 ( V_aa_2 != V_ba_2 % 1.45/1.48 => ( 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)) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> ( V_x_2 != V_y_2 % 1.45/1.48 & ( V_y_2 = V_aa_2 % 1.45/1.48 => 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)) ) % 1.45/1.48 & ( V_y_2 != V_aa_2 % 1.45/1.48 => ( ( V_x_2 = V_aa_2 % 1.45/1.48 => ( V_y_2 = V_ba_2 % 1.45/1.48 | 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)) ) ) % 1.45/1.48 & ( V_x_2 != V_aa_2 % 1.45/1.48 => 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)) ) ) ) ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inv__f__eq,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.45/1.48 => 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 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inv__f__f,axiom, % 1.45/1.48 ! [V_x_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => 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 ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inv__into__f__eq,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.45/1.48 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inv__into__f__f,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => 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 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subsetD,axiom, % 1.45/1.48 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__fun__def,axiom, % 1.45/1.48 ! [V_g_2,V_f_2,T_a,T_b] : % 1.45/1.48 ( class_Orderings_Oord(T_b) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 1.45/1.48 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.45/1.48 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_psubsetD,axiom, % 1.45/1.48 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_pred__subset__eq2,axiom, % 1.45/1.48 ! [V_S_2,V_R_2,T_b,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 <=> 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)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_set__mp,axiom, % 1.45/1.48 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_set__rev__mp,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_in__mono,axiom, % 1.45/1.48 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__UNIV,axiom, % 1.45/1.48 ! [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)))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_pred__subset__eq,axiom, % 1.45/1.48 ! [V_S_2,V_R_2,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_below__Lin,axiom, % 1.45/1.48 ! [V_L_2,V_y_2,V_x_2] : % 1.45/1.48 ( V_x_2 != V_y_2 % 1.45/1.48 => ( 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)) % 1.45/1.48 => 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)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_PiE,axiom, % 1.45/1.48 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) % 1.45/1.48 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_funcset__mem,axiom, % 1.45/1.48 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( 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)))) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Pi__mem,axiom, % 1.45/1.48 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__add__one,axiom, % 1.45/1.48 ! [V_a,T_a] : % 1.45/1.48 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.48 => 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)))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__le__mono,axiom, % 1.45/1.48 ! [V_d,V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.45/1.48 => 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))) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__less__mono,axiom, % 1.45/1.48 ! [V_d,V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.45/1.48 => 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))) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_equalityI,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) % 1.45/1.48 => V_A_2 = V_B_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__refl,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_psubset__eq,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 & V_A_2 != V_B_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_set__eq__subset,axiom, % 1.45/1.48 ! [T_a,V_B_2,V_A_2] : % 1.45/1.48 ( V_A_2 = V_B_2 % 1.45/1.48 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__iff__psubset__eq,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 | V_A_2 = V_B_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_rev__predicate1D,axiom, % 1.45/1.48 ! [V_Q_2,T_a,V_x_2,V_Pa_2] : % 1.45/1.48 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) % 1.45/1.48 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_equalityD1,axiom, % 1.45/1.48 ! [T_a,V_B_2,V_A_2] : % 1.45/1.48 ( V_A_2 = V_B_2 % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_equalityD2,axiom, % 1.45/1.48 ! [T_a,V_B_2,V_A_2] : % 1.45/1.48 ( V_A_2 = V_B_2 % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_psubset__imp__subset,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_predicate1D,axiom, % 1.45/1.48 ! [V_x_2,V_Q_2,V_Pa_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) % 1.45/1.48 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.45/1.48 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_psubset__subset__trans,axiom, % 1.45/1.48 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__psubset__trans,axiom, % 1.45/1.48 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__trans,axiom, % 1.45/1.48 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_predicate2D,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_b,T_a] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_equalityE,axiom, % 1.45/1.48 ! [T_a,V_B_2,V_A_2] : % 1.45/1.48 ( V_A_2 = V_B_2 % 1.45/1.48 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_rev__predicate2D,axiom, % 1.45/1.48 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 1.45/1.48 => ( 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)) % 1.45/1.48 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_psubset__trans,axiom, % 1.45/1.48 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__neqE__linordered__idom,axiom, % 1.45/1.48 ! [V_y,V_x,T_a] : % 1.45/1.48 ( class_Rings_Olinordered__idom(T_a) % 1.45/1.48 => ( V_x != V_y % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__right__imp__eq,axiom, % 1.45/1.48 ! [V_c,V_a,V_b,T_a] : % 1.45/1.48 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.45/1.48 => ( 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) % 1.45/1.48 => V_b = V_c ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__imp__eq,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 1.45/1.48 => ( 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) % 1.45/1.48 => V_b = V_c ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__left__imp__eq,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.45/1.48 => ( 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) % 1.45/1.48 => V_b = V_c ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__right__cancel,axiom, % 1.45/1.48 ! [V_ca_2,V_aa_2,V_ba_2,T_a] : % 1.45/1.48 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.45/1.48 => ( 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) % 1.45/1.48 <=> V_ba_2 = V_ca_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__left__cancel,axiom, % 1.45/1.48 ! [V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.45/1.48 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.45/1.48 => ( 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) % 1.45/1.48 <=> V_ba_2 = V_ca_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oab__semigroup__add(T_a) % 1.45/1.48 => 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)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_one__reorient,axiom, % 1.45/1.48 ! [V_x_2,T_a] : % 1.45/1.48 ( class_Groups_Oone(T_a) % 1.45/1.48 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 1.45/1.48 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Pi__anti__mono,axiom, % 1.45/1.48 ! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Prof__def,axiom, % 1.45/1.48 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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__imp__le__left,axiom, % 1.45/1.48 ! [V_b,V_a,V_c,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__imp__le__right,axiom, % 1.45/1.48 ! [V_b,V_c,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__mono,axiom, % 1.45/1.48 ! [V_d,V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.45/1.48 => 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))) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__left__mono,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__right__mono,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__cancel__left,axiom, % 1.45/1.48 ! [V_ba_2,V_aa_2,V_ca_2,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__cancel__right,axiom, % 1.45/1.48 ! [V_ba_2,V_ca_2,V_aa_2,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__cancel__right,axiom, % 1.45/1.48 ! [V_ba_2,V_ca_2,V_aa_2,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__cancel__left,axiom, % 1.45/1.48 ! [V_ba_2,V_aa_2,V_ca_2,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__strict__right__mono,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__strict__left__mono,axiom, % 1.45/1.48 ! [V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__strict__mono,axiom, % 1.45/1.48 ! [V_d,V_c,V_b,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.45/1.48 => 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))) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__imp__less__right,axiom, % 1.45/1.48 ! [V_b,V_c,V_a,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__imp__less__left,axiom, % 1.45/1.48 ! [V_b,V_a,V_c,T_a] : % 1.45/1.48 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.45/1.48 => ( 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))) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_funcset__id,axiom, % 1.45/1.48 ! [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)))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Pi__UNIV,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__fun,axiom, % 1.45/1.48 ! [T_c,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_dictatorI,axiom, % 1.45/1.48 ! [V_i_2,V_Fa_2] : % 1.45/1.48 ( 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)))) % 1.45/1.48 => ( ! [B_x] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ! [B_a,B_b] : % 1.45/1.48 ( B_a != B_b % 1.45/1.48 => ( 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))) % 1.45/1.48 => 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))) ) ) ) % 1.45/1.48 => c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_injD,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.45/1.48 => V_x_2 = V_y_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__eq,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.45/1.48 <=> V_x_2 = V_y_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__inj__on,axiom, % 1.45/1.48 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__leE,axiom, % 1.45/1.48 ! [V_n,V_k,V_m] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.48 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__less__cases,axiom, % 1.45/1.48 ! [V_Pa_2,V_na_2,V_m_2] : % 1.45/1.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.45/1.48 => ( ( V_m_2 = V_na_2 % 1.45/1.48 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.45/1.48 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.45/1.48 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__not__refl3,axiom, % 1.45/1.48 ! [V_t,V_s] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 1.45/1.48 => V_s != V_t ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__not__refl2,axiom, % 1.45/1.48 ! [V_m,V_n] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.45/1.48 => V_m != V_n ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__irrefl__nat,axiom, % 1.45/1.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_linorder__neqE__nat,axiom, % 1.45/1.48 ! [V_y,V_x] : % 1.45/1.48 ( V_x != V_y % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__neq__iff,axiom, % 1.45/1.48 ! [V_na_2,V_m_2] : % 1.45/1.48 ( V_m_2 != V_na_2 % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.48 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__not__refl,axiom, % 1.45/1.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__commute,axiom, % 1.45/1.48 ! [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) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__left__commute,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__assoc,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__left__cancel,axiom, % 1.45/1.48 ! [V_na_2,V_m_2,V_k_2] : % 1.45/1.48 ( 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) % 1.45/1.48 <=> V_m_2 = V_na_2 ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__right__cancel,axiom, % 1.45/1.48 ! [V_na_2,V_k_2,V_m_2] : % 1.45/1.48 ( 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) % 1.45/1.48 <=> V_m_2 = V_na_2 ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__refl,axiom, % 1.45/1.48 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__le__linear,axiom, % 1.45/1.48 ! [V_n,V_m] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.48 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_eq__imp__le,axiom, % 1.45/1.48 ! [V_n,V_m] : % 1.45/1.48 ( V_m = V_n % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__trans,axiom, % 1.45/1.48 ! [V_k,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__antisym,axiom, % 1.45/1.48 ! [V_n,V_m] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 1.45/1.48 => V_m = V_n ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__on__def,axiom, % 1.45/1.48 ! [V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 <=> ! [B_x] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.45/1.48 => ! [B_xa] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 1.45/1.48 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 1.45/1.48 => B_x = B_xa ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__on__add__nat,axiom, % 1.45/1.48 ! [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) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__on__id2,axiom, % 1.45/1.48 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 1.45/1.48 % 1.45/1.48 fof(fact_dictator__def,axiom, % 1.45/1.48 ! [V_i_2,V_Fa_2] : % 1.45/1.48 ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) % 1.45/1.48 <=> ! [B_x] : % 1.45/1.48 ( 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)) % 1.45/1.48 => hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__onD,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.45/1.48 => V_x_2 = V_y_2 ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__on__iff,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.45/1.48 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.45/1.48 <=> V_x_2 = V_y_2 ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_inj__on__contraD,axiom, % 1.45/1.48 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( V_x_2 != V_y_2 % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.45/1.48 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__lessD1,axiom, % 1.45/1.48 ! [V_k,V_j,V_i] : % 1.45/1.48 ( 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)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__add__eq__less,axiom, % 1.45/1.48 ! [V_n,V_m,V_l,V_k] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.45/1.48 => ( 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) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__mono,axiom, % 1.45/1.48 ! [V_l,V_k,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__less__mono1,axiom, % 1.45/1.48 ! [V_k,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_trans__less__add2,axiom, % 1.45/1.48 ! [V_m,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_trans__less__add1,axiom, % 1.45/1.48 ! [V_m,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__left__cancel__less,axiom, % 1.45/1.48 ! [V_na_2,V_m_2,V_k_2] : % 1.45/1.48 ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_not__add__less2,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_not__add__less1,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__or__eq__imp__le,axiom, % 1.45/1.48 ! [V_n,V_m] : % 1.45/1.48 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.48 | V_m = V_n ) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__neq__implies__less,axiom, % 1.45/1.48 ! [V_n,V_m] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.48 => ( V_m != V_n % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__imp__le__nat,axiom, % 1.45/1.48 ! [V_n,V_m] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__eq__less__or__eq,axiom, % 1.45/1.48 ! [V_na_2,V_m_2] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.48 | V_m_2 = V_na_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__less__le,axiom, % 1.45/1.48 ! [V_na_2,V_m_2] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.48 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.45/1.48 & V_m_2 != V_na_2 ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__add2,axiom, % 1.45/1.48 ! [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))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__add1,axiom, % 1.45/1.48 ! [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))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le__iff__add,axiom, % 1.45/1.48 ! [V_na_2,V_m_2] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.45/1.48 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_nat__add__left__cancel__le,axiom, % 1.45/1.48 ! [V_na_2,V_m_2,V_k_2] : % 1.45/1.48 ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_trans__le__add1,axiom, % 1.45/1.48 ! [V_m,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_trans__le__add2,axiom, % 1.45/1.48 ! [V_m,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__mono1,axiom, % 1.45/1.48 ! [V_k,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__le__mono,axiom, % 1.45/1.48 ! [V_l,V_k,V_j,V_i] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__leD2,axiom, % 1.45/1.48 ! [V_n,V_k,V_m] : % 1.45/1.48 ( 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)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_add__leD1,axiom, % 1.45/1.48 ! [V_n,V_k,V_m] : % 1.45/1.48 ( 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)) % 1.45/1.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_unanimity__def,axiom, % 1.45/1.48 ! [V_Fa_2] : % 1.45/1.48 ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) % 1.45/1.48 <=> ! [B_x] : % 1.45/1.48 ( 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)) % 1.45/1.48 => ! [B_a,B_b] : % 1.45/1.48 ( ! [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))) % 1.45/1.48 => 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))) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_iso__tuple__UNIV__I,axiom, % 1.45/1.48 ! [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)))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__inj,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( 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)))) % 1.45/1.48 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.48 => 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))) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Pi__mono,axiom, % 1.45/1.48 ! [V_C_2,V_B_2,T_b,V_A_2,T_a] : % 1.45/1.48 ( ! [B_x] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.45/1.48 => 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))) ) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_Pi__I,axiom, % 1.45/1.48 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] : % 1.45/1.48 ( ! [B_x] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) ) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__indi,axiom, % 1.45/1.48 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__bij,axiom, % 1.45/1.48 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( 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)))) % 1.45/1.48 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.48 => ( 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)))) % 1.45/1.48 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.48 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__psubset,axiom, % 1.45/1.48 ! [V_A_2,V_B_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( 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))) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_psubset__card__mono,axiom, % 1.45/1.48 ! [V_A_2,V_B_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__seteq,axiom, % 1.45/1.48 ! [V_A_2,V_B_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( 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))) % 1.45/1.48 => V_A_2 = V_B_2 ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__mono,axiom, % 1.45/1.48 ! [V_A_2,V_B_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite,axiom, % 1.45/1.48 ! [V_A_2,T_a] : % 1.45/1.48 ( class_Finite__Set_Ofinite(T_a) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__code,axiom, % 1.45/1.48 ! [V_A_2,T_a] : % 1.45/1.48 ( class_Finite__Set_Ofinite(T_a) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__UNIV__unit,axiom, % 1.45/1.48 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) ). % 1.45/1.48 % 1.45/1.48 fof(fact_rev__finite__subset,axiom, % 1.45/1.48 ! [V_A_2,V_B_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__subset,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__UNIV,axiom, % 1.45/1.48 ! [T_a] : % 1.45/1.48 ( class_Finite__Set_Ofinite(T_a) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__Prod__UNIV,axiom, % 1.45/1.48 ! [T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 1.45/1.48 => 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))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__Plus__UNIV__iff,axiom, % 1.45/1.48 ! [T_b,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__option__UNIV,axiom, % 1.45/1.48 ! [T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))) % 1.45/1.48 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 1.45/1.48 ! [V_A_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.48 => ( 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))) % 1.45/1.48 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__fun__UNIVD2,axiom, % 1.45/1.48 ! [T_b,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_in__finite__psubset,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_a] : % 1.45/1.48 ( 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))) % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.48 & c_Finite__Set_Ofinite(T_a,V_B_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__Plus,axiom, % 1.45/1.48 ! [V_B_2,T_b,V_A_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.48 => 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)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card_Oinsert,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => 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)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.45/1.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) % 1.45/1.48 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insertCI,axiom, % 1.45/1.48 ! [V_ba_2,V_B_2,V_aa_2,T_a] : % 1.45/1.48 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) % 1.45/1.48 => V_aa_2 = V_ba_2 ) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insertE,axiom, % 1.45/1.48 ! [V_A_2,V_ba_2,V_aa_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) % 1.45/1.48 => ( V_aa_2 != V_ba_2 % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite_OinsertI,axiom, % 1.45/1.48 ! [V_aa_2,V_A_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.45/1.48 => 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)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__insert,axiom, % 1.45/1.48 ! [V_A_2,V_aa_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) % 1.45/1.48 <=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_folding__image__simple__idem_Oidem,axiom, % 1.45/1.48 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.45/1.48 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__absorb,axiom, % 1.45/1.48 ! [V_A_2,V_aa_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) % 1.45/1.48 => c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insertI2,axiom, % 1.45/1.48 ! [V_ba_2,V_B_2,V_aa_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) % 1.45/1.48 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__ident,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.45/1.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 1.45/1.48 => ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2) % 1.45/1.48 <=> V_A_2 = V_B_2 ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__iff,axiom, % 1.45/1.48 ! [V_A_2,V_ba_2,V_aa_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) % 1.45/1.48 <=> ( V_aa_2 = V_ba_2 % 1.45/1.48 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insertI1,axiom, % 1.45/1.48 ! [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))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__mono,axiom, % 1.45/1.48 ! [V_aa_2,V_D_2,V_C_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_D_2)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__insertI2,axiom, % 1.45/1.48 ! [V_ba_2,V_B_2,V_A_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.48 => 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))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__insertI,axiom, % 1.45/1.48 ! [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))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__absorb2,axiom, % 1.45/1.48 ! [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) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__commute,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__code,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,V_y_2,T_a] : % 1.45/1.48 ( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) % 1.45/1.48 <=> ( V_y_2 = V_x_2 % 1.45/1.48 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__Plus__iff,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.45/1.48 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__Plus,axiom, % 1.45/1.48 ! [V_B_2,T_b,V_A_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.48 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__PlusD_I1_J,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.45/1.48 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_finite__PlusD_I2_J,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.45/1.48 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_insert__subset,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.45/1.48 ( 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)) % 1.45/1.48 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 1.45/1.48 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_subset__insert,axiom, % 1.45/1.48 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.45/1.48 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.48 => ( 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))) % 1.45/1.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__insert__le,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 => 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)))) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.45/1.48 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.45/1.48 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_UNIV__Plus__UNIV,axiom, % 1.45/1.48 ! [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)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_card__Plus__conv__if,axiom, % 1.45/1.48 ! [V_B_2,T_b,V_A_2,T_a] : % 1.45/1.48 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.45/1.48 => 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)) ) % 1.45/1.48 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.48 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.45/1.48 => 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) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_folding__image__simple_Oinsert,axiom, % 1.45/1.48 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.45/1.48 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.45/1.48 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.45/1.48 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.45/1.48 => 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)) ) ) ) ). % 1.45/1.48 % 1.45/1.48 fof(fact_less__zeroE,axiom, % 1.45/1.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.45/1.48 % 1.45/1.48 fof(fact_le0,axiom, % 1.45/1.48 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.45/1.48 % 1.45/1.48 fof(fact_not__less0,axiom, % 1.45/1.48 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_neq0__conv,axiom, % 1.45/1.49 ! [V_na_2] : % 1.45/1.49 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__nat__zero__code,axiom, % 1.45/1.49 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_gr__implies__not0,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.49 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_gr0I,axiom, % 1.45/1.49 ! [V_n] : % 1.45/1.49 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__eq__self__zero,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 1.45/1.49 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__is__0,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Nat_Oadd__0__right,axiom, % 1.45/1.49 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 1.45/1.49 % 1.45/1.49 fof(fact_plus__nat_Oadd__0,axiom, % 1.45/1.49 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 1.45/1.49 % 1.45/1.49 fof(fact_le__0__eq,axiom, % 1.45/1.49 ! [V_na_2] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.45/1.49 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 1.45/1.49 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__reorient,axiom, % 1.45/1.49 ! [V_x_2,T_a] : % 1.45/1.49 ( class_Groups_Ozero(T_a) % 1.45/1.49 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 1.45/1.49 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_one__neq__zero,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Ozero__neq__one(T_a) % 1.45/1.49 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__neq__one,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Ozero__neq__one(T_a) % 1.45/1.49 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__0__left,axiom, % 1.45/1.49 ! [V_a,T_a] : % 1.45/1.49 ( class_Groups_Omonoid__add(T_a) % 1.45/1.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__0,axiom, % 1.45/1.49 ! [V_a,T_a] : % 1.45/1.49 ( class_Groups_Ocomm__monoid__add(T_a) % 1.45/1.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_double__zero__sym,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.45/1.49 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) % 1.45/1.49 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__0__right,axiom, % 1.45/1.49 ! [V_a,T_a] : % 1.45/1.49 ( class_Groups_Omonoid__add(T_a) % 1.45/1.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add_Ocomm__neutral,axiom, % 1.45/1.49 ! [V_a,T_a] : % 1.45/1.49 ( class_Groups_Ocomm__monoid__add(T_a) % 1.45/1.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__nonneg__nonneg,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__nonneg__eq__0__iff,axiom, % 1.45/1.49 ! [V_y_2,V_x_2,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 1.45/1.49 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.45/1.49 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 1.45/1.49 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__increasing,axiom, % 1.45/1.49 ! [V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__increasing2,axiom, % 1.45/1.49 ! [V_a,V_b,V_c,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__nonpos__nonpos,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__pos__pos,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_pos__add__strict,axiom, % 1.45/1.49 ! [V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__neg__neg,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_not__one__le__zero,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.49 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__le__one,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_not__one__less__zero,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.49 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__less__one,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__gr__0,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( 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))) % 1.45/1.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 1.45/1.49 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__infinite,axiom, % 1.45/1.49 ! [V_A_2,T_a] : % 1.45/1.49 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__pos__nonneg,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__nonneg__pos,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__strict__increasing,axiom, % 1.45/1.49 ! [V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__strict__increasing2,axiom, % 1.45/1.49 ! [V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__neg__nonpos,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__nonpos__neg,axiom, % 1.45/1.49 ! [V_b,V_a,T_a] : % 1.45/1.49 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__less__two,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Olinordered__semidom(T_a) % 1.45/1.49 => 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)))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__ge__0__finite,axiom, % 1.45/1.49 ! [V_A_2,T_a] : % 1.45/1.49 ( 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))) % 1.45/1.49 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__UNIV__card__ge__0,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => 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))))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_even__less__0__iff,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Rings_Olinordered__idom(T_a) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__fun__UNIVD1,axiom, % 1.45/1.49 ! [T_b,T_a] : % 1.45/1.49 ( 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))) % 1.45/1.49 => ( 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)) % 1.45/1.49 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 1.45/1.49 ! [V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__mono,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_lessI,axiom, % 1.45/1.49 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_zero__less__Suc,axiom, % 1.45/1.49 ! [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))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__neq__Zero,axiom, % 1.45/1.49 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Zero__neq__Suc,axiom, % 1.45/1.49 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Osimps_I3_J,axiom, % 1.45/1.49 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__not__Zero,axiom, % 1.45/1.49 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Osimps_I2_J,axiom, % 1.45/1.49 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Zero__not__Suc,axiom, % 1.45/1.49 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__less__SucD,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__lessD,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__SucE,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 1.45/1.49 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.49 => V_m = V_n ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__trans__Suc,axiom, % 1.45/1.49 ! [V_k,V_j,V_i] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__lessI,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.49 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__SucI,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__antisym,axiom, % 1.45/1.49 ! [V_m,V_n] : % 1.45/1.49 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 1.45/1.49 => V_m = V_n ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_not__less__less__Suc__eq,axiom, % 1.45/1.49 ! [V_m_2,V_na_2] : % 1.45/1.49 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.45/1.49 <=> V_na_2 = V_m_2 ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__less__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__Suc__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.45/1.49 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.49 | V_m_2 = V_na_2 ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_not__less__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__Suc__right,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__Suc,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__Suc__shift,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__n__not__le__n,axiom, % 1.45/1.49 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_not__less__eq__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_le__Suc__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.45/1.49 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.45/1.49 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__le__mono,axiom, % 1.45/1.49 ! [V_m_2,V_na_2] : % 1.45/1.49 ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),V_m_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_le__SucI,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_le__SucE,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) % 1.45/1.49 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.49 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__leD,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.45/1.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_n__not__Suc__n,axiom, % 1.45/1.49 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__n__not__n,axiom, % 1.45/1.49 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Oinject,axiom, % 1.45/1.49 ! [V_nat_H_2,V_nat_2] : % 1.45/1.49 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 1.45/1.49 <=> V_nat_2 = V_nat_H_2 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__inject,axiom, % 1.45/1.49 ! [V_y,V_x] : % 1.45/1.49 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 1.45/1.49 => V_x = V_y ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__Suc,axiom, % 1.45/1.49 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 1.45/1.49 % 1.45/1.49 fof(fact_gr0__conv__Suc,axiom, % 1.45/1.49 ! [V_na_2] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 1.45/1.49 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__Suc0,axiom, % 1.45/1.49 ! [V_na_2] : % 1.45/1.49 ( 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)))) % 1.45/1.49 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__Suc__eq__0__disj,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.45/1.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 | ? [B_j] : % 1.45/1.49 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 1.45/1.49 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_one__is__add,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( 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) % 1.45/1.49 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.45/1.49 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.45/1.49 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__is__1,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( 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)) % 1.45/1.49 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.45/1.49 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.45/1.49 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.45/1.49 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__iff__Suc__add,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.45/1.49 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__add__Suc2,axiom, % 1.45/1.49 ! [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)))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__add__Suc1,axiom, % 1.45/1.49 ! [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)))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__le__lessD,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_le__less__Suc__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.45/1.49 <=> V_na_2 = V_m_2 ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__leI,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.45/1.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_le__imp__less__Suc,axiom, % 1.45/1.49 ! [V_n,V_m] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__le__eq,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__Suc__eq__le,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__eq__Suc__le,axiom, % 1.45/1.49 ! [V_m_2,V_na_2] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_One__nat__def,axiom, % 1.45/1.49 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__eq__Suc__le__raw,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 1.45/1.49 ! [V_d,V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 1.45/1.49 ! [V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 1.45/1.49 ! [V_c,V_b,V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 1.45/1.49 ! [V_d,V_c,V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 1.45/1.49 ! [V_d,V_c,V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 1.45/1.49 ! [V_c,V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__insert__disjoint,axiom, % 1.45/1.49 ! [V_x_2,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.49 => 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)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__insert__if,axiom, % 1.45/1.49 ! [V_x_2,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.49 => 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) ) % 1.45/1.49 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.49 => 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)) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_double__eq__0__iff,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.45/1.49 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.45/1.49 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_add__0__iff,axiom, % 1.45/1.49 ! [V_aa_2,V_ba_2,T_a] : % 1.45/1.49 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 1.45/1.49 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) % 1.45/1.49 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 1.45/1.49 ! [V_a,T_a] : % 1.45/1.49 ( class_Rings_Ocomm__semiring__1(T_a) % 1.45/1.49 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__eq__plus1__left,axiom, % 1.45/1.49 ! [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) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Suc__eq__plus1,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Osize_I2_J,axiom, % 1.45/1.49 ! [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))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Osize_I4_J,axiom, % 1.45/1.49 ! [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))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat__size,axiom, % 1.45/1.49 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Osize_I3_J,axiom, % 1.45/1.49 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat_Osize_I1_J,axiom, % 1.45/1.49 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Ints__odd__less__0,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Rings_Olinordered__idom(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_ex__least__nat__less,axiom, % 1.45/1.49 ! [V_na_2,V_Pa_2] : % 1.45/1.49 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.45/1.49 => ( hBOOL(hAPP(V_Pa_2,V_na_2)) % 1.45/1.49 => ? [B_k] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2)) % 1.45/1.49 & ! [B_i] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) % 1.45/1.49 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 1.45/1.49 & 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)))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Ints__0,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Oring__1(T_a) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Ints__add,axiom, % 1.45/1.49 ! [V_ba_2,V_aa_2,T_a] : % 1.45/1.49 ( class_Rings_Oring__1(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Int_Oring__1__class_OInts(T_a))) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Ints__1,axiom, % 1.45/1.49 ! [T_a] : % 1.45/1.49 ( class_Rings_Oring__1(T_a) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Ints__double__eq__0__iff,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Int_Oring__char__0(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.45/1.49 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.45/1.49 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_Ints__odd__nonzero,axiom, % 1.45/1.49 ! [V_aa_2,T_a] : % 1.45/1.49 ( class_Int_Oring__char__0(T_a) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.45/1.49 => 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) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card_Oeq__fold__g,axiom, % 1.45/1.49 ! [V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__def,axiom, % 1.45/1.49 ! [V_A_2,T_a] : % 1.45/1.49 ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => 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) ) % 1.45/1.49 & ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 1.45/1.49 ! [V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.45/1.49 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.45/1.49 => 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) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_surjh,axiom, % 1.45/1.49 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)))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 1.45/1.49 ! [V_na_2,V_m_2] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 1.45/1.49 <=> 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__eqI,axiom, % 1.45/1.49 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_ba_2] : % 1.45/1.49 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__imageI,axiom, % 1.45/1.49 ! [V_ha_2,T_b,V_Fa_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_Fa_2) % 1.45/1.49 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_pigeonhole,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( 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))) % 1.45/1.49 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__image__mem__iff,axiom, % 1.45/1.49 ! [V_A_2,V_aa_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_range__ex1__eq,axiom, % 1.45/1.49 ! [V_ba_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => ( 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))))) % 1.45/1.49 <=> ? [B_x] : % 1.45/1.49 ( V_ba_2 = hAPP(V_f_2,B_x) % 1.45/1.49 & ! [B_y] : % 1.45/1.49 ( V_ba_2 = hAPP(V_f_2,B_y) % 1.45/1.49 => B_y = B_x ) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_insert__image,axiom, % 1.45/1.49 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_range__eqI,axiom, % 1.45/1.49 ! [T_b,T_a,V_x_2,V_f_2,V_ba_2] : % 1.45/1.49 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.45/1.49 => 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))))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_rangeI,axiom, % 1.45/1.49 ! [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))))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__surj,axiom, % 1.45/1.49 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( 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))) % 1.45/1.49 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__imageD,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) % 1.45/1.49 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 1.45/1.49 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__image__eq__iff,axiom, % 1.45/1.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => ( 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) % 1.45/1.49 <=> V_A_2 = V_B_2 ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__image,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inv__into__injective,axiom, % 1.45/1.49 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_b,T_a] : % 1.45/1.49 ( 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) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.45/1.49 => V_x_2 = V_y_2 ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inv__into__into,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,V_x_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.45/1.49 => 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_f__inv__into__f,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,V_y_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.45/1.49 => 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 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__inv__into__cancel,axiom, % 1.45/1.49 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 1.45/1.49 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_A_H_2 % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_H_2),V_A_H_2)) % 1.45/1.49 => 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 ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__surj__f__inv__f,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_a,T_b] : % 1.45/1.49 ( 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)) % 1.45/1.49 => 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 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_surj__f__inv__f,axiom, % 1.45/1.49 ! [V_y_2,V_f_2,T_a,T_b] : % 1.45/1.49 ( 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)) % 1.45/1.49 => 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 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_surj__iff__all,axiom, % 1.45/1.49 ! [V_f_2,T_a,T_b] : % 1.45/1.49 ( 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)) % 1.45/1.49 <=> ! [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 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__on__strict__subset,axiom, % 1.45/1.49 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.45/1.49 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.45/1.49 => 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))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_rev__image__eqI,axiom, % 1.45/1.49 ! [T_b,V_f_2,V_ba_2,V_A_2,V_x_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.49 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_imageI,axiom, % 1.45/1.49 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.45/1.49 => 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))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__iff,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.45/1.49 <=> ? [B_x] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 1.45/1.49 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__insert,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_range__composition,axiom, % 1.45/1.49 ! [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)))) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__image,axiom, % 1.45/1.49 ! [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) ). % 1.45/1.49 % 1.45/1.49 fof(fact_subset__image__iff,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.45/1.49 ( 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))) % 1.45/1.49 <=> ? [B_AA] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2)) % 1.45/1.49 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__mono,axiom, % 1.45/1.49 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 1.45/1.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.45/1.49 => 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))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__ident,axiom, % 1.45/1.49 ! [V_Y_2,T_a] : c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2 ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat__case__Suc,axiom, % 1.45/1.49 ! [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) ). % 1.45/1.49 % 1.45/1.49 fof(fact_nat__case__0,axiom, % 1.45/1.49 ! [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 ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__range__imageI,axiom, % 1.45/1.49 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 1.45/1.49 ( 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)))) % 1.45/1.49 => 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)))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_eq__card__imp__inj__on,axiom, % 1.45/1.49 ! [V_f_2,T_b,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( 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) % 1.45/1.49 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__on__iff__eq__card,axiom, % 1.45/1.49 ! [V_f_2,T_b,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.49 <=> 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) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__image__le,axiom, % 1.45/1.49 ! [V_f_2,T_b,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => 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))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__image__subset__iff,axiom, % 1.45/1.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => ( 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))) % 1.45/1.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__UNIV__inj__surj,axiom, % 1.45/1.49 ! [V_f_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => 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)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__UNIV__surj__inj,axiom, % 1.45/1.49 ! [V_f_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => ( 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)) % 1.45/1.49 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_endo__inj__surj,axiom, % 1.45/1.49 ! [V_f_2,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( 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)) % 1.45/1.49 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 1.45/1.49 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__surj__inj,axiom, % 1.45/1.49 ! [V_f_2,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( 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))) % 1.45/1.49 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__on__inv__into,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.45/1.49 ( 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))) % 1.45/1.49 => 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) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inv__into__image__cancel,axiom, % 1.45/1.49 ! [V_S_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_S_2),V_A_2)) % 1.45/1.49 => 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 ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__imp__surj__inv,axiom, % 1.45/1.49 ! [V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__inv__f__f,axiom, % 1.45/1.49 ! [V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => 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 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inv__image__comp,axiom, % 1.45/1.49 ! [V_X_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.45/1.49 => 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 ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_surj__imp__inj__inv,axiom, % 1.45/1.49 ! [V_f_2,T_a,T_b] : % 1.45/1.49 ( 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)) % 1.45/1.49 => 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))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_funcset__image,axiom, % 1.45/1.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( 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)))) % 1.45/1.49 => 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)) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__bij__eq,axiom, % 1.45/1.49 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.49 => ( 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)) % 1.45/1.49 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.45/1.49 => ( 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)) % 1.45/1.49 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.49 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_card__inj__on__le,axiom, % 1.45/1.49 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.45/1.49 => ( 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)) % 1.45/1.49 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.49 => 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 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, % 1.45/1.49 ~ ! [B_h] : % 1.45/1.49 ( 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))) % 1.45/1.49 => 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)))) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_inj__on__iff__card__le,axiom, % 1.45/1.49 ! [V_B_2,T_b,V_A_2,T_a] : % 1.45/1.49 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.45/1.49 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.45/1.49 => ( ? [B_f] : % 1.45/1.49 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 1.45/1.49 & 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)) ) % 1.45/1.49 <=> 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))) ) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__atLeastLessThan,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__Suc__atLeastLessThan,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_image__add__atLeastLessThan,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__nat__set__iff__bounded,axiom, % 1.45/1.49 ! [V_N_2] : % 1.45/1.49 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.45/1.49 <=> ? [B_m] : % 1.45/1.49 ! [B_x] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.45/1.49 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 1.45/1.49 % 1.45/1.49 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 1.45/1.49 ! [V_N_2] : % 1.45/1.49 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.45/1.49 <=> ? [B_m] : % 1.45/1.49 ! [B_x] : % 1.45/1.49 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.45/1.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x),B_m)) ) ) ). % 1.45/1.49 % 1.45/1.49 %----Arity declarations (33) % 1.45/1.49 fof(arity_fun__Orderings_Opreorder,axiom, % 1.45/1.49 ! [T_2,T_1] : % 1.45/1.49 ( class_Orderings_Opreorder(T_1) % 1.45/1.49 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_fun__Finite__Set_Ofinite,axiom, % 1.45/1.49 ! [T_1,T_2] : % 1.45/1.49 ( ( class_Finite__Set_Ofinite(T_2) % 1.45/1.49 & class_Finite__Set_Ofinite(T_1) ) % 1.45/1.49 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_fun__Orderings_Oorder,axiom, % 1.45/1.49 ! [T_2,T_1] : % 1.45/1.49 ( class_Orderings_Oorder(T_1) % 1.45/1.49 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_fun__Orderings_Otop,axiom, % 1.45/1.49 ! [T_2,T_1] : % 1.45/1.49 ( class_Orderings_Otop(T_1) % 1.45/1.49 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_fun__Orderings_Oord,axiom, % 1.45/1.49 ! [T_2,T_1] : % 1.45/1.49 ( class_Orderings_Oord(T_1) % 1.45/1.49 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 1.45/1.49 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 1.45/1.49 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 1.45/1.49 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 1.45/1.49 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 1.45/1.49 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 1.45/1.49 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 1.45/1.49 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 1.45/1.49 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 1.45/1.49 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 1.45/1.49 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 1.45/1.49 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 1.45/1.49 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 1.45/1.49 class_Orderings_Opreorder(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 1.45/1.49 class_Orderings_Olinorder(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 1.45/1.49 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 1.45/1.49 class_Orderings_Oorder(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 1.45/1.49 class_Orderings_Oord(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 1.45/1.49 class_Groups_Ozero(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Nat__Onat__Groups_Oone,axiom, % 1.45/1.49 class_Groups_Oone(tc_Nat_Onat) ). % 1.45/1.49 % 1.45/1.49 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 1.45/1.49 class_Orderings_Opreorder(tc_HOL_Obool) ). % 1.45/1.49 % 1.45/1.49 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 1.45/1.49 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 1.45/1.49 % 1.45/1.49 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 1.45/1.49 class_Orderings_Oorder(tc_HOL_Obool) ). % 1.45/1.49 % 1.45/1.49 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 1.45/1.49 class_Orderings_Otop(tc_HOL_Obool) ). % 1.45/1.49 % 1.45/1.49 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 1.45/1.49 class_Orderings_Oord(tc_HOL_Obool) ). % 1.45/1.49 % 1.45/1.49 fof(arity_sum__Finite__Set_Ofinite,axiom, % 1.45/1.49 ! [T_1,T_2] : % 1.45/1.49 ( ( class_Finite__Set_Ofinite(T_2) % 1.45/1.49 & class_Finite__Set_Ofinite(T_1) ) % 1.45/1.49 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 1.45/1.49 ! [T_1] : % 1.45/1.49 ( class_Finite__Set_Ofinite(T_1) % 1.45/1.49 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_prod__Finite__Set_Ofinite,axiom, % 1.45/1.49 ! [T_1,T_2] : % 1.45/1.49 ( ( class_Finite__Set_Ofinite(T_2) % 1.45/1.49 & class_Finite__Set_Ofinite(T_1) ) % 1.45/1.49 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 1.45/1.49 % 1.45/1.49 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 1.45/1.49 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 1.45/1.49 % 1.45/1.49 %----Helper facts (8) % 1.45/1.49 fof(help_c__COMBI__1,axiom, % 1.45/1.49 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 1.45/1.49 % 1.45/1.49 fof(help_c__COMBK__1,axiom, % 1.45/1.49 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 1.45/1.49 % 1.45/1.49 fof(help_c__COMBB__1,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(help_c__COMBC__1,axiom, % 1.45/1.49 ! [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) ). % 1.45/1.49 % 1.45/1.49 fof(help_c__COMBS__1,axiom, % 1.45/1.49 ! [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)) ). % 1.45/1.49 % 1.45/1.49 fof(help_c__fequal__1,axiom, % 1.45/1.49 ! [V_y_2,V_x_2] : % 1.45/1.49 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 1.45/1.49 | V_x_2 = V_y_2 ) ). % 1.45/1.49 % 1.45/1.49 fof(help_c__fequal__2,axiom, % 1.45/1.49 ! [V_y_2,V_x_2] : % 1.45/1.49 ( V_x_2 != V_y_2 % 1.45/1.49 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 1.45/1.49 % 1.45/1.49 fof(help_c__fFalse__1,axiom, % 1.45/1.49 ~ hBOOL(c_fFalse) ). % 1.45/1.49 % 1.45/1.49 %----Conjectures (1) % 1.45/1.49 fof(conj_0,conjecture, % 1.45/1.49 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____)))))) ). % 1.45/1.49 % 1.45/1.49 %------------------------------------------------------------------------------ % 1.45/1.49 %------------------------------------------- % 1.45/1.49 % Proof found % 1.45/1.49 % SZS status Theorem for theBenchmark % 1.45/1.49 % SZS output start Proof % 1.45/1.49 %ClaNum:1053(EqnAxiom:265) % 1.45/1.49 %VarNum:5257(SingletonVarNum:1731) % 1.45/1.49 %MaxLitNum:10 % 1.45/1.49 %MaxfuncDepth:12 % 1.45/1.49 %SharedTerms:270 % 1.45/1.49 %goalClause: 398 % 1.45/1.49 %singleGoalClaCount:1 % 1.45/1.49 [266]P1(a1) % 1.45/1.49 [267]P2(a1) % 1.45/1.49 [268]P4(a2) % 1.45/1.49 [269]P5(a2) % 1.45/1.49 [270]P5(a91) % 1.45/1.49 [271]P6(a91) % 1.45/1.49 [272]P27(a2) % 1.45/1.49 [273]P27(a91) % 1.45/1.49 [274]P28(a2) % 1.45/1.49 [275]P28(a91) % 1.45/1.49 [276]P29(a91) % 1.45/1.49 [277]P7(a91) % 1.45/1.49 [278]P8(a91) % 1.45/1.49 [279]P9(a91) % 1.45/1.49 [280]P10(a91) % 1.45/1.49 [281]P18(a91) % 1.45/1.49 [282]P22(a91) % 1.45/1.49 [283]P23(a91) % 1.45/1.49 [284]P11(a2) % 1.45/1.49 [285]P11(a92) % 1.45/1.49 [286]P24(a91) % 1.45/1.49 [287]P32(a91) % 1.45/1.49 [288]P19(a91) % 1.45/1.49 [289]P20(a91) % 1.45/1.49 [290]P25(a91) % 1.45/1.49 [291]P30(a91) % 1.45/1.49 [292]P34(a91) % 1.45/1.49 [377]~E(a104,a103) % 1.45/1.49 [378]~E(a101,a100) % 1.45/1.49 [379]~P35(a39) % 1.45/1.49 [293]E(f20(f3(a91)),f3(a91)) % 1.45/1.49 [295]E(f27(a21,f3(a91)),f4(a91)) % 1.45/1.49 [301]P12(a89,f30(f94(a89,a2))) % 1.45/1.49 [332]P13(a89,a91,a97,f30(f94(a89,a2))) % 1.45/1.49 [333]P13(a89,a91,a44,f30(f94(a89,a2))) % 1.45/1.49 [302]E(f14(a92,f30(f94(a92,a2))),f4(a91)) % 1.45/1.49 [334]P35(f27(f27(f29(a91),a106),f14(a89,f30(f94(a89,a2))))) % 1.45/1.49 [335]P35(f27(f27(f29(a91),a45),f14(a89,f30(f94(a89,a2))))) % 1.45/1.49 [336]P35(f27(f27(f29(a91),a50),f14(a89,f30(f94(a89,a2))))) % 1.45/1.49 [343]E(f31(a91,f3(a91),f14(a89,f30(f94(a89,a2)))),f36(a89,a91,a97,f30(f94(a89,a2)))) % 1.45/1.49 [344]E(f31(a91,f3(a91),f14(a89,f30(f94(a89,a2)))),f36(a89,a91,a44,f30(f94(a89,a2)))) % 1.45/1.49 [348]P35(f27(f27(f34(f94(f96(a90,a90),a2)),a98),a7)) % 1.45/1.49 [349]P35(f27(f27(f34(f94(f96(a90,a90),a2)),a99),a7)) % 1.45/1.49 [350]P35(f27(f27(f34(f94(f96(a90,a90),a2)),a51),a7)) % 1.45/1.49 [351]P35(f27(f27(f34(f94(f96(a90,a90),a2)),a52),a7)) % 1.45/1.49 [354]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),a99)) % 1.45/1.49 [355]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),a52)) % 1.45/1.49 [356]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a98)) % 1.45/1.49 [357]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a51)) % 1.45/1.49 [396]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),a98)) % 1.45/1.49 [397]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.49 [359]E(f17(a89,f94(f96(a90,a90),a2),f30(f94(a89,a2)),f27(f15(f94(f94(f96(a90,a90),a2),a2),a89),a7)),a8) % 1.45/1.49 [362]P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),a102),a8)) % 1.45/1.49 [368]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,f27(f22(a89,a91,f30(f94(a89,a2)),a97),a106)))) % 1.45/1.49 [369]P35(f27(f27(f34(f94(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2))),a1),f17(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2),a8,f27(f15(f94(f94(f96(a90,a90),a2),a2),f94(a89,f94(f96(a90,a90),a2))),a7)))) % 1.45/1.49 [371]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),f27(f27(f19(a91),a106),f4(a91))))),a98)),a99)))) % 1.45/1.49 [372]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),f27(f27(f19(a91),a45),f4(a91))))),a98)),a99)))) % 1.45/1.49 [373]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),f27(f27(f19(a91),a50),f4(a91))))),a98)),a99)))) % 1.45/1.49 [374]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(a1,f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a10),a102)),a105)),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,a38),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f27(f6(a89,a90,f94(a90,f94(f96(a90,a90),a2))),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(a90,f94(f96(a90,a90),a2))),a89,a11),a102)),a103)),a105)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a12),a102)),a105)))))) % 1.45/1.49 [375]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a105),a104)),f27(a1,f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a10),a102)),a105)),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,a38),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f27(f6(a89,a90,f94(a90,f94(f96(a90,a90),a2))),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(a90,f94(f96(a90,a90),a2))),a89,a11),a102)),a103)),a105)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a12),a102)),a105)))))) % 1.45/1.49 [376]P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a10),a102)),a105)),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,a38),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f27(f6(a89,a90,f94(a90,f94(f96(a90,a90),a2))),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(a90,f94(f96(a90,a90),a2))),a89,a11),a102)),a103)),a105)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a12),a102)),a105)))),a8)) % 1.45/1.49 [398]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a1,f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a10),a102)),a105)),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,a38),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f27(f6(a89,a90,f94(a90,f94(f96(a90,a90),a2))),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(a90,f94(f96(a90,a90),a2))),a89,a11),a102)),a103)),a105)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a12),a102)),a105)))))) % 1.45/1.49 [323]P13(a91,a91,a21,x3231) % 1.45/1.49 [294]E(f26(a91,x2941),x2941) % 1.45/1.49 [381]~E(f27(a21,x3811),x3811) % 1.45/1.49 [387]~E(f27(a21,x3871),f3(a91)) % 1.45/1.49 [298]E(f27(f27(f19(a91),x2981),f3(a91)),x2981) % 1.45/1.49 [299]E(f28(a91,f27(a21,x2991)),f27(f29(a91),x2991)) % 1.45/1.49 [303]E(f27(f27(f19(a91),x3031),f4(a91)),f27(a21,x3031)) % 1.45/1.49 [305]P35(f27(f28(a91,x3051),x3051)) % 1.45/1.49 [313]P35(f27(f27(f29(a91),x3131),f27(a21,x3131))) % 1.45/1.49 [314]P35(f27(f27(f29(a91),f3(a91)),f27(a21,x3141))) % 1.45/1.49 [392]~P35(f27(f27(f29(a91),x3921),f3(a91))) % 1.45/1.49 [300]E(f27(f27(f19(a91),f3(a91)),x3001),x3001) % 1.45/1.49 [304]E(f27(f27(f19(a91),f4(a91)),x3041),f27(a21,x3041)) % 1.45/1.49 [307]P35(f27(f28(a91,f3(a91)),x3071)) % 1.45/1.49 [310]E(f27(f27(f19(a91),f20(x3101)),f27(a21,f3(a91))),f20(f27(a21,x3101))) % 1.45/1.49 [315]E(f27(f27(f19(a91),f26(a91,x3151)),f27(a21,f3(a91))),f26(a91,f27(a21,x3151))) % 1.45/1.49 [389]~P35(f27(f27(f29(a91),x3891),x3891)) % 1.45/1.49 [393]~P35(f27(f28(a91,f27(a21,x3931)),x3931)) % 1.45/1.49 [370]P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),x3701))),a98)),a99)),a8)) % 1.45/1.49 [311]P12(a91,f31(a91,x3111,x3112)) % 1.45/1.49 [325]P13(x3251,x3251,f5(x3251),x3252) % 1.45/1.49 [297]E(f27(f5(x2971),x2972),x2972) % 1.45/1.49 [326]E(f36(x3261,x3261,f5(x3261),x3262),x3262) % 1.45/1.49 [342]E(f36(a91,a91,a21,f31(a91,x3421,x3422)),f31(a91,f27(a21,x3421),f27(a21,x3422))) % 1.45/1.49 [308]E(f27(f27(f19(a91),x3081),x3082),f27(f27(f19(a91),x3082),x3081)) % 1.45/1.49 [312]P35(f27(f30(f94(x3121,a2)),x3122)) % 1.45/1.49 [316]E(f27(f27(f19(a91),f27(a21,x3161)),x3162),f27(f27(f19(a91),x3161),f27(a21,x3162))) % 1.45/1.49 [318]P35(f27(f28(f94(x3181,a2),x3182),x3182)) % 1.45/1.49 [321]P35(f27(f27(f34(x3211),x3212),f30(f94(x3211,a2)))) % 1.45/1.49 [330]P35(f27(f28(f94(x3301,a2),x3302),f30(f94(x3301,a2)))) % 1.45/1.49 [341]E(f37(x3411,x3412,f30(f94(x3411,a2)),f30(f94(x3412,a2))),f30(f94(f95(x3411,x3412),a2))) % 1.45/1.49 [353]P13(a91,a91,f27(f27(f6(a91,a91,a91),f19(a91)),x3531),x3532) % 1.45/1.49 [317]E(f27(f27(f19(a91),x3171),f27(a21,x3172)),f27(a21,f27(f27(f19(a91),x3171),x3172))) % 1.45/1.49 [319]E(f27(f27(f19(a91),f27(a21,x3191)),x3192),f27(a21,f27(f27(f19(a91),x3191),x3192))) % 1.45/1.49 [327]P35(f27(f28(a91,x3271),f27(f27(f19(a91),x3272),x3271))) % 1.45/1.49 [328]P35(f27(f28(a91,x3281),f27(f27(f19(a91),x3281),x3282))) % 1.45/1.49 [345]P35(f27(f27(f29(a91),x3451),f27(a21,f27(f27(f19(a91),x3452),x3451)))) % 1.45/1.49 [346]P35(f27(f27(f29(a91),x3461),f27(a21,f27(f27(f19(a91),x3461),x3462)))) % 1.45/1.49 [365]P35(f27(f27(f34(f94(x3651,x3651)),f5(x3651)),f17(x3651,x3651,x3652,f27(f15(f94(x3651,a2),x3651),x3652)))) % 1.45/1.49 [394]~P35(f27(f27(f29(a91),f27(f27(f19(a91),x3941),x3942)),x3942)) % 1.45/1.49 [395]~P35(f27(f27(f29(a91),f27(f27(f19(a91),x3951),x3952)),x3951)) % 1.45/1.49 [322]E(f35(x3221,x3222,f35(x3221,x3222,x3223)),f35(x3221,x3222,x3223)) % 1.45/1.49 [324]E(f25(x3241,x3242,x3243,f3(a91)),x3242) % 1.45/1.49 [337]P35(f27(f27(f34(x3371),x3372),f35(x3371,x3372,x3373))) % 1.45/1.49 [340]P35(f27(f28(f94(x3401,a2),x3402),f35(x3401,x3403,x3402))) % 1.45/1.49 [329]E(f27(f27(f19(a91),x3291),f27(f27(f19(a91),x3292),x3293)),f27(f27(f19(a91),x3292),f27(f27(f19(a91),x3291),x3293))) % 1.45/1.49 [352]E(f17(x3521,x3522,x3523,f27(f15(f94(x3522,a2),x3521),f30(f94(x3522,a2)))),f30(f94(f94(x3521,x3522),a2))) % 1.45/1.49 [360]E(f36(a91,a91,f27(f27(f6(a91,a91,a91),f19(a91)),x3601),f31(a91,x3602,x3603)),f31(a91,f27(f27(f19(a91),x3602),x3601),f27(f27(f19(a91),x3603),x3601))) % 1.45/1.49 [339]E(f27(f27(f19(a91),f27(f27(f19(a91),x3391),x3392)),x3393),f27(f27(f19(a91),x3391),f27(f27(f19(a91),x3392),x3393))) % 1.45/1.49 [331]E(f25(x3311,x3312,x3313,f27(a21,x3314)),f27(x3313,x3314)) % 1.45/1.49 [338]E(f35(x3381,x3382,f35(x3381,x3383,x3384)),f35(x3381,x3383,f35(x3381,x3382,x3384))) % 1.45/1.49 [309]E(f27(f27(f15(x3091,x3092),x3093),x3094),x3093) % 1.45/1.49 [363]P35(f27(f27(f34(x3631),f27(x3632,x3633)),f36(x3634,x3631,x3632,f30(f94(x3634,a2))))) % 1.45/1.49 [358]E(f36(x3581,x3582,x3583,f35(x3581,x3584,x3585)),f35(x3582,f27(x3583,x3584),f36(x3581,x3582,x3583,x3585))) % 1.45/1.49 [366]E(f36(x3661,x3662,f27(f9(x3663,x3662,x3661,x3664),x3665),f30(f94(x3661,a2))),f36(x3663,x3662,x3664,f36(x3661,x3663,x3665,f30(f94(x3661,a2))))) % 1.45/1.49 [367]E(f27(f16(x3671,x3672,x3673,x3674,x3675),x3676),f27(f27(x3674,x3676),f27(x3675,x3676))) % 1.45/1.49 [361]E(f27(f27(f9(x3611,x3612,x3613,x3614),x3615),x3616),f27(x3614,f27(x3615,x3616))) % 1.45/1.49 [364]E(f36(x3641,x3642,x3643,f36(x3644,x3641,x3645,x3646)),f36(x3644,x3642,f27(f9(x3641,x3642,x3644,x3643),x3645),x3646)) % 1.45/1.49 [347]E(f27(f27(f27(f6(x3471,x3472,x3473),x3474),x3475),x3476),f27(f27(x3474,x3476),x3475)) % 1.45/1.49 [1048]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a1,a102)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a1,f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a10),a102)),a105)),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,a38),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f27(f6(a89,a90,f94(a90,f94(f96(a90,a90),a2))),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(a90,f94(f96(a90,a90),a2))),a89,a11),a102)),a103)),a105)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a12),a102)),a105)))))) % 1.45/1.49 [1052]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a105),a104)),f27(a1,f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a10),a102)),a105)),f16(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2),f16(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,a38),a97)),a106)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f27(f6(a89,a90,f94(a90,f94(f96(a90,a90),a2))),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(a90,f94(f96(a90,a90),a2))),a89,a11),a102)),a103)),a105)),f27(f27(f6(a89,a90,f94(f96(a90,a90),a2)),f27(f9(f94(f96(a90,a90),a2),f94(a90,f94(f96(a90,a90),a2)),a89,a12),a102)),a105))))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),a106))),a98)),a99)))) % 1.45/1.49 [399]~P11(x3991)+P11(f93(x3991)) % 1.45/1.49 [401]~P32(x4011)+~E(f4(x4011),f3(x4011)) % 1.45/1.49 [458]~P29(x4581)+P35(f27(f28(x4581,f3(x4581)),f4(x4581))) % 1.45/1.49 [463]E(x4631,f3(a91))+~P35(f27(f28(a91,x4631),f3(a91))) % 1.45/1.49 [472]~P33(x4721)+P35(f27(f27(f34(x4721),f4(x4721)),f24(x4721))) % 1.45/1.49 [473]~P33(x4731)+P35(f27(f27(f34(x4731),f3(x4731)),f24(x4731))) % 1.45/1.49 [474]~P29(x4741)+P35(f27(f27(f29(x4741),f3(x4741)),f4(x4741))) % 1.45/1.49 [513]~P29(x5131)+~P35(f27(f28(x5131,f4(x5131)),f3(x5131))) % 1.45/1.49 [542]~P29(x5421)+~P35(f27(f27(f29(x5421),f4(x5421)),f3(x5421))) % 1.45/1.49 [451]E(x4511,f3(a91))+P35(f27(f27(f29(a91),f3(a91)),x4511)) % 1.45/1.49 [509]E(f27(a21,f60(x5091)),x5091)+~P35(f27(f27(f29(a91),f3(a91)),x5091)) % 1.45/1.49 [521]~P12(x5211,f30(f94(x5211,a2)))+P12(f93(x5211),f30(f94(f93(x5211),a2))) % 1.45/1.49 [528]P12(x5281,f30(f94(x5281,a2)))+~P12(f93(x5281),f30(f94(f93(x5281),a2))) % 1.45/1.49 [549]E(x5491,f3(a91))+~P35(f27(f27(f29(a91),x5491),f27(a21,f3(a91)))) % 1.45/1.49 [655]~P29(x6551)+P35(f27(f27(f29(x6551),f3(x6551)),f27(f27(f19(x6551),f4(x6551)),f4(x6551)))) % 1.45/1.49 [825]P1(x8251)+P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f83(x8251)),a8)) % 1.45/1.49 [826]P1(x8261)+P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f46(x8261)),a8)) % 1.45/1.49 [827]P2(x8271)+P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f63(x8271)),a8)) % 1.45/1.49 [841]P2(x8411)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f62(x8411)),f65(x8411))),f27(x8411,f63(x8411)))) % 1.45/1.49 [676]~P12(x6761,f30(f94(x6761,a2)))+P35(f27(f27(f29(a91),f3(a91)),f14(x6761,f30(f94(x6761,a2))))) % 1.45/1.49 [915]~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9151),a7))+P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f27(f15(f94(f96(a90,a90),a2),a89),x9151)),a8)) % 1.45/1.49 [1045]~P35(f27(f28(a91,x10451),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),x10451))),a98)),a99)))) % 1.45/1.49 [1046]~P35(f27(f28(a91,x10461),a45))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),x10461))),a98)),a99)))) % 1.45/1.49 [1047]~P35(f27(f28(a91,x10471),a50))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),f27(a1,f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f96(a90,a90),a2)),f27(f27(f6(a89,f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),f27(f9(a2,f94(f94(f96(a90,a90),a2),f94(f94(f96(a90,a90),a2),f94(f96(a90,a90),a2))),a89,f23(f94(f96(a90,a90),a2))),f27(f27(f6(a89,a91,a2),f27(f9(a91,f94(a91,a2),a89,f29(a91)),a97)),x10471))),a98)),a99)))) % 1.45/1.49 [403]~P11(x4031)+P12(x4031,x4032) % 1.45/1.49 [405]P12(x4051,x4052)+E(f14(x4051,x4052),f3(a91)) % 1.45/1.49 [406]~P4(x4062)+P4(f94(x4061,x4062)) % 1.45/1.49 [407]~P5(x4072)+P5(f94(x4071,x4072)) % 1.45/1.49 [408]~P27(x4082)+P27(f94(x4081,x4082)) % 1.45/1.49 [409]~P28(x4092)+P28(f94(x4091,x4092)) % 1.45/1.49 [411]E(x4111,x4112)+~E(f27(a21,x4111),f27(a21,x4112)) % 1.45/1.49 [416]~P19(x4161)+E(f27(f27(f19(x4161),x4162),f3(x4161)),x4162) % 1.45/1.49 [417]~P20(x4171)+E(f27(f27(f19(x4171),x4172),f3(x4171)),x4172) % 1.45/1.49 [418]~P30(x4181)+E(f27(f27(f19(x4181),x4182),f3(x4181)),x4182) % 1.45/1.49 [427]~E(x4271,x4272)+P35(f27(f27(a38,x4271),x4272)) % 1.45/1.49 [430]~E(x4301,x4302)+P35(f27(f28(a91,x4301),x4302)) % 1.45/1.49 [435]~P5(x4351)+P35(f27(f28(x4351,x4352),x4352)) % 1.45/1.49 [447]~P4(x4471)+P35(f27(f28(x4471,x4472),f30(x4471))) % 1.45/1.49 [457]E(x4571,x4572)+~P35(f27(f27(a38,x4571),x4572)) % 1.45/1.49 [459]E(x4591,x4592)+~E(f27(x4591,f53(x4592,x4591)),f27(x4592,f53(x4592,x4591))) % 1.45/1.49 [464]P3(x4641,x4642)+~E(f27(x4641,f56(x4642,x4641)),f27(f56(x4642,x4641),x4642)) % 1.45/1.49 [466]~E(x4661,x4662)+P35(f27(f27(f29(a91),x4661),f27(a21,x4662))) % 1.45/1.49 [469]~E(x4691,f3(a91))+P35(f27(f27(f29(a91),x4691),f27(a21,x4692))) % 1.45/1.49 [481]P35(f27(f28(a91,x4812),x4811))+P35(f27(f28(a91,x4811),x4812)) % 1.45/1.49 [512]E(f27(f27(f19(a91),x5121),f61(x5122,x5121)),x5122)+~P35(f27(f28(a91,x5121),x5122)) % 1.45/1.49 [546]~P35(f27(f28(a91,x5461),x5462))+P35(f27(f28(a91,x5461),f27(a21,x5462))) % 1.45/1.49 [570]~P35(f27(f28(a91,x5701),x5702))+P35(f27(f27(f29(a91),x5701),f27(a21,x5702))) % 1.45/1.49 [571]P12(x5711,x5712)+~P35(f27(f27(f29(a91),f3(a91)),f14(x5711,x5712))) % 1.45/1.49 [590]P35(f27(f28(a91,x5901),x5902))+~P35(f27(f27(f29(a91),x5901),f27(a21,x5902))) % 1.45/1.49 [615]~P35(f27(f28(a91,x6151),x6152))+P35(f27(f28(a91,f27(a21,x6151)),f27(a21,x6152))) % 1.45/1.49 [654]P35(f27(f28(a91,x6541),x6542))+~P35(f27(f28(a91,f27(a21,x6541)),f27(a21,x6542))) % 1.45/1.49 [985]~P12(x9851,x9852)+E(f18(a91,x9851,f19(a91),f27(f15(a91,x9851),f4(a91)),f3(a91),x9852),f14(x9851,x9852)) % 1.45/1.49 [422]~P19(x4221)+E(f27(f27(f19(x4221),f3(x4221)),x4222),x4222) % 1.45/1.49 [423]~P20(x4231)+E(f27(f27(f19(x4231),f3(x4231)),x4232),x4232) % 1.45/1.49 [424]~P30(x4241)+E(f27(f27(f19(x4241),f3(x4241)),x4242),x4242) % 1.45/1.49 [426]E(x4261,f3(a91))+~E(f27(f27(f19(a91),x4262),x4261),x4262) % 1.45/1.49 [431]E(x4311,f3(a91))+~E(f27(f27(f19(a91),x4312),x4311),f3(a91)) % 1.45/1.49 [432]E(x4321,f3(a91))+~E(f27(f27(f19(a91),x4321),x4322),f3(a91)) % 1.45/1.49 [460]~E(x4601,f27(a21,x4602))+P35(f27(f27(f29(a91),f3(a91)),x4601)) % 1.45/1.49 [480]~E(x4801,x4802)+~P35(f27(f27(f29(a91),x4801),x4802)) % 1.45/1.49 [482]~E(x4821,f3(a91))+~P35(f27(f27(f29(a91),x4822),x4821)) % 1.45/1.49 [494]~P5(x4941)+~P35(f27(f27(f29(x4941),x4942),x4942)) % 1.45/1.49 [523]P12(a91,x5231)+P35(f27(f27(f34(a91),f78(x5231,x5232)),x5231)) % 1.45/1.49 [524]P12(a91,x5241)+P35(f27(f27(f34(a91),f81(x5241,x5242)),x5241)) % 1.45/1.49 [541]P35(f27(f28(a91,x5411),x5412))+~P35(f27(f27(f29(a91),x5411),x5412)) % 1.45/1.49 [543]P35(f27(f27(f29(a91),x5432),f27(a21,x5431)))+P35(f27(f27(f29(a91),x5431),x5432)) % 1.45/1.49 [550]P35(f27(f28(a91,x5501),x5502))+P35(f27(f28(a91,f27(a21,x5502)),x5501)) % 1.45/1.49 [585]P35(f27(f27(f29(a91),x5851),f27(a21,x5852)))+~P35(f27(f27(f29(a91),x5851),x5852)) % 1.45/1.49 [589]P12(a91,x5891)+~P35(f27(f28(a91,f81(x5891,x5892)),x5892)) % 1.45/1.49 [591]E(f27(a21,f27(f27(f19(a91),x5911),f71(x5912,x5911))),x5912)+~P35(f27(f27(f29(a91),x5911),x5912)) % 1.45/1.49 [604]~P35(f27(f27(f29(a91),x6041),x6042))+P35(f27(f28(a91,f27(a21,x6041)),x6042)) % 1.45/1.49 [611]P12(a91,x6111)+~P35(f27(f27(f29(a91),f78(x6111,x6112)),x6112)) % 1.45/1.49 [617]P35(f27(f28(a91,x6171),x6172))+~P35(f27(f28(a91,f27(a21,x6171)),x6172)) % 1.45/1.49 [619]~P29(x6191)+P35(f27(f27(f29(x6191),x6192),f27(f27(f19(x6191),x6192),f4(x6191)))) % 1.45/1.49 [633]P35(f27(f27(f29(a91),x6331),x6332))+~P35(f27(f28(a91,f27(a21,x6331)),x6332)) % 1.45/1.49 [634]~P35(f27(f27(f29(a91),x6342),f27(a21,x6341)))+~P35(f27(f27(f29(a91),x6341),x6342)) % 1.45/1.49 [635]P12(x6351,f30(f94(x6351,a2)))+~P12(f94(x6352,x6351),f30(f94(f94(x6352,x6351),a2))) % 1.45/1.49 [636]P12(x6361,f30(f94(x6361,a2)))+~P12(f95(x6362,x6361),f30(f94(f95(x6362,x6361),a2))) % 1.45/1.49 [637]P12(x6371,f30(f94(x6371,a2)))+~P12(f95(x6371,x6372),f30(f94(f95(x6371,x6372),a2))) % 1.45/1.49 [643]P35(f27(f27(f29(a91),f27(a21,x6431)),f27(a21,x6432)))+~P35(f27(f27(f29(a91),x6431),x6432)) % 1.45/1.49 [644]~P35(f27(f28(a91,x6441),x6442))+~P35(f27(f28(a91,f27(a21,x6442)),x6441)) % 1.45/1.49 [645]P35(f27(f27(f29(a91),x6451),x6452))+~P35(f27(f27(f29(a91),f27(a21,x6451)),x6452)) % 1.45/1.49 [674]~P35(f27(f27(f29(a91),f27(a21,x6741)),f27(a21,x6742)))+P35(f27(f27(f29(a91),x6741),x6742)) % 1.45/1.49 [752]P35(f25(a2,a39,f28(a91,x7521),x7522))+~P35(f27(f28(a91,f27(a21,x7521)),x7522)) % 1.45/1.49 [785]~P35(f25(a2,a39,f28(a91,x7851),x7852))+P35(f27(f28(a91,f27(a21,x7851)),x7852)) % 1.45/1.49 [808]P2(x8081)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f62(x8081)),f65(x8081))),f27(f63(x8081),x8082))) % 1.45/1.49 [831]P3(x8311,x8312)+P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f56(x8312,x8311)),a8)) % 1.45/1.49 [874]P17(x8741,x8742)+~P35(f27(f27(f34(f96(x8741,x8741)),f27(f27(f32(x8741,x8741),f66(x8742,x8741)),f66(x8742,x8741))),x8742)) % 1.45/1.49 [846]P35(f27(f27(f34(f94(f96(a90,a90),a2)),f27(f27(a10,x8461),x8462)),a7))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8461),a7)) % 1.45/1.49 [847]P35(f27(f27(f34(f94(f96(a90,a90),a2)),f27(f27(a12,x8471),x8472)),a7))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8471),a7)) % 1.45/1.49 [468]~P12(x4681,x4683)+P12(x4681,f35(x4681,x4682,x4683)) % 1.45/1.49 [522]P12(x5221,x5222)+~P12(x5221,f35(x5221,x5223,x5222)) % 1.45/1.49 [484]~E(x4842,x4843)+P35(f27(f27(f34(x4841),x4842),f27(a38,x4843))) % 1.45/1.49 [547]E(x5471,x5472)+~P35(f27(f27(f34(x5473),x5471),f27(a38,x5472))) % 1.45/1.49 [969]P12(x9691,x9692)+~P35(f27(f27(f34(f96(f94(x9691,a2),f94(x9691,a2))),f27(f27(f32(f94(x9691,a2),f94(x9691,a2)),x9693),x9692)),f41(x9691))) % 1.45/1.49 [433]~P4(x4332)+E(f27(f30(f94(x4331,x4332)),x4333),f30(x4332)) % 1.45/1.49 [452]~P30(x4521)+E(f27(f27(f19(x4521),x4522),x4523),f27(f27(f19(x4521),x4523),x4522)) % 1.45/1.49 [470]E(x4701,x4702)+~E(f27(f27(f19(a91),x4703),x4701),f27(f27(f19(a91),x4703),x4702)) % 1.45/1.49 [471]E(x4711,x4712)+~E(f27(f27(f19(a91),x4711),x4713),f27(f27(f19(a91),x4712),x4713)) % 1.45/1.49 [475]~E(x4752,f27(f27(f19(a91),x4751),x4753))+P35(f27(f28(a91,x4751),x4752)) % 1.45/1.49 [483]~P35(f27(x4833,x4832))+P35(f27(f27(f34(x4831),x4832),x4833)) % 1.45/1.49 [495]~E(x4953,x4952)+P35(f27(f28(f94(x4951,a2),x4952),x4953)) % 1.45/1.49 [501]~E(x5012,x5013)+P35(f27(f28(f94(x5011,a2),x5012),x5013)) % 1.45/1.49 [519]P35(f27(x5191,x5192))+~P35(f27(f27(f34(x5193),x5192),x5191)) % 1.45/1.49 [536]E(f35(x5361,x5362,x5363),x5363)+~P35(f27(f27(f34(x5361),x5362),x5363)) % 1.45/1.49 [721]~P12(x7211,x7212)+P35(f27(f28(a91,f14(x7211,x7212)),f14(x7211,f35(x7211,x7213,x7212)))) % 1.45/1.49 [804]E(x8041,x8042)+~E(f27(f27(f6(x8043,f94(x8043,a2),a2),f34(x8043)),x8041),f27(f27(f6(x8043,f94(x8043,a2),a2),f34(x8043)),x8042)) % 1.45/1.49 [830]~P13(x8302,x8301,x8303,f30(f94(x8302,a2)))+E(f36(x8301,x8302,f22(x8302,x8301,f30(f94(x8302,a2)),x8303),f30(f94(x8301,a2))),f30(f94(x8302,a2))) % 1.45/1.49 [832]P13(x8321,x8322,f22(x8322,x8321,f30(f94(x8322,a2)),x8323),f30(f94(x8321,a2)))+~E(f36(x8322,x8321,x8323,f30(f94(x8322,a2))),f30(f94(x8321,a2))) % 1.45/1.49 [875]~E(f27(x8753,f27(f22(x8751,x8752,f30(f94(x8751,a2)),x8753),f73(x8753,x8752,x8751))),f73(x8753,x8752,x8751))+E(f36(x8751,x8752,x8753,f30(f94(x8751,a2))),f30(f94(x8752,a2))) % 1.45/1.49 [566]~E(x5662,f27(a21,f27(f27(f19(a91),x5661),x5663)))+P35(f27(f27(f29(a91),x5661),x5662)) % 1.45/1.49 [639]~P35(f27(f28(a91,x6391),x6393))+P35(f27(f28(a91,x6391),f27(f27(f19(a91),x6392),x6393))) % 1.45/1.49 [641]~P35(f27(f28(a91,x6411),x6412))+P35(f27(f28(a91,x6411),f27(f27(f19(a91),x6412),x6413))) % 1.45/1.49 [663]~P35(f27(f27(f29(a91),x6631),x6633))+P35(f27(f27(f29(a91),x6631),f27(f27(f19(a91),x6632),x6633))) % 1.45/1.49 [665]~P35(f27(f27(f29(a91),x6651),x6652))+P35(f27(f27(f29(a91),x6651),f27(f27(f19(a91),x6652),x6653))) % 1.45/1.49 [675]~E(x6751,x6752)+~P35(f27(f27(f29(f94(x6753,a2)),x6751),x6752)) % 1.45/1.49 [711]P35(f27(f28(f94(x7111,a2),x7112),x7113))+~P35(f27(f27(f29(f94(x7111,a2)),x7112),x7113)) % 1.45/1.49 [734]~P35(f27(f28(a91,x7342),x7343))+P35(f27(f28(a91,f27(f27(f19(a91),x7341),x7342)),f27(f27(f19(a91),x7341),x7343))) % 1.45/1.49 [735]~P35(f27(f28(a91,x7351),x7353))+P35(f27(f28(a91,f27(f27(f19(a91),x7351),x7352)),f27(f27(f19(a91),x7353),x7352))) % 1.45/1.49 [746]~P35(f27(f27(f29(a91),x7462),x7463))+P35(f27(f27(f29(a91),f27(f27(f19(a91),x7461),x7462)),f27(f27(f19(a91),x7461),x7463))) % 1.45/1.49 [747]~P35(f27(f27(f29(a91),x7471),x7473))+P35(f27(f27(f29(a91),f27(f27(f19(a91),x7471),x7472)),f27(f27(f19(a91),x7473),x7472))) % 1.45/1.49 [792]P35(f27(f28(a91,x7921),x7922))+~P35(f27(f28(a91,f27(f27(f19(a91),x7923),x7921)),f27(f27(f19(a91),x7923),x7922))) % 1.45/1.49 [803]P35(f27(f27(f29(a91),x8031),x8032))+~P35(f27(f27(f29(a91),f27(f27(f19(a91),x8033),x8031)),f27(f27(f19(a91),x8033),x8032))) % 1.45/1.49 [956]~P35(f27(f28(f94(x9561,a2),x9562),x9563))+P35(f27(f28(f94(x9561,a2),f27(f27(f6(x9561,f94(x9561,a2),a2),f34(x9561)),x9562)),f27(f27(f6(x9561,f94(x9561,a2),a2),f34(x9561)),x9563))) % 1.45/1.49 [976]~P35(f27(f27(f34(f96(f94(x9761,a2),f94(x9761,a2))),f27(f27(f32(f94(x9761,a2),f94(x9761,a2)),x9762),x9763)),f41(x9761)))+P35(f27(f27(f29(f94(x9761,a2)),x9762),x9763)) % 1.45/1.49 [991]P35(f27(f28(f94(x9911,a2),x9912),x9913))+~P35(f27(f28(f94(x9911,a2),f27(f27(f6(x9911,f94(x9911,a2),a2),f34(x9911)),x9912)),f27(f27(f6(x9911,f94(x9911,a2),a2),f34(x9911)),x9913))) % 1.45/1.49 [739]P35(f27(f28(a91,x7391),x7392))+~P35(f27(f28(a91,f27(f27(f19(a91),x7393),x7391)),x7392)) % 1.45/1.49 [740]P35(f27(f28(a91,x7401),x7402))+~P35(f27(f28(a91,f27(f27(f19(a91),x7401),x7403)),x7402)) % 1.45/1.49 [754]P35(f27(f27(f29(a91),x7541),x7542))+~P35(f27(f27(f29(a91),f27(f27(f19(a91),x7541),x7543)),x7542)) % 1.45/1.49 [797]~P17(x7971,x7973)+P35(f27(f27(f34(f96(x7971,x7971)),f27(f27(f32(x7971,x7971),x7972),x7972)),x7973)) % 1.45/1.49 [687]~P12(x6872,x6874)+P12(x6871,f36(x6872,x6871,x6873,x6874)) % 1.45/1.49 [761]P12(x7611,x7612)+~P12(f95(x7613,x7611),f37(x7613,x7611,x7614,x7612)) % 1.45/1.49 [762]P12(x7621,x7622)+~P12(f95(x7621,x7623),f37(x7621,x7623,x7622,x7624)) % 1.45/1.49 [790]P13(x7901,x7902,x7903,x7904)+~E(f57(x7904,x7903,x7902,x7901),f59(x7904,x7903,x7902,x7901)) % 1.45/1.49 [560]~E(x5602,x5604)+P35(f27(f35(x5601,x5602,x5603),x5604)) % 1.45/1.49 [588]~P35(f27(x5883,x5884))+P35(f27(f35(x5881,x5882,x5883),x5884)) % 1.45/1.49 [610]~E(x6102,x6103)+P35(f27(f27(f34(x6101),x6102),f35(x6101,x6103,x6104))) % 1.45/1.49 [698]P12(x6982,x6984)+E(f14(f95(x6981,x6982),f37(x6981,x6982,x6983,x6984)),f3(a91)) % 1.45/1.49 [699]P12(x6991,x6993)+E(f14(f95(x6991,x6992),f37(x6991,x6992,x6993,x6994)),f3(a91)) % 1.45/1.49 [775]~P13(x7752,x7751,x7753,x7754)+E(f14(x7751,f36(x7752,x7751,x7753,x7754)),f14(x7752,x7754)) % 1.45/1.49 [806]~P13(x8061,x8062,x8063,f30(f94(x8061,a2)))+E(f27(f22(x8061,x8062,f30(f94(x8061,a2)),x8063),f27(x8063,x8064)),x8064) % 1.45/1.49 [821]P13(x8214,x8213,x8211,x8212)+E(f27(x8211,f57(x8212,x8211,x8213,x8214)),f27(x8211,f59(x8212,x8211,x8213,x8214))) % 1.45/1.49 [833]P35(f27(f27(f34(f96(x8331,x8331)),f27(f27(f32(x8331,x8331),x8332),x8333)),f40(x8331,x8334)))+~P35(f27(f27(f29(a91),f27(x8334,x8332)),f27(x8334,x8333))) % 1.45/1.49 [843]~P13(x8432,x8431,x8433,f30(f94(x8432,a2)))+E(f36(x8431,x8432,f22(x8432,x8431,f30(f94(x8432,a2)),x8433),f36(x8432,x8431,x8433,x8434)),x8434) % 1.45/1.49 [850]~P35(f27(f27(f34(f96(x8504,x8504)),f27(f27(f32(x8504,x8504),x8502),x8503)),f40(x8504,x8501)))+P35(f27(f27(f29(a91),f27(x8501,x8502)),f27(x8501,x8503))) % 1.45/1.49 [949]~P12(x9492,x9494)+P35(f27(f28(a91,f14(x9491,f36(x9492,x9491,x9493,x9494))),f14(x9492,x9494))) % 1.45/1.49 [989]~P13(x9891,x9892,x9893,x9894)+~P35(f27(f27(f29(a91),f14(x9892,f36(x9891,x9892,x9893,x9894))),f14(x9891,x9894))) % 1.45/1.49 [681]P35(f27(f27(f34(x6811),x6812),f35(x6811,x6813,x6814)))+~P35(f27(f27(f34(x6811),x6812),x6814)) % 1.45/1.49 [716]P35(f27(f28(f94(x7161,a2),x7162),f35(x7161,x7163,x7164)))+~P35(f27(f28(f94(x7161,a2),x7162),x7164)) % 1.45/1.49 [795]P35(f27(f27(f34(x7951),x7952),x7953))+~P35(f27(f28(f94(x7951,a2),f35(x7951,x7952,x7954)),x7953)) % 1.45/1.49 [798]P35(f27(f28(f94(x7981,a2),f35(x7981,x7982,x7983)),f35(x7981,x7982,x7984)))+~P35(f27(f28(f94(x7981,a2),x7983),x7984)) % 1.45/1.49 [807]~P35(f27(f28(f94(x8071,a2),f35(x8071,x8074,x8072)),x8073))+P35(f27(f28(f94(x8071,a2),x8072),x8073)) % 1.45/1.49 [834]~E(x8341,x8342)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8343),x8341)),f27(f27(a12,x8344),x8342))) % 1.45/1.49 [835]~E(x8351,x8352)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8351),x8353)),f27(f27(a10,x8354),x8352))) % 1.45/1.49 [852]~P13(x8521,x8523,x8524,f30(f94(x8521,a2)))+P13(x8521,f94(x8522,x8523),f27(f9(x8523,f94(x8522,x8523),x8521,f15(x8523,x8522)),x8524),f30(f94(x8521,a2))) % 1.45/1.49 [860]P13(x8601,x8602,x8603,x8604)+P35(f27(f27(f34(x8601),f57(x8604,x8603,x8602,x8601)),x8604)) % 1.45/1.49 [861]P13(x8611,x8612,x8613,x8614)+P35(f27(f27(f34(x8611),f59(x8614,x8613,x8612,x8611)),x8614)) % 1.45/1.49 [601]~P30(x6011)+E(f27(f27(f19(x6011),x6012),f27(f27(f19(x6011),x6013),x6014)),f27(f27(f19(x6011),x6013),f27(f27(f19(x6011),x6012),x6014))) % 1.45/1.49 [659]~P10(x6591)+E(f27(f27(f19(x6591),f27(f27(f19(x6591),x6592),x6593)),x6594),f27(f27(f19(x6591),x6592),f27(f27(f19(x6591),x6593),x6594))) % 1.45/1.49 [660]~P30(x6601)+E(f27(f27(f19(x6601),f27(f27(f19(x6601),x6602),x6603)),x6604),f27(f27(f19(x6601),x6602),f27(f27(f19(x6601),x6603),x6604))) % 1.45/1.49 [685]~P30(x6851)+E(f27(f27(f19(x6851),f27(f27(f19(x6851),x6852),x6853)),x6854),f27(f27(f19(x6851),f27(f27(f19(x6851),x6852),x6854)),x6853)) % 1.45/1.49 [840]~E(f36(x8402,x8403,x8401,f30(f94(x8402,a2))),f30(f94(x8403,a2)))+E(f27(x8401,f27(f22(x8402,x8403,f30(f94(x8402,a2)),x8401),x8404)),x8404) % 1.45/1.49 [867]~E(f36(x8671,x8672,x8673,f30(f94(x8671,a2))),f30(f94(x8672,a2)))+E(f36(x8671,x8672,x8673,f36(x8672,x8671,f22(x8671,x8672,f30(f94(x8671,a2)),x8673),x8674)),x8674) % 1.45/1.49 [1037]E(x10371,x10372)+~E(f27(f27(f6(x10373,f94(f96(x10373,x10374),a2),f94(x10374,a2)),f27(f9(f94(x10374,f94(f94(f96(x10373,x10374),a2),a2)),f94(f94(f96(x10373,x10374),a2),f94(x10374,a2)),x10373,f6(x10374,f94(f96(x10373,x10374),a2),a2)),f27(f9(f94(x10374,f96(x10373,x10374)),f94(x10374,f94(f94(f96(x10373,x10374),a2),a2)),x10373,f9(f96(x10373,x10374),f94(f94(f96(x10373,x10374),a2),a2),x10374,f34(f96(x10373,x10374)))),f32(x10373,x10374)))),x10371),f27(f27(f6(x10373,f94(f96(x10373,x10374),a2),f94(x10374,a2)),f27(f9(f94(x10374,f94(f94(f96(x10373,x10374),a2),a2)),f94(f94(f96(x10373,x10374),a2),f94(x10374,a2)),x10373,f6(x10374,f94(f96(x10373,x10374),a2),a2)),f27(f9(f94(x10374,f96(x10373,x10374)),f94(x10374,f94(f94(f96(x10373,x10374),a2),a2)),x10373,f9(f96(x10373,x10374),f94(f94(f96(x10373,x10374),a2),a2),x10374,f34(f96(x10373,x10374)))),f32(x10373,x10374)))),x10372)) % 1.45/1.49 [1043]~P35(f27(f28(f94(f96(x10431,x10432),a2),x10433),x10434))+P35(f27(f28(f94(x10431,f94(x10432,a2)),f27(f27(f6(x10431,f94(f96(x10431,x10432),a2),f94(x10432,a2)),f27(f9(f94(x10432,f94(f94(f96(x10431,x10432),a2),a2)),f94(f94(f96(x10431,x10432),a2),f94(x10432,a2)),x10431,f6(x10432,f94(f96(x10431,x10432),a2),a2)),f27(f9(f94(x10432,f96(x10431,x10432)),f94(x10432,f94(f94(f96(x10431,x10432),a2),a2)),x10431,f9(f96(x10431,x10432),f94(f94(f96(x10431,x10432),a2),a2),x10432,f34(f96(x10431,x10432)))),f32(x10431,x10432)))),x10433)),f27(f27(f6(x10431,f94(f96(x10431,x10432),a2),f94(x10432,a2)),f27(f9(f94(x10432,f94(f94(f96(x10431,x10432),a2),a2)),f94(f94(f96(x10431,x10432),a2),f94(x10432,a2)),x10431,f6(x10432,f94(f96(x10431,x10432),a2),a2)),f27(f9(f94(x10432,f96(x10431,x10432)),f94(x10432,f94(f94(f96(x10431,x10432),a2),a2)),x10431,f9(f96(x10431,x10432),f94(f94(f96(x10431,x10432),a2),a2),x10432,f34(f96(x10431,x10432)))),f32(x10431,x10432)))),x10434))) % 1.45/1.49 [1044]P35(f27(f28(f94(f96(x10441,x10442),a2),x10443),x10444))+~P35(f27(f28(f94(x10441,f94(x10442,a2)),f27(f27(f6(x10441,f94(f96(x10441,x10442),a2),f94(x10442,a2)),f27(f9(f94(x10442,f94(f94(f96(x10441,x10442),a2),a2)),f94(f94(f96(x10441,x10442),a2),f94(x10442,a2)),x10441,f6(x10442,f94(f96(x10441,x10442),a2),a2)),f27(f9(f94(x10442,f96(x10441,x10442)),f94(x10442,f94(f94(f96(x10441,x10442),a2),a2)),x10441,f9(f96(x10441,x10442),f94(f94(f96(x10441,x10442),a2),a2),x10442,f34(f96(x10441,x10442)))),f32(x10441,x10442)))),x10443)),f27(f27(f6(x10441,f94(f96(x10441,x10442),a2),f94(x10442,a2)),f27(f9(f94(x10442,f94(f94(f96(x10441,x10442),a2),a2)),f94(f94(f96(x10441,x10442),a2),f94(x10442,a2)),x10441,f6(x10442,f94(f96(x10441,x10442),a2),a2)),f27(f9(f94(x10442,f96(x10441,x10442)),f94(x10442,f94(f94(f96(x10441,x10442),a2),a2)),x10441,f9(f96(x10441,x10442),f94(f94(f96(x10441,x10442),a2),a2),x10442,f34(f96(x10441,x10442)))),f32(x10441,x10442)))),x10444))) % 1.45/1.49 [838]P35(f27(f27(f34(f96(x8381,x8381)),f27(f27(f32(x8381,x8381),x8382),x8383)),f43(x8381,x8384,x8385)))+~P35(f27(f27(f29(a91),f27(x8384,x8382)),f27(x8384,x8383))) % 1.45/1.49 [857]E(f27(x8571,f72(x8572,x8571,x8573,x8574)),x8574)+~P35(f27(f27(f34(x8575),x8574),f36(x8573,x8575,x8571,x8572))) % 1.45/1.49 [873]P13(x8731,x8732,f22(x8732,x8731,x8733,x8734),x8735)+~P35(f27(f28(f94(x8731,a2),x8735),f36(x8732,x8731,x8734,x8733))) % 1.45/1.49 [954]E(f36(x9541,x9542,x9543,f76(x9544,x9543,x9541,x9545,x9542)),x9545)+~P35(f27(f28(f94(x9542,a2),x9545),f36(x9541,x9542,x9543,x9544))) % 1.45/1.49 [784]E(f35(x7841,f27(x7842,x7843),f36(x7844,x7841,x7842,x7845)),f36(x7844,x7841,x7842,x7845))+~P35(f27(f27(f34(x7844),x7843),x7845)) % 1.45/1.49 [829]P35(f27(f27(f34(x8291),f27(x8292,x8293)),f36(x8294,x8291,x8292,x8295)))+~P35(f27(f27(f34(x8294),x8293),x8295)) % 1.45/1.49 [879]E(f27(x8791,f27(f22(x8792,x8793,x8794,x8791),x8795)),x8795)+~P35(f27(f27(f34(x8793),x8795),f36(x8792,x8793,x8791,x8794))) % 1.45/1.49 [904]P35(f27(f28(f94(x9041,a2),f36(x9042,x9041,x9043,x9044)),f36(x9042,x9041,x9043,x9045)))+~P35(f27(f28(f94(x9042,a2),x9044),x9045)) % 1.45/1.49 [920]~P12(x9203,f36(x9202,x9203,x9205,f30(f94(x9202,a2))))+P12(x9201,f36(x9202,x9201,f27(f9(x9203,x9201,x9202,x9204),x9205),f30(f94(x9202,a2)))) % 1.45/1.49 [927]P35(f27(f28(f94(f94(x9271,x9272),a2),f17(x9271,x9272,x9273,x9274)),f17(x9271,x9272,x9275,x9274)))+~P35(f27(f28(f94(x9271,a2),x9275),x9273)) % 1.45/1.49 [937]~P35(f27(f27(f34(x9375),x9374),f36(x9371,x9375,x9373,x9372)))+P35(f27(f27(f34(x9371),f72(x9372,x9373,x9371,x9374)),x9372)) % 1.45/1.49 [1008]P35(f27(f27(f34(f94(x10081,x10084)),x10083),f17(x10081,x10084,x10085,x10082)))+P35(f27(f27(f34(x10081),f68(x10082,x10083,x10084,x10085,x10081)),x10085)) % 1.45/1.49 [1009]~P35(f27(f28(f94(x10095,a2),x10094),f36(x10091,x10095,x10093,x10092)))+P35(f27(f28(f94(x10091,a2),f76(x10092,x10093,x10091,x10094,x10095)),x10092)) % 1.45/1.49 [1012]P35(f27(f28(f94(f94(x10121,x10124),a2),f17(x10121,x10124,x10125,x10123)),f17(x10121,x10124,x10125,x10122)))+P35(f27(f27(f34(x10121),f67(x10122,x10123,x10124,x10125,x10121)),x10125)) % 1.45/1.49 [1030]P35(f27(f27(f34(f94(x10301,x10302)),x10303),f17(x10301,x10302,x10304,x10305)))+~P35(f27(f27(f34(x10302),f27(x10303,f68(x10305,x10303,x10302,x10304,x10301))),f27(x10305,f68(x10305,x10303,x10302,x10304,x10301)))) % 1.45/1.49 [1031]P35(f27(f28(f94(f94(x10311,x10312),a2),f17(x10311,x10312,x10313,x10314)),f17(x10311,x10312,x10313,x10315)))+~P35(f27(f28(f94(x10312,a2),f27(x10314,f67(x10315,x10314,x10312,x10313,x10311))),f27(x10315,f67(x10315,x10314,x10312,x10313,x10311)))) % 1.45/1.49 [731]~P30(x7311)+E(f27(f27(f19(x7311),f27(f27(f19(x7311),x7312),x7313)),f27(f27(f19(x7311),x7314),x7315)),f27(f27(f19(x7311),f27(f27(f19(x7311),x7312),x7314)),f27(f27(f19(x7311),x7313),x7315))) % 1.45/1.49 [828]~E(x8282,f27(x8284,x8285))+P35(f27(f27(f34(x8281),x8282),f36(x8283,x8281,x8284,f30(f94(x8283,a2))))) % 1.45/1.49 [982]~P35(f27(f27(f34(x9822),x9825),f36(x9821,x9822,x9824,x9823)))+P35(f27(f27(f34(x9821),f27(f22(x9821,x9822,x9823,x9824),x9825)),x9823)) % 1.45/1.49 [883]P14(x8831,x8832,x8833,x8834,x8835)+~P35(f27(f27(f34(f96(x8831,x8832)),f27(f27(f32(x8831,x8832),x8834),x8835)),x8833)) % 1.45/1.49 [889]~P14(x8891,x8892,x8895,x8893,x8894)+P35(f27(f27(f34(f96(x8891,x8892)),f27(f27(f32(x8891,x8892),x8893),x8894)),x8895)) % 1.45/1.49 [972]P35(f27(f28(f94(x9721,a2),f36(x9722,x9721,x9723,x9724)),x9725))+~P35(f27(f27(f34(f94(x9722,x9721)),x9723),f17(x9722,x9721,x9724,f27(f15(f94(x9721,a2),x9722),x9725)))) % 1.45/1.49 [999]~P15(x9993,x9994,x9991,x9995,x9996,x9997)+E(f27(f27(x9991,x9992),x9992),x9992) % 1.45/1.49 [1005]P35(f27(f27(f34(f96(f96(x10051,x10052),f96(x10051,x10052))),f27(f27(f32(f96(x10051,x10052),f96(x10051,x10052)),f27(f27(f32(x10051,x10052),x10053),x10054)),f27(f27(f32(x10051,x10052),x10055),x10056))),f42(x10051,x10052,x10057,x10058)))+~P35(f27(f27(f34(f96(x10051,x10051)),f27(f27(f32(x10051,x10051),x10053),x10055)),x10057)) % 1.45/1.49 [859]P1(x8591)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x8591)),f48(x8591))),f27(x8591,f46(x8591))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x8591)),f48(x8591))),f27(x8591,f83(x8591)))) % 1.45/1.49 [914]P1(x9141)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x9141)),f48(x9141))),f27(x9141,f46(x9141))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x9141)),f48(x9141))),f27(x9141,f83(x9141)))) % 1.45/1.49 [886]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x8861)))+~P35(f27(f27(f29(a91),f27(a97,x8861)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a10,f27(a102,x8861)),a105))) % 1.45/1.49 [894]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x8941)))+~P35(f27(f27(f29(a91),f27(a97,x8941)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a10,f27(a102,x8941)),a105))) % 1.45/1.49 [892]~P35(f27(f27(f29(a91),f27(a97,x8921)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a105),a104)),f27(f27(a10,f27(a102,x8921)),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),a98)) % 1.45/1.49 [412]~P11(x4122)+~P11(x4121)+P11(f96(x4121,x4122)) % 1.45/1.49 [413]~P11(x4132)+~P11(x4131)+P11(f94(x4131,x4132)) % 1.45/1.49 [414]~P11(x4142)+~P11(x4141)+P11(f95(x4141,x4142)) % 1.45/1.49 [548]E(x5481,x5482)+~P35(f27(f28(a91,x5482),x5481))+~P35(f27(f28(a91,x5481),x5482)) % 1.45/1.49 [573]E(x5731,f3(a91))+E(f27(a21,f69(x5732,x5731)),x5731)+~P35(f27(f27(f29(a91),x5731),f27(a21,x5732))) % 1.45/1.49 [581]E(x5811,f27(a21,x5812))+P35(f27(f28(a91,x5811),x5812))+~P35(f27(f28(a91,x5811),f27(a21,x5812))) % 1.45/1.49 [618]E(x6181,x6182)+~P35(f27(f28(a91,x6182),x6181))+~P35(f27(f27(f29(a91),x6181),f27(a21,x6182))) % 1.45/1.49 [715]~P21(x7151)+~P35(f27(f28(x7151,x7152),f3(x7151)))+P35(f27(f28(x7151,f27(f27(f19(x7151),x7152),x7152)),f3(x7151))) % 1.45/1.49 [729]~P31(x7291)+~P35(f27(f27(f29(x7291),x7292),f3(x7291)))+P35(f27(f27(f29(x7291),f27(f27(f19(x7291),x7292),x7292)),f3(x7291))) % 1.45/1.49 [730]~P21(x7301)+~P35(f27(f27(f29(x7301),x7302),f3(x7301)))+P35(f27(f27(f29(x7301),f27(f27(f19(x7301),x7302),x7302)),f3(x7301))) % 1.45/1.49 [767]~P21(x7671)+~P35(f27(f28(x7671,f27(f27(f19(x7671),x7672),x7672)),f3(x7671)))+P35(f27(f28(x7671,x7672),f3(x7671))) % 1.45/1.49 [780]~P31(x7801)+~P35(f27(f27(f29(x7801),f27(f27(f19(x7801),x7802),x7802)),f3(x7801)))+P35(f27(f27(f29(x7801),x7802),f3(x7801))) % 1.45/1.49 [781]~P21(x7811)+~P35(f27(f27(f29(x7811),f27(f27(f19(x7811),x7812),x7812)),f3(x7811)))+P35(f27(f27(f29(x7811),x7812),f3(x7811))) % 1.45/1.49 [415]~E(x4152,f3(a91))+~E(x4151,f3(a91))+E(f27(f27(f19(a91),x4151),x4152),f3(a91)) % 1.45/1.49 [421]~P21(x4211)+~E(x4212,f3(x4211))+E(f27(f27(f19(x4211),x4212),x4212),f3(x4211)) % 1.45/1.49 [442]~E(x4422,f3(a91))+~E(x4421,f27(a21,f3(a91)))+E(f27(f27(f19(a91),x4421),x4422),f27(a21,f3(a91))) % 1.45/1.49 [443]~E(x4431,f3(a91))+~E(x4432,f27(a21,f3(a91)))+E(f27(f27(f19(a91),x4431),x4432),f27(a21,f3(a91))) % 1.45/1.49 [446]~P21(x4462)+E(x4461,f3(x4462))+~E(f27(f27(f19(x4462),x4461),x4461),f3(x4462)) % 1.45/1.49 [449]E(x4491,f3(a91))+E(x4492,f3(a91))+~E(f27(f27(f19(a91),x4492),x4491),f27(a21,f3(a91))) % 1.45/1.49 [455]E(x4551,f3(a91))+E(x4551,f27(a21,f3(a91)))+~E(f27(f27(f19(a91),x4552),x4551),f27(a21,f3(a91))) % 1.45/1.49 [456]E(x4561,f3(a91))+E(x4561,f27(a21,f3(a91)))+~E(f27(f27(f19(a91),x4561),x4562),f27(a21,f3(a91))) % 1.45/1.49 [462]E(x4621,f27(a21,f3(a91)))+E(x4622,f27(a21,f3(a91)))+~E(f27(f27(f19(a91),x4621),x4622),f27(a21,f3(a91))) % 1.45/1.49 [511]E(x5111,x5112)+P35(f27(f27(f29(a91),x5112),x5111))+P35(f27(f27(f29(a91),x5111),x5112)) % 1.45/1.49 [527]E(x5271,x5272)+~P35(f27(f28(a91,x5271),x5272))+P35(f27(f27(f29(a91),x5271),x5272)) % 1.45/1.49 [565]~P12(a91,x5652)+P35(f27(f28(a91,x5651),f82(x5652)))+~P35(f27(f27(f34(a91),x5651),x5652)) % 1.45/1.49 [567]E(x5671,f30(f94(x5672,a2)))+~P12(x5672,f30(f94(x5672,a2)))+~E(f14(x5672,x5671),f14(x5672,f30(f94(x5672,a2)))) % 1.45/1.49 [579]~P12(a91,x5792)+P35(f27(f27(f29(a91),x5791),f79(x5792)))+~P35(f27(f27(f34(a91),x5791),x5792)) % 1.45/1.49 [582]~P35(f27(x5821,x5822))+P35(f27(x5821,f3(a91)))+P35(f27(f27(f29(a91),f70(x5822,x5821)),x5822)) % 1.45/1.49 [608]E(x6081,x6082)+~P35(f27(f27(f29(a91),x6081),f27(a21,x6082)))+P35(f27(f27(f29(a91),x6081),x6082)) % 1.45/1.49 [626]E(f27(a21,x6261),x6262)+~P35(f27(f27(f29(a91),x6261),x6262))+P35(f27(f27(f29(a91),f27(a21,x6261)),x6262)) % 1.45/1.49 [648]~P12(x6482,f30(f94(x6482,a2)))+~P12(x6481,f30(f94(x6481,a2)))+P12(f96(x6481,x6482),f30(f94(f96(x6481,x6482),a2))) % 1.45/1.49 [649]~P12(x6492,f30(f94(x6492,a2)))+~P12(x6491,f30(f94(x6491,a2)))+P12(f95(x6491,x6492),f30(f94(f95(x6491,x6492),a2))) % 1.45/1.49 [661]E(x6611,f3(a91))+~P35(f27(f27(f29(a91),x6611),f27(a21,x6612)))+P35(f27(f27(f29(a91),f69(x6612,x6611)),x6612)) % 1.45/1.49 [672]P12(x6722,f30(f94(x6722,a2)))+E(f14(x6721,f30(f94(x6721,a2))),f27(a21,f3(a91)))+~P12(f94(x6722,x6721),f30(f94(f94(x6722,x6721),a2))) % 1.45/1.49 [682]~P35(f27(x6821,x6822))+P35(f27(x6821,f3(a91)))+P35(f27(x6821,f27(f27(f19(a91),f70(x6822,x6821)),f4(a91)))) % 1.45/1.49 [772]~P13(x7721,x7721,x7722,f30(f94(x7721,a2)))+~P12(x7721,f30(f94(x7721,a2)))+E(f36(x7721,x7721,x7722,f30(f94(x7721,a2))),f30(f94(x7721,a2))) % 1.45/1.49 [777]P13(x7771,x7771,x7772,f30(f94(x7771,a2)))+~P12(x7771,f30(f94(x7771,a2)))+~E(f36(x7771,x7771,x7772,f30(f94(x7771,a2))),f30(f94(x7771,a2))) % 1.45/1.49 [884]P1(x8841)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x8841)),f48(x8841))),f27(f46(x8841),x8842)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x8841)),f48(x8841))),f27(f83(x8841),x8842))) % 1.45/1.49 [885]P1(x8851)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x8851)),f48(x8851))),f27(f83(x8851),x8852)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f47(x8851)),f48(x8851))),f27(f46(x8851),x8852))) % 1.45/1.49 [678]~P21(x6781)+~P35(f27(f28(x6781,f3(x6781)),x6782))+P35(f27(f28(x6781,f3(x6781)),f27(f27(f19(x6781),x6782),x6782))) % 1.45/1.49 [697]~P21(x6971)+~P35(f27(f27(f29(x6971),f3(x6971)),x6972))+P35(f27(f27(f29(x6971),f3(x6971)),f27(f27(f19(x6971),x6972),x6972))) % 1.45/1.49 [706]~P21(x7061)+P35(f27(f28(x7061,f3(x7061)),x7062))+~P35(f27(f28(x7061,f3(x7061)),f27(f27(f19(x7061),x7062),x7062))) % 1.45/1.49 [718]P35(f27(f27(f29(a91),f3(a91)),x7182))+P35(f27(f27(f29(a91),f3(a91)),x7181))+~P35(f27(f27(f29(a91),f3(a91)),f27(f27(f19(a91),x7182),x7181))) % 1.45/1.49 [719]~P21(x7191)+P35(f27(f27(f29(x7191),f3(x7191)),x7192))+~P35(f27(f27(f29(x7191),f3(x7191)),f27(f27(f19(x7191),x7192),x7192))) % 1.45/1.49 [720]~P26(x7201)+~P35(f27(f27(f34(x7201),x7202),f24(x7201)))+~E(f27(f27(f19(x7201),f27(f27(f19(x7201),f4(x7201)),x7202)),x7202),f3(x7201)) % 1.45/1.49 [1018]P3(x10181,x10182)+~E(f58(x10182,x10181),f54(x10182,x10181))+~P35(f27(f27(f34(f94(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2))),x10181),f17(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2),a8,f27(f15(f94(f94(f96(a90,a90),a2),a2),f94(a89,f94(f96(a90,a90),a2))),a7)))) % 1.45/1.49 [1019]P3(x10191,x10192)+P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),f55(x10192,x10191)),a8))+~P35(f27(f27(f34(f94(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2))),x10191),f17(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2),a8,f27(f15(f94(f94(f96(a90,a90),a2),a2),f94(a89,f94(f96(a90,a90),a2))),a7)))) % 1.45/1.49 [1020]P3(x10201,x10202)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f54(x10202,x10201)),f58(x10202,x10201))),f27(f55(x10202,x10201),x10202)))+~P35(f27(f27(f34(f94(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2))),x10201),f17(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2),a8,f27(f15(f94(f94(f96(a90,a90),a2),a2),f94(a89,f94(f96(a90,a90),a2))),a7)))) % 1.45/1.49 [1021]P3(x10211,x10212)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),f54(x10212,x10211)),f58(x10212,x10211))),f27(x10211,f55(x10212,x10211))))+~P35(f27(f27(f34(f94(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2))),x10211),f17(f94(a89,f94(f96(a90,a90),a2)),f94(f96(a90,a90),a2),a8,f27(f15(f94(f94(f96(a90,a90),a2),a2),f94(a89,f94(f96(a90,a90),a2))),a7)))) % 1.45/1.49 [437]~E(x4372,x4373)+~P5(x4371)+P35(f27(f28(x4371,x4372),x4373)) % 1.45/1.49 [439]~E(x4392,x4393)+~P28(x4391)+P35(f27(f28(x4391,x4392),x4393)) % 1.45/1.49 [487]~P6(x4871)+P35(f27(f28(x4871,x4873),x4872))+P35(f27(f28(x4871,x4872),x4873)) % 1.45/1.49 [600]~P35(f27(f28(a91,x6001),x6003))+P35(f27(f28(a91,x6001),x6002))+~P35(f27(f28(a91,x6003),x6002)) % 1.45/1.49 [855]~P12(x8551,x8553)+P13(x8551,x8551,x8552,x8553)+~P35(f27(f28(f94(x8551,a2),x8553),f36(x8551,x8551,x8552,x8553))) % 1.45/1.49 [419]~P34(x4191)+~E(x4193,f3(x4191))+E(f27(f27(f19(x4191),x4192),x4193),x4192) % 1.45/1.49 [444]~P34(x4442)+E(x4441,f3(x4442))+~E(f27(f27(f19(x4442),x4443),x4441),x4443) % 1.45/1.49 [507]~E(x5071,x5072)+~P6(x5073)+~P35(f27(f27(f29(x5073),x5071),x5072)) % 1.45/1.49 [508]~E(x5081,x5082)+~P28(x5083)+~P35(f27(f27(f29(x5083),x5081),x5082)) % 1.45/1.49 [518]~P6(x5181)+P35(f27(f28(x5181,x5182),x5183))+P35(f27(f27(f29(x5181),x5183),x5182)) % 1.45/1.49 [562]~P5(x5621)+P35(f27(f28(x5621,x5622),x5623))+~P35(f27(f27(f29(x5621),x5622),x5623)) % 1.45/1.49 [564]~P28(x5641)+P35(f27(f28(x5641,x5642),x5643))+~P35(f27(f27(f29(x5641),x5642),x5643)) % 1.45/1.49 [587]~P12(x5871,x5873)+E(f14(x5871,f35(x5871,x5872,x5873)),f27(a21,f14(x5871,x5873)))+P35(f27(f27(f34(x5871),x5872),x5873)) % 1.45/1.49 [592]~P5(x5921)+~P35(f27(f28(x5921,x5922),x5923))+~P35(f27(f27(f29(x5921),x5923),x5922)) % 1.45/1.49 [595]~P6(x5951)+~P35(f27(f28(x5951,x5952),x5953))+~P35(f27(f27(f29(x5951),x5953),x5952)) % 1.45/1.49 [598]P12(x5981,x5982)+~P12(x5981,x5983)+~P35(f27(f28(f94(x5981,a2),x5982),x5983)) % 1.45/1.49 [599]~E(x5991,f27(a21,x5993))+P35(f27(f27(f29(a91),x5991),f27(a21,x5992)))+~P35(f27(f27(f29(a91),x5993),x5992)) % 1.45/1.49 [612]~P12(x6121,x6123)+E(f14(x6121,f35(x6121,x6122,x6123)),f14(x6121,x6123))+~P35(f27(f27(f34(x6121),x6122),x6123)) % 1.45/1.49 [614]~P12(x6141,x6143)+E(f14(x6141,f35(x6141,x6142,x6143)),f27(f27(f19(a91),f4(a91)),f14(x6141,x6143)))+P35(f27(f27(f34(x6141),x6142),x6143)) % 1.45/1.49 [623]~P5(x6231)+~P35(f27(f27(f29(x6231),x6233),x6232))+~P35(f27(f27(f29(x6231),x6232),x6233)) % 1.45/1.49 [624]~P6(x6241)+~P35(f27(f27(f29(x6241),x6243),x6242))+~P35(f27(f27(f29(x6241),x6242),x6243)) % 1.45/1.49 [625]~P28(x6251)+~P35(f27(f27(f29(x6251),x6253),x6252))+~P35(f27(f27(f29(x6251),x6252),x6253)) % 1.45/1.49 [677]~P35(f27(f27(f29(a91),x6771),x6773))+~P35(f27(f27(f29(a91),x6773),x6772))+P35(f27(f27(f29(a91),f27(a21,x6771)),x6772)) % 1.45/1.49 [686]~P12(x6861,x6863)+P35(f27(f28(a91,f14(x6861,x6862)),f14(x6861,x6863)))+~P35(f27(f28(f94(x6861,a2),x6862),x6863)) % 1.45/1.49 [696]E(x6961,x6962)+~P35(f27(f28(f94(x6963,a2),x6961),x6962))+~P35(f27(f28(f94(x6963,a2),x6962),x6961)) % 1.45/1.49 [701]E(x7011,x7012)+~P35(f27(f28(f94(x7013,a2),x7011),x7012))+P35(f27(f27(f29(f94(x7013,a2)),x7011),x7012)) % 1.45/1.49 [732]~P12(x7321,x7323)+P35(f27(f27(f29(a91),f14(x7321,x7322)),f14(x7321,x7323)))+~P35(f27(f27(f29(f94(x7321,a2)),x7322),x7323)) % 1.45/1.49 [930]~P12(x9301,x9303)+P35(f27(f27(f34(f96(f94(x9301,a2),f94(x9301,a2))),f27(f27(f32(f94(x9301,a2),f94(x9301,a2)),x9302),x9303)),f41(x9301)))+~P35(f27(f27(f29(f94(x9301,a2)),x9302),x9303)) % 1.45/1.49 [851]E(x8511,x8512)+P35(f27(f27(f34(f94(f96(a90,a90),a2)),f13(x8513,x8511,x8512)),a7))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8513),a7)) % 1.45/1.49 [858]E(x8581,x8582)+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8583),a7))+P35(f27(f27(f34(f94(f96(a90,a90),a2)),f27(f27(f27(a11,x8583),x8581),x8582)),a7)) % 1.45/1.49 [932]~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9323),x9322)),x9321))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9322),x9323)),x9321))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9321),a7)) % 1.45/1.49 [854]~P3(x8541,x8543)+E(f27(x8541,x8542),f27(x8542,x8543))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x8542),a8)) % 1.45/1.49 [703]~P12(x7032,x7034)+~P12(x7031,x7033)+P12(f95(x7031,x7032),f37(x7031,x7032,x7033,x7034)) % 1.45/1.49 [815]P12(x8151,x8152)+~P13(x8151,x8153,x8154,x8152)+~P12(x8153,f36(x8151,x8153,x8154,x8152)) % 1.45/1.49 [657]E(x6571,x6572)+P35(f27(x6573,x6572))+~P35(f27(f35(x6574,x6571,x6573),x6572)) % 1.45/1.49 [725]~P12(x7252,x7254)+~P12(x7251,x7253)+E(f14(f95(x7251,x7252),f37(x7251,x7252,x7253,x7254)),f27(f27(f19(a91),f14(x7251,x7253)),f14(x7252,x7254))) % 1.45/1.49 [800]~P12(x8001,x8004)+P13(x8001,x8002,x8003,x8004)+~E(f14(x8002,f36(x8001,x8002,x8003,x8004)),f14(x8001,x8004)) % 1.45/1.49 [489]~P8(x4893)+E(x4891,x4892)+~E(f27(f27(f19(x4893),x4894),x4891),f27(f27(f19(x4893),x4894),x4892)) % 1.45/1.49 [490]~P9(x4903)+E(x4901,x4902)+~E(f27(f27(f19(x4903),x4904),x4901),f27(f27(f19(x4903),x4904),x4902)) % 1.45/1.49 [492]~P8(x4923)+E(x4921,x4922)+~E(f27(f27(f19(x4923),x4921),x4924),f27(f27(f19(x4923),x4922),x4924)) % 1.45/1.49 [630]P35(f27(x6301,x6302))+~P35(f27(x6303,x6302))+~P35(f27(f28(f94(x6304,a2),x6303),x6301)) % 1.45/1.49 [647]~E(f27(f27(f19(a91),x6473),x6472),f27(f27(f19(a91),x6471),x6474))+~P35(f27(f27(f29(a91),x6473),x6474))+P35(f27(f27(f29(a91),x6471),x6472)) % 1.45/1.49 [694]P35(f27(f27(f34(x6941),x6942),x6943))+~P35(f27(f27(f34(x6941),x6942),x6944))+~P35(f27(f28(f94(x6941,a2),x6944),x6943)) % 1.45/1.49 [708]E(x7081,x7082)+~P35(f27(f27(f34(x7083),x7081),f35(x7083,x7082,x7084)))+P35(f27(f27(f34(x7083),x7081),x7084)) % 1.45/1.49 [728]~P35(f27(f28(f94(x7281,a2),x7282),x7284))+~P35(f27(f28(f94(x7281,a2),x7284),x7283))+P35(f27(f28(f94(x7281,a2),x7282),x7283)) % 1.45/1.49 [766]~P35(f27(f28(f94(x7661,a2),x7663),f35(x7661,x7662,x7664)))+P35(f27(f27(f34(x7661),x7662),x7663))+P35(f27(f28(f94(x7661,a2),x7663),x7664)) % 1.45/1.49 [791]~P35(f27(f27(f34(x7911),x7912),x7914))+~P35(f27(f28(f94(x7911,a2),x7913),x7914))+P35(f27(f28(f94(x7911,a2),f35(x7911,x7912,x7913)),x7914)) % 1.45/1.49 [836]~E(x8361,x8362)+~E(x8361,x8363)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8362),x8361)),f27(f27(a10,x8364),x8363))) % 1.45/1.49 [837]~E(x8371,x8372)+~E(x8371,x8373)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8371),x8372)),f27(f27(a12,x8374),x8373))) % 1.45/1.49 [1004]~P27(x10042)+~P35(f27(f28(x10042,f27(x10043,f49(x10044,x10043,x10041,x10042))),f27(x10044,f49(x10044,x10043,x10041,x10042))))+P35(f27(f28(f94(x10041,x10042),x10043),x10044)) % 1.45/1.49 [722]~P27(x7222)+P35(f27(f28(f94(x7221,x7222),x7223),x7224))+~P35(f27(f27(f29(f94(x7221,x7222)),x7223),x7224)) % 1.45/1.49 [733]P35(f27(f27(f34(x7331),x7332),x7333))+~P35(f27(f27(f34(x7331),x7332),x7334))+~P35(f27(f27(f29(f94(x7331,a2)),x7334),x7333)) % 1.45/1.49 [750]~P27(x7501)+~P35(f27(f28(f94(x7502,x7501),x7503),x7504))+~P35(f27(f27(f29(f94(x7502,x7501)),x7504),x7503)) % 1.45/1.49 [755]~P22(x7551)+~P35(f27(f28(x7551,x7553),x7554))+P35(f27(f28(x7551,f27(f27(f19(x7551),x7552),x7553)),f27(f27(f19(x7551),x7552),x7554))) % 1.45/1.49 [756]~P23(x7561)+~P35(f27(f28(x7561,x7563),x7564))+P35(f27(f28(x7561,f27(f27(f19(x7561),x7562),x7563)),f27(f27(f19(x7561),x7562),x7564))) % 1.45/1.49 [757]~P22(x7571)+~P35(f27(f28(x7571,x7572),x7574))+P35(f27(f28(x7571,f27(f27(f19(x7571),x7572),x7573)),f27(f27(f19(x7571),x7574),x7573))) % 1.45/1.49 [758]~P23(x7581)+~P35(f27(f28(x7581,x7582),x7584))+P35(f27(f28(x7581,f27(f27(f19(x7581),x7582),x7583)),f27(f27(f19(x7581),x7584),x7583))) % 1.45/1.49 [763]~P35(f27(f28(a91,x7632),x7634))+~P35(f27(f28(a91,x7631),x7633))+P35(f27(f28(a91,f27(f27(f19(a91),x7631),x7632)),f27(f27(f19(a91),x7633),x7634))) % 1.45/1.49 [768]~P7(x7681)+~P35(f27(f27(f29(x7681),x7683),x7684))+P35(f27(f27(f29(x7681),f27(f27(f19(x7681),x7682),x7683)),f27(f27(f19(x7681),x7682),x7684))) % 1.45/1.49 [769]~P22(x7691)+~P35(f27(f27(f29(x7691),x7693),x7694))+P35(f27(f27(f29(x7691),f27(f27(f19(x7691),x7692),x7693)),f27(f27(f19(x7691),x7692),x7694))) % 1.45/1.50 [770]~P7(x7701)+~P35(f27(f27(f29(x7701),x7702),x7704))+P35(f27(f27(f29(x7701),f27(f27(f19(x7701),x7702),x7703)),f27(f27(f19(x7701),x7704),x7703))) % 1.45/1.50 [771]~P22(x7711)+~P35(f27(f27(f29(x7711),x7712),x7714))+P35(f27(f27(f29(x7711),f27(f27(f19(x7711),x7712),x7713)),f27(f27(f19(x7711),x7714),x7713))) % 1.45/1.50 [778]~P35(f27(f27(f29(a91),x7782),x7784))+~P35(f27(f27(f29(a91),x7781),x7783))+P35(f27(f27(f29(a91),f27(f27(f19(a91),x7781),x7782)),f27(f27(f19(a91),x7783),x7784))) % 1.45/1.50 [786]~P35(f27(f28(f94(x7861,a2),x7864),x7863))+~P35(f27(f27(f29(f94(x7861,a2)),x7862),x7864))+P35(f27(f27(f29(f94(x7861,a2)),x7862),x7863)) % 1.45/1.50 [787]~P35(f27(f28(f94(x7871,a2),x7872),x7874))+~P35(f27(f27(f29(f94(x7871,a2)),x7874),x7873))+P35(f27(f27(f29(f94(x7871,a2)),x7872),x7873)) % 1.45/1.50 [811]~P22(x8111)+P35(f27(f28(x8111,x8112),x8113))+~P35(f27(f28(x8111,f27(f27(f19(x8111),x8114),x8112)),f27(f27(f19(x8111),x8114),x8113))) % 1.45/1.50 [813]~P22(x8131)+P35(f27(f28(x8131,x8132),x8133))+~P35(f27(f28(x8131,f27(f27(f19(x8131),x8132),x8134)),f27(f27(f19(x8131),x8133),x8134))) % 1.45/1.50 [814]~P35(f27(f27(f29(f94(x8141,a2)),x8142),x8144))+P35(f27(f27(f29(f94(x8141,a2)),x8142),x8143))+~P35(f27(f27(f29(f94(x8141,a2)),x8144),x8143)) % 1.45/1.50 [817]~P22(x8171)+P35(f27(f27(f29(x8171),x8172),x8173))+~P35(f27(f27(f29(x8171),f27(f27(f19(x8171),x8174),x8172)),f27(f27(f19(x8171),x8174),x8173))) % 1.45/1.50 [819]~P22(x8191)+P35(f27(f27(f29(x8191),x8192),x8193))+~P35(f27(f27(f29(x8191),f27(f27(f19(x8191),x8192),x8194)),f27(f27(f19(x8191),x8193),x8194))) % 1.45/1.50 [893]~P13(x8934,x8933,x8931,f30(f94(x8934,a2)))+E(f27(x8931,f74(x8932,x8931,x8933,x8934)),x8932)+~P35(f27(f27(f34(x8933),x8932),f36(x8934,x8933,x8931,f30(f94(x8934,a2))))) % 1.45/1.50 [871]E(x8711,x8712)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8713),x8711)),f27(f27(a10,x8714),x8712)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8713),x8711)),x8714)) % 1.45/1.50 [872]E(x8721,x8722)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8721),x8723)),f27(f27(a12,x8724),x8722)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8721),x8723)),x8724)) % 1.45/1.50 [684]E(x6841,x6842)+~E(f27(x6843,x6841),f27(x6843,x6842))+~P13(x6844,x6845,x6843,f30(f94(x6844,a2))) % 1.45/1.50 [820]E(x8201,x8202)+~E(f36(x8203,x8204,x8205,x8201),f36(x8203,x8204,x8205,x8202))+~P13(x8203,x8204,x8205,f30(f94(x8203,a2))) % 1.45/1.50 [848]P12(x8481,x8482)+~P12(x8483,x8484)+~P35(f27(f28(f94(x8481,a2),x8482),f36(x8483,x8481,x8485,x8484))) % 1.45/1.50 [690]~P27(x6901)+P35(f27(f28(x6901,f27(x6902,x6903)),f27(x6904,x6903)))+~P35(f27(f28(f94(x6905,x6901),x6902),x6904)) % 1.45/1.50 [776]P13(x7761,x7762,x7763,x7764)+~P13(x7761,x7762,x7763,x7765)+~P35(f27(f28(f94(x7761,a2),x7764),x7765)) % 1.45/1.50 [802]~P13(x8021,x8022,x8024,x8023)+E(f27(f22(x8021,x8022,x8023,x8024),f27(x8024,x8025)),x8025)+~P35(f27(f27(f34(x8021),x8025),x8023)) % 1.45/1.50 [849]~P13(x8492,x8491,x8494,x8493)+E(f36(x8491,x8492,f22(x8492,x8491,x8493,x8494),f36(x8492,x8491,x8494,x8495)),x8495)+~P35(f27(f28(f94(x8492,a2),x8495),x8493)) % 1.45/1.50 [868]~P13(x8681,x8684,x8685,f30(f94(x8681,a2)))+~P35(f27(f27(f34(x8684),f27(x8685,x8682)),f36(x8681,x8684,x8685,x8683)))+P35(f27(f27(f34(x8681),x8682),x8683)) % 1.45/1.50 [979]~P13(x9791,x9794,x9795,f30(f94(x9791,a2)))+~P35(f27(f28(f94(x9794,a2),f36(x9791,x9794,x9795,x9792)),f36(x9791,x9794,x9795,x9793)))+P35(f27(f28(f94(x9791,a2),x9792),x9793)) % 1.45/1.50 [805]~E(f27(x8053,x8055),x8054)+~P13(x8051,x8052,x8053,f30(f94(x8051,a2)))+E(f27(f22(x8051,x8052,f30(f94(x8051,a2)),x8053),x8054),x8055) % 1.45/1.50 [946]~P13(x9462,x9461,x9463,x9465)+P35(f27(f27(f29(f94(x9461,a2)),f36(x9462,x9461,x9463,x9464)),f36(x9462,x9461,x9463,x9465)))+~P35(f27(f27(f29(f94(x9462,a2)),x9464),x9465)) % 1.45/1.50 [899]P35(f27(f27(f34(f96(x8991,x8991)),f27(f27(f32(x8991,x8991),x8992),x8993)),f43(x8991,x8994,x8995)))+~P35(f27(f28(a91,f27(x8994,x8992)),f27(x8994,x8993)))+~P35(f27(f27(f34(f96(x8991,x8991)),f27(f27(f32(x8991,x8991),x8992),x8993)),x8995)) % 1.45/1.50 [824]~E(x8242,f27(x8244,x8246))+P35(f27(f27(f34(x8241),x8242),f36(x8243,x8241,x8244,x8245)))+~P35(f27(f27(f34(x8243),x8246),x8245)) % 1.45/1.50 [844]~E(x8442,f36(x8443,x8441,x8444,x8446))+P35(f27(f28(f94(x8441,a2),x8442),f36(x8443,x8441,x8444,x8445)))+~P35(f27(f28(f94(x8443,a2),x8446),x8445)) % 1.45/1.50 [862]~E(f36(x8621,x8622,x8623,x8624),x8626)+E(f36(x8621,x8622,x8623,f36(x8622,x8621,f22(x8621,x8622,x8624,x8623),x8625)),x8625)+~P35(f27(f28(f94(x8622,a2),x8625),x8626)) % 1.45/1.50 [870]~P35(f27(f27(f34(f94(x8705,x8701)),x8702),f17(x8705,x8701,x8706,x8704)))+P35(f27(f27(f34(x8701),f27(x8702,x8703)),f27(x8704,x8703)))+~P35(f27(f27(f34(x8705),x8703),x8706)) % 1.45/1.50 [749]P35(f27(f27(x7491,x7492),x7493))+~P35(f27(f27(x7494,x7492),x7493))+~P35(f27(f28(f94(x7495,f94(x7496,a2)),x7494),x7491)) % 1.45/1.50 [913]P35(f27(f27(f34(x9131),f27(x9132,x9133)),x9134))+~P35(f27(f27(f34(x9135),x9133),x9136))+~P35(f27(f27(f34(f94(x9135,x9131)),x9132),f17(x9135,x9131,x9136,f27(f15(f94(x9131,a2),x9135),x9134)))) % 1.45/1.50 [1014]~P12(x10144,x10142)+~P16(x10143,x10144,x10145,x10147,x10146,x10141)+E(f27(x10141,x10142),f18(x10143,x10144,x10145,x10146,x10147,x10142)) % 1.45/1.50 [1007]~P35(f27(x10076,x10073))+~P35(f27(f27(f34(f96(x10072,x10072)),f27(f27(f32(x10072,x10072),x10074),x10075)),f27(x10077,x10073)))+P35(f27(f27(f34(f96(f96(x10071,x10072),f96(x10071,x10072))),f27(f27(f32(f96(x10071,x10072),f96(x10071,x10072)),f27(f27(f32(x10071,x10072),x10073),x10074)),f27(f27(f32(x10071,x10072),x10073),x10075))),f33(x10071,x10072,x10076,x10077))) % 1.45/1.50 [1000]~P12(x10002,x10004)+~P15(x10007,x10002,x10005,x10008,x10006,x10001)+E(f27(x10001,f35(x10002,x10003,x10004)),f27(f27(x10005,f27(x10006,x10003)),f27(x10001,x10004))) % 1.45/1.50 [1006]~E(x10063,x10065)+P35(f27(f27(f34(f96(f96(x10061,x10062),f96(x10061,x10062))),f27(f27(f32(f96(x10061,x10062),f96(x10061,x10062)),f27(f27(f32(x10061,x10062),x10063),x10064)),f27(f27(f32(x10061,x10062),x10065),x10066))),f42(x10061,x10062,x10067,x10068)))+~P35(f27(f27(f34(f96(x10062,x10062)),f27(f27(f32(x10062,x10062),x10064),x10066)),x10068)) % 1.45/1.50 [1013]E(x10131,x10132)+~P35(f27(f27(f34(f96(f96(x10133,x10135),f96(x10133,x10135))),f27(f27(f32(f96(x10133,x10135),f96(x10133,x10135)),f27(f27(f32(x10133,x10135),x10131),x10136)),f27(f27(f32(x10133,x10135),x10132),x10137))),f42(x10133,x10135,x10134,x10138)))+P35(f27(f27(f34(f96(x10133,x10133)),f27(f27(f32(x10133,x10133),x10131),x10132)),x10134)) % 1.45/1.50 [1017]~P35(f27(f27(f34(f96(f96(x10171,x10175),f96(x10171,x10175))),f27(f27(f32(f96(x10171,x10175),f96(x10171,x10175)),f27(f27(f32(x10171,x10175),x10172),x10176)),f27(f27(f32(x10171,x10175),x10173),x10177))),f42(x10171,x10175,x10174,x10178)))+P35(f27(f27(f34(f96(x10171,x10171)),f27(f27(f32(x10171,x10171),x10172),x10173)),x10174))+P35(f27(f27(f34(f96(x10175,x10175)),f27(f27(f32(x10175,x10175),x10176),x10177)),x10178)) % 1.45/1.50 [881]E(f27(a97,x8811),a106)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x8811)))+P35(f27(f27(f29(a91),f27(a97,x8811)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a12,f27(a102,x8811)),a105))) % 1.45/1.50 [891]E(f27(a97,x8911),a106)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x8911)))+P35(f27(f27(f29(a91),f27(a97,x8911)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a12,f27(a102,x8911)),a105))) % 1.45/1.50 [955]E(f27(a97,x9551),a106)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x9551)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a12,f27(a102,x9551)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a10,f27(a102,x9551)),a105))) % 1.45/1.50 [877]E(f27(a97,x8771),a106)+P35(f27(f27(f29(a91),f27(a97,x8771)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a105),a104)),f27(f27(a12,f27(a102,x8771)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),a99)) % 1.45/1.50 [896]~E(f27(a97,x8961),a106)+P35(f27(f27(f29(a91),f27(a97,x8961)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a105),a104)),f27(f27(f27(a11,f27(a102,x8961)),a103),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a100),a101)),a99)) % 1.45/1.50 [897]~E(f27(a97,x8971),a106)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x8971)))+P35(f27(f27(f29(a91),f27(a97,x8971)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(f27(a11,f27(a102,x8971)),a103),a105))) % 1.45/1.50 [903]~P35(f27(f27(f29(a91),f27(a97,x9031)),f27(f27(f19(a91),a106),f4(a91))))+~P35(f27(f27(f29(a91),f27(a97,x9031)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a10,f27(a102,x9031)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a98)) % 1.45/1.50 [916]~E(f27(a97,x9161),a106)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x9161)))+P35(f27(f27(f29(a91),f27(a97,x9161)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(f27(a11,f27(a102,x9161)),a103),a105))) % 1.45/1.50 [971]~E(f27(a97,x9711),a106)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x9711)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a10,f27(a102,x9711)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(f27(a11,f27(a102,x9711)),a103),a105))) % 1.45/1.50 [975]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x9751)))+P35(f27(f27(f29(a91),f27(a97,x9751)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a12,f27(a102,x9751)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(f27(a11,f27(a102,x9751)),a103),a105))) % 1.45/1.50 [990]P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(a102,x9901)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a12,f27(a102,x9901)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(a10,f27(a102,x9901)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a104)),f27(f27(f27(a11,f27(a102,x9901)),a103),a105))) % 1.45/1.50 [890]~P31(x8901)+~P35(f27(f27(f34(x8901),x8902),f24(x8901)))+P35(f27(f27(f29(x8901),f27(f27(f19(x8901),f27(f27(f19(x8901),f4(x8901)),x8902)),x8902)),f3(x8901)))+~P35(f27(f27(f29(x8901),x8902),f3(x8901))) % 1.45/1.50 [951]~P31(x9511)+~P35(f27(f27(f34(x9511),x9512),f24(x9511)))+~P35(f27(f27(f29(x9511),f27(f27(f19(x9511),f27(f27(f19(x9511),f4(x9511)),x9512)),x9512)),f3(x9511)))+P35(f27(f27(f29(x9511),x9512),f3(x9511))) % 1.45/1.50 [568]~P26(x5681)+~E(x5682,f3(x5681))+E(f27(f27(f19(x5681),x5682),x5682),f3(x5681))+~P35(f27(f27(f34(x5681),x5682),f24(x5681))) % 1.45/1.50 [583]~P26(x5832)+E(x5831,f3(x5832))+~E(f27(f27(f19(x5832),x5831),x5831),f3(x5832))+~P35(f27(f27(f34(x5832),x5831),f24(x5832))) % 1.45/1.50 [577]E(x5771,x5772)+~P28(x5773)+~P35(f27(f28(x5773,x5772),x5771))+~P35(f27(f28(x5773,x5771),x5772)) % 1.45/1.50 [616]~P35(f27(x6161,x6162))+~P35(f27(x6161,x6163))+~P35(f27(f28(a91,x6163),f70(x6162,x6161)))+P35(f27(x6161,f3(a91))) % 1.45/1.50 [753]~P25(x7531)+~P35(f27(f28(x7531,x7533),f3(x7531)))+~P35(f27(f28(x7531,x7532),f3(x7531)))+P35(f27(f28(x7531,f27(f27(f19(x7531),x7532),x7533)),f3(x7531))) % 1.45/1.50 [764]~P25(x7641)+~P35(f27(f28(x7641,x7643),f3(x7641)))+~P35(f27(f27(f29(x7641),x7642),f3(x7641)))+P35(f27(f27(f29(x7641),f27(f27(f19(x7641),x7642),x7643)),f3(x7641))) % 1.45/1.50 [765]~P25(x7651)+~P35(f27(f28(x7651,x7652),f3(x7651)))+~P35(f27(f27(f29(x7651),x7653),f3(x7651)))+P35(f27(f27(f29(x7651),f27(f27(f19(x7651),x7652),x7653)),f3(x7651))) % 1.45/1.50 [773]~P33(x7731)+~P35(f27(f27(f34(x7731),x7733),f24(x7731)))+~P35(f27(f27(f34(x7731),x7732),f24(x7731)))+P35(f27(f27(f34(x7731),f27(f27(f19(x7731),x7732),x7733)),f24(x7731))) % 1.45/1.50 [774]~P25(x7741)+~P35(f27(f27(f29(x7741),x7743),f3(x7741)))+~P35(f27(f27(f29(x7741),x7742),f3(x7741)))+P35(f27(f27(f29(x7741),f27(f27(f19(x7741),x7742),x7743)),f3(x7741))) % 1.45/1.50 [520]~E(x5202,x5203)+~P6(x5201)+P35(f27(f28(x5201,x5202),x5203))+P35(f27(f27(f29(x5201),x5202),x5203)) % 1.45/1.50 [534]~P31(x5343)+E(x5341,x5342)+P35(f27(f27(f29(x5343),x5342),x5341))+P35(f27(f27(f29(x5343),x5341),x5342)) % 1.45/1.50 [535]~P6(x5353)+E(x5351,x5352)+P35(f27(f27(f29(x5353),x5352),x5351))+P35(f27(f27(f29(x5353),x5351),x5352)) % 1.45/1.50 [551]~P28(x5513)+E(x5511,x5512)+~P35(f27(f28(x5513,x5512),x5511))+P35(f27(f27(f29(x5513),x5512),x5511)) % 1.45/1.50 [553]~P6(x5533)+E(x5531,x5532)+~P35(f27(f28(x5533,x5531),x5532))+P35(f27(f27(f29(x5533),x5531),x5532)) % 1.45/1.50 [559]~P28(x5593)+E(x5591,x5592)+~P35(f27(f28(x5593,x5591),x5592))+P35(f27(f27(f29(x5593),x5591),x5592)) % 1.45/1.50 [613]~P5(x6131)+~P35(f27(f28(x6131,x6133),x6132))+P35(f27(f28(x6131,x6132),x6133))+P35(f27(f27(f29(x6131),x6133),x6132)) % 1.45/1.50 [717]E(x7171,x7172)+~P12(x7173,x7171)+~P35(f27(f28(a91,f14(x7173,x7171)),f14(x7173,x7172)))+~P35(f27(f28(f94(x7173,a2),x7172),x7171)) % 1.45/1.50 [941]~P12(x9411,x9413)+~P13(x9411,x9411,x9412,x9413)+E(f36(x9411,x9411,x9412,x9413),x9413)+~P35(f27(f28(f94(x9411,a2),f36(x9411,x9411,x9412,x9413)),x9413)) % 1.45/1.50 [736]~P25(x7361)+~P35(f27(f27(f29(x7361),f3(x7361)),x7363))+~P35(f27(f27(f29(x7361),f3(x7361)),x7362))+P35(f27(f27(f29(x7361),f3(x7361)),f27(f27(f19(x7361),x7362),x7363))) % 1.45/1.50 [783]~P12(x7831,x7833)+~P35(f27(f27(f29(a91),f14(x7831,x7832)),f14(x7831,x7833)))+~P35(f27(f28(f94(x7831,a2),x7832),x7833))+P35(f27(f27(f29(f94(x7831,a2)),x7832),x7833)) % 1.45/1.50 [878]E(x8781,x8782)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8781),x8782)),x8783))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8782),x8781)),x8783))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8783),a7)) % 1.45/1.50 [627]~P28(x6271)+~P35(f27(f28(x6271,x6274),x6273))+P35(f27(f28(x6271,x6272),x6273))+~P35(f27(f28(x6271,x6272),x6274)) % 1.45/1.50 [628]~P5(x6281)+~P35(f27(f28(x6281,x6282),x6284))+P35(f27(f28(x6281,x6282),x6283))+~P35(f27(f28(x6281,x6284),x6283)) % 1.45/1.50 [809]~P12(x8092,x8093)+~P12(x8091,x8094)+P13(x8091,x8092,f80(x8093,x8092,x8094,x8091),x8094)+~P35(f27(f28(a91,f14(x8091,x8094)),f14(x8092,x8093))) % 1.45/1.50 [646]E(x6461,x6462)+~E(f35(x6463,x6464,x6461),f35(x6463,x6464,x6462))+P35(f27(f27(f34(x6463),x6464),x6462))+P35(f27(f27(f34(x6463),x6464),x6461)) % 1.45/1.50 [650]~P28(x6501)+~P35(f27(f28(x6501,x6502),x6504))+~P35(f27(f27(f29(x6501),x6504),x6503))+P35(f27(f27(f29(x6501),x6502),x6503)) % 1.45/1.50 [651]~P28(x6511)+~P35(f27(f28(x6511,x6514),x6513))+~P35(f27(f27(f29(x6511),x6512),x6514))+P35(f27(f27(f29(x6511),x6512),x6513)) % 1.45/1.50 [652]~P5(x6521)+~P35(f27(f28(x6521,x6524),x6523))+~P35(f27(f27(f29(x6521),x6522),x6524))+P35(f27(f27(f29(x6521),x6522),x6523)) % 1.45/1.50 [653]~P5(x6531)+~P35(f27(f28(x6531,x6532),x6534))+~P35(f27(f27(f29(x6531),x6534),x6533))+P35(f27(f27(f29(x6531),x6532),x6533)) % 1.45/1.50 [668]~P28(x6681)+~P35(f27(f27(f29(x6681),x6684),x6683))+P35(f27(f27(f29(x6681),x6682),x6683))+~P35(f27(f27(f29(x6681),x6682),x6684)) % 1.45/1.50 [669]~P5(x6691)+~P35(f27(f27(f29(x6691),x6692),x6694))+P35(f27(f27(f29(x6691),x6692),x6693))+~P35(f27(f27(f29(x6691),x6694),x6693)) % 1.45/1.50 [793]~E(x7933,x7931)+E(x7931,x7932)+E(x7933,x7932)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x7932),x7933)),f27(f27(a10,x7934),x7931))) % 1.45/1.50 [794]~E(x7943,x7941)+E(x7941,x7942)+E(x7943,x7942)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x7943),x7942)),f27(f27(a12,x7944),x7941))) % 1.45/1.50 [704]~P25(x7041)+~P35(f27(f28(x7041,x7042),x7043))+~P35(f27(f28(x7041,f3(x7041)),x7044))+P35(f27(f28(x7041,x7042),f27(f27(f19(x7041),x7043),x7044))) % 1.45/1.50 [705]~P25(x7051)+~P35(f27(f28(x7051,x7052),x7054))+~P35(f27(f28(x7051,f3(x7051)),x7053))+P35(f27(f28(x7051,x7052),f27(f27(f19(x7051),x7053),x7054))) % 1.45/1.50 [713]~P25(x7131)+~P35(f27(f28(x7131,x7132),x7134))+~P35(f27(f27(f29(x7131),f3(x7131)),x7133))+P35(f27(f27(f29(x7131),x7132),f27(f27(f19(x7131),x7133),x7134))) % 1.45/1.50 [714]~P25(x7141)+~P35(f27(f28(x7141,f3(x7141)),x7143))+~P35(f27(f27(f29(x7141),x7142),x7144))+P35(f27(f27(f29(x7141),x7142),f27(f27(f19(x7141),x7143),x7144))) % 1.45/1.50 [723]~P29(x7231)+~P35(f27(f27(f29(x7231),f3(x7231)),x7233))+~P35(f27(f27(f29(x7231),x7232),x7234))+P35(f27(f27(f29(x7231),x7232),f27(f27(f19(x7231),x7233),x7234))) % 1.45/1.50 [751]~P27(x7512)+~P35(f27(f28(f94(x7511,x7512),x7514),x7513))+P35(f27(f28(f94(x7511,x7512),x7513),x7514))+P35(f27(f27(f29(f94(x7511,x7512)),x7514),x7513)) % 1.45/1.50 [988]~P12(x9882,x9884)+~P12(x9881,x9883)+~P35(f27(f28(a91,f14(x9882,x9884)),f14(x9881,x9883)))+P35(f27(f28(f94(x9881,a2),f36(x9882,x9881,f80(x9883,x9881,x9884,x9882),x9884)),x9883)) % 1.45/1.50 [863]E(x8631,x8632)+E(x8633,x8632)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8633),x8631)),f27(f27(a10,x8634),x8632)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8633),x8631)),x8634)) % 1.45/1.50 [864]E(x8641,x8642)+E(x8643,x8642)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8643),x8641)),f27(f27(a12,x8644),x8642)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8643),x8641)),x8644)) % 1.45/1.50 [865]E(x8651,x8652)+E(x8653,x8651)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8653),x8651)),f27(f27(a12,x8654),x8652)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8653),x8651)),x8654)) % 1.45/1.50 [866]E(x8661,x8662)+E(x8661,x8663)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8661),x8663)),f27(f27(a10,x8664),x8662)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8661),x8663)),x8664)) % 1.45/1.50 [997]~P2(x9973)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9971),x9972)),f27(x9973,x9974)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9971),x9972)),f27(x9974,f64(x9973,x9974,x9971,x9972))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x9974),a8)) % 1.45/1.50 [940]~P12(x9403,x9404)+~P13(x9401,x9403,x9405,x9402)+P35(f27(f28(a91,f14(x9401,x9402)),f14(x9403,x9404)))+~P35(f27(f28(f94(x9403,a2),f36(x9401,x9403,x9405,x9402)),x9404)) % 1.45/1.50 [782]~P23(x7821)+~P35(f27(f28(x7821,x7823),x7825))+~P35(f27(f28(x7821,x7822),x7824))+P35(f27(f28(x7821,f27(f27(f19(x7821),x7822),x7823)),f27(f27(f19(x7821),x7824),x7825))) % 1.45/1.50 [788]~P7(x7881)+~P35(f27(f28(x7881,x7883),x7885))+~P35(f27(f27(f29(x7881),x7882),x7884))+P35(f27(f27(f29(x7881),f27(f27(f19(x7881),x7882),x7883)),f27(f27(f19(x7881),x7884),x7885))) % 1.45/1.50 [789]~P7(x7891)+~P35(f27(f28(x7891,x7892),x7894))+~P35(f27(f27(f29(x7891),x7893),x7895))+P35(f27(f27(f29(x7891),f27(f27(f19(x7891),x7892),x7893)),f27(f27(f19(x7891),x7894),x7895))) % 1.45/1.50 [796]~P7(x7961)+~P35(f27(f27(f29(x7961),x7963),x7965))+~P35(f27(f27(f29(x7961),x7962),x7964))+P35(f27(f27(f29(x7961),f27(f27(f19(x7961),x7962),x7963)),f27(f27(f19(x7961),x7964),x7965))) % 1.45/1.50 [880]~E(x8802,f27(x8803,x8801))+E(x8801,f74(x8802,x8803,x8804,x8805))+~P13(x8805,x8804,x8803,f30(f94(x8805,a2)))+~P35(f27(f27(f34(x8804),x8802),f36(x8805,x8804,x8803,f30(f94(x8805,a2))))) % 1.45/1.50 [876]E(x8761,x8762)+~E(x8763,x8764)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8763),x8764)),f13(x8765,x8761,x8762)))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8765),a7)) % 1.45/1.50 [887]E(x8871,x8872)+~E(x8873,x8874)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8873),x8874)),f27(f27(f27(a11,x8875),x8871),x8872)))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8875),a7)) % 1.45/1.50 [931]~P12(x9313,x9314)+~P13(x9311,x9313,x9315,x9312)+P35(f27(f28(a91,f14(x9311,x9312)),f14(x9313,x9314)))+~P35(f27(f27(f34(f94(x9311,x9313)),x9315),f17(x9311,x9313,x9312,f27(f15(f94(x9313,a2),x9311),x9314)))) % 1.45/1.50 [968]E(x9681,x9682)+~E(f27(f22(x9683,x9684,x9685,x9686),x9681),f27(f22(x9683,x9684,x9685,x9686),x9682))+~P35(f27(f27(f34(x9684),x9682),f36(x9683,x9684,x9686,x9685)))+~P35(f27(f27(f34(x9684),x9681),f36(x9683,x9684,x9686,x9685))) % 1.45/1.50 [801]~P13(x8011,x8012,x8014,x8013)+~E(f27(x8014,x8016),x8015)+E(f27(f22(x8011,x8012,x8013,x8014),x8015),x8016)+~P35(f27(f27(f34(x8011),x8016),x8013)) % 1.45/1.50 [1001]~P15(x10017,x10016,x10011,x10018,x10012,x10014)+~P12(x10016,x10015)+E(f27(f27(x10011,f27(x10012,x10013)),f27(x10014,x10015)),f27(x10014,x10015))+~P35(f27(f27(f34(x10016),x10013),x10015)) % 1.45/1.50 [1002]~P12(x10022,x10024)+~P16(x10027,x10022,x10025,x10028,x10026,x10021)+E(f27(x10021,f35(x10022,x10023,x10024)),f27(f27(x10025,f27(x10026,x10023)),f27(x10021,x10024)))+P35(f27(f27(f34(x10022),x10023),x10024)) % 1.45/1.50 [1003]~P15(x10036,x10035,x10031,x10037,x10038,x10032)+~P12(x10035,x10034)+E(f27(f27(x10031,f27(x10032,x10033)),f27(x10032,x10034)),f27(x10032,x10034))+~P35(f27(f28(f94(x10035,a2),x10033),x10034)) % 1.45/1.50 [900]E(f27(a97,x9001),a106)+P35(f27(f27(f29(a91),f27(a97,x9001)),f27(f27(f19(a91),a106),f4(a91))))+P35(f27(f27(f29(a91),f27(a97,x9001)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a12,f27(a102,x9001)),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.50 [901]E(f27(a97,x9011),a106)+~P35(f27(f27(f29(a91),f27(a97,x9011)),f27(f27(f19(a91),a106),f4(a91))))+P35(f27(f27(f29(a91),f27(a97,x9011)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a12,f27(a102,x9011)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a98)) % 1.45/1.50 [928]~E(f27(a97,x9281),a106)+~P35(f27(f27(f29(a91),f27(a97,x9281)),f27(f27(f19(a91),a106),f4(a91))))+P35(f27(f27(f29(a91),f27(a97,x9281)),a106))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(f27(a11,f27(a102,x9281)),a103),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a98)) % 1.45/1.50 [938]~E(f27(a97,x9381),a106)+P35(f27(f27(f29(a91),f27(a97,x9381)),f27(f27(f19(a91),a106),f4(a91))))+P35(f27(f27(f29(a91),f27(a97,x9381)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(f27(a11,f27(a102,x9381)),a103),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.50 [963]E(f27(a97,x9631),a106)+P35(f27(f27(f29(a91),f27(a97,x9631)),f27(f27(f19(a91),a106),f4(a91))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a12,f27(a102,x9631)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a10,f27(a102,x9631)),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.50 [978]~E(f27(a97,x9781),a106)+P35(f27(f27(f29(a91),f27(a97,x9781)),f27(f27(f19(a91),a106),f4(a91))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a10,f27(a102,x9781)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(f27(a11,f27(a102,x9781)),a103),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.50 [980]P35(f27(f27(f29(a91),f27(a97,x9801)),f27(f27(f19(a91),a106),f4(a91))))+P35(f27(f27(f29(a91),f27(a97,x9801)),a106))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a12,f27(a102,x9801)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(f27(a11,f27(a102,x9801)),a103),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.50 [995]P35(f27(f27(f29(a91),f27(a97,x9951)),f27(f27(f19(a91),a106),f4(a91))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a12,f27(a102,x9951)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(a10,f27(a102,x9951)),a105)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a103),a105)),f27(f27(f27(a11,f27(a102,x9951)),a103),a105)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),a101),a100)),a99)) % 1.45/1.50 [666]~P25(x6662)+E(x6661,f3(x6662))+~E(f27(f27(f19(x6662),x6663),x6661),f3(x6662))+~P35(f27(f28(x6662,f3(x6662)),x6663))+~P35(f27(f28(x6662,f3(x6662)),x6661)) % 1.45/1.50 [667]~P25(x6672)+E(x6671,f3(x6672))+~E(f27(f27(f19(x6672),x6671),x6673),f3(x6672))+~P35(f27(f28(x6672,f3(x6672)),x6673))+~P35(f27(f28(x6672,f3(x6672)),x6671)) % 1.45/1.50 [918]E(x9181,x9182)+~E(x9185,x9181)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9183),x9185)),f13(x9184,x9181,x9182)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9183),x9182)),x9184))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9184),a7)) % 1.45/1.50 [934]E(x9341,x9342)+~E(x9345,x9341)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9345),x9343)),f27(f27(f27(a11,x9344),x9342),x9341)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9342),x9343)),x9344))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9344),a7)) % 1.45/1.50 [745]E(x7451,x7452)+~P13(x7454,x7455,x7453,x7456)+~E(f27(x7453,x7451),f27(x7453,x7452))+~P35(f27(f27(f34(x7454),x7452),x7456))+~P35(f27(f27(f34(x7454),x7451),x7456)) % 1.45/1.50 [656]~P25(x6561)+~E(x6563,f3(x6561))+~E(x6562,f3(x6561))+E(f27(f27(f19(x6561),x6562),x6563),f3(x6561))+~P35(f27(f28(x6561,f3(x6561)),x6563))+~P35(f27(f28(x6561,f3(x6561)),x6562)) % 1.45/1.50 [906]~E(x9063,x9061)+E(x9061,x9062)+E(x9063,x9064)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9064),x9063)),f13(x9065,x9061,x9062)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9064),x9062)),x9065))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9065),a7)) % 1.45/1.50 [919]E(x9191,x9192)+E(x9191,x9193)+E(x9194,x9191)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9194),x9193)),f13(x9195,x9191,x9192)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9194),x9193)),x9195))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9195),a7)) % 1.45/1.50 [922]~E(x9223,x9221)+E(x9221,x9222)+E(x9223,x9224)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9223),x9224)),f27(f27(f27(a11,x9225),x9222),x9221)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9222),x9224)),x9225))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9225),a7)) % 1.45/1.50 [935]E(x9351,x9352)+E(x9351,x9353)+E(x9354,x9351)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9353),x9354)),f27(f27(f27(a11,x9355),x9352),x9351)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9353),x9354)),x9355))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9355),a7)) % 1.45/1.50 [1010]E(x10101,x10102)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10101),x10102)),f27(a1,x10104)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10102),x10101)),f27(a1,x10103)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10102),x10101)),f27(x10103,f77(x10103,x10104,x10102,x10101))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10101),x10102)),f27(x10104,f77(x10103,x10104,x10102,x10101))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10103),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10104),a8)) % 1.45/1.50 [1011]E(x10111,x10112)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10111),x10112)),f27(a1,x10114)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10112),x10111)),f27(a1,x10113)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10112),x10111)),f27(x10113,f77(x10114,x10113,x10111,x10112))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10111),x10112)),f27(x10114,f77(x10114,x10113,x10111,x10112))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10113),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10114),a8)) % 1.45/1.50 [1015]E(x10151,x10152)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10151),x10152)),f27(a1,x10154)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10152),x10151)),f27(a1,x10153)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10152),x10151)),f27(x10153,f77(x10153,x10154,x10152,x10151))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10151),x10152)),f27(x10154,f77(x10153,x10154,x10152,x10151))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10153),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10154),a8)) % 1.45/1.50 [1016]E(x10161,x10162)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10161),x10162)),f27(a1,x10164)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10162),x10161)),f27(a1,x10163)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10162),x10161)),f27(x10163,f77(x10164,x10163,x10161,x10162))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10161),x10162)),f27(x10164,f77(x10164,x10163,x10161,x10162))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10163),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10164),a8)) % 1.45/1.50 [853]~E(x8533,x8532)+~E(x8534,x8531)+E(x8531,x8532)+E(x8531,x8533)+E(x8534,x8533)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8534),x8533)),f13(x8535,x8531,x8532)))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8535),a7)) % 1.45/1.50 [856]~E(x8563,x8562)+~E(x8564,x8561)+E(x8561,x8562)+E(x8561,x8563)+E(x8564,x8563)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x8563),x8564)),f27(f27(f27(a11,x8565),x8562),x8561)))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x8565),a7)) % 1.45/1.50 [907]E(x9074,x9073)+E(x9071,x9072)+E(x9073,x9071)+E(x9074,x9071)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9074),x9073)),f13(x9075,x9071,x9072)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9074),x9073)),x9075))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9075),a7)) % 1.45/1.50 [908]~E(x9083,x9081)+E(x9081,x9082)+E(x9083,x9082)+E(x9084,x9083)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9084),x9083)),f13(x9085,x9082,x9081)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9084),x9083)),x9085))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9085),a7)) % 1.45/1.50 [909]~E(x9094,x9091)+E(x9091,x9092)+E(x9091,x9093)+E(x9094,x9092)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9094),x9092)),f13(x9095,x9091,x9093)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9093),x9092)),x9095))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9095),a7)) % 1.45/1.50 [910]~E(x9104,x9102)+~E(x9103,x9101)+E(x9101,x9102)+E(x9103,x9104)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9103),x9104)),f13(x9105,x9101,x9102)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9103),x9102)),x9105))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9105),a7)) % 1.45/1.50 [921]E(x9213,x9211)+E(x9211,x9212)+E(x9213,x9212)+~E(x9215,x9213)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9215),x9211)),f13(x9214,x9213,x9212)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9212),x9211)),x9214))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9214),a7)) % 1.45/1.50 [923]E(x9234,x9233)+E(x9231,x9232)+E(x9233,x9231)+E(x9234,x9231)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9234),x9233)),f27(f27(f27(a11,x9235),x9232),x9231)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9234),x9233)),x9235))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9235),a7)) % 1.45/1.50 [924]~E(x9243,x9241)+E(x9241,x9242)+E(x9243,x9242)+E(x9243,x9244)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9243),x9244)),f27(f27(f27(a11,x9245),x9241),x9242)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9243),x9244)),x9245))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9245),a7)) % 1.45/1.50 [925]~E(x9254,x9251)+E(x9251,x9252)+E(x9251,x9253)+E(x9254,x9253)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9253),x9254)),f27(f27(f27(a11,x9255),x9252),x9251)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9253),x9252)),x9255))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9255),a7)) % 1.45/1.50 [926]~E(x9264,x9262)+~E(x9263,x9261)+E(x9261,x9262)+E(x9263,x9264)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9264),x9263)),f27(f27(f27(a11,x9265),x9262),x9261)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9262),x9263)),x9265))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9265),a7)) % 1.45/1.50 [936]E(x9363,x9361)+E(x9361,x9362)+E(x9363,x9362)+~E(x9365,x9363)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9361),x9365)),f27(f27(f27(a11,x9364),x9362),x9363)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9361),x9362)),x9364))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9364),a7)) % 1.45/1.50 [959]E(x9591,x9592)+E(x9593,x9592)+E(x9594,x9593)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9594),x9593)),f13(x9595,x9592,x9591)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9594),x9593)),x9595))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9591),x9593)),x9595))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9595),a7)) % 1.45/1.50 [960]E(x9601,x9602)+E(x9603,x9601)+E(x9603,x9604)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9603),x9604)),f13(x9605,x9601,x9602)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9603),x9604)),x9605))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9603),x9602)),x9605))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9605),a7)) % 1.45/1.50 [961]~E(x9614,x9611)+E(x9611,x9612)+E(x9613,x9614)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9613),x9614)),f13(x9615,x9612,x9611)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9613),x9614)),x9615))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9613),x9611)),x9615))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9615),a7)) % 1.45/1.50 [962]~E(x9623,x9621)+E(x9621,x9622)+E(x9623,x9624)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9623),x9624)),f13(x9625,x9621,x9622)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9622),x9624)),x9625))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9623),x9622)),x9625))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9625),a7)) % 1.45/1.50 [964]E(x9641,x9642)+E(x9643,x9641)+E(x9644,x9643)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9644),x9643)),f27(f27(f27(a11,x9645),x9642),x9641)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9644),x9643)),x9645))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9642),x9643)),x9645))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9645),a7)) % 1.45/1.50 [965]E(x9651,x9652)+E(x9653,x9652)+E(x9653,x9654)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9653),x9654)),f27(f27(f27(a11,x9655),x9651),x9652)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9653),x9654)),x9655))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9653),x9651)),x9655))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9655),a7)) % 1.45/1.50 [966]~E(x9663,x9661)+E(x9661,x9662)+E(x9663,x9664)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9663),x9664)),f27(f27(f27(a11,x9665),x9661),x9662)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9663),x9664)),x9665))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9661),x9664)),x9665))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9665),a7)) % 1.45/1.50 [967]~E(x9673,x9671)+E(x9671,x9672)+E(x9673,x9674)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9674),x9673)),f27(f27(f27(a11,x9675),x9672),x9671)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9672),x9673)),x9675))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9674),x9672)),x9675))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9675),a7)) % 1.45/1.50 [986]E(x9861,x9862)+E(x9863,x9864)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9863),x9864)),f13(x9865,x9862,x9861)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9863),x9864)),x9865))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9861),x9864)),x9865))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9863),x9861)),x9865))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9865),a7)) % 1.45/1.50 [987]E(x9871,x9872)+E(x9873,x9874)+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9873),x9874)),f27(f27(f27(a11,x9875),x9871),x9872)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9873),x9874)),x9875))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9871),x9874)),x9875))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x9873),x9871)),x9875))+~P35(f27(f27(f34(f94(f96(a90,a90),a2)),x9875),a7)) % 1.45/1.50 [1024]~P1(x10243)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10241),x10242)),f27(x10243,x10245)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10241),x10242)),f27(x10243,x10244)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10241),x10242)),f27(x10245,f86(x10243,x10244,x10245,x10241,x10242))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10241),x10242)),f27(x10244,f86(x10243,x10244,x10245,x10241,x10242))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10244),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10245),a8)) % 1.45/1.50 [1025]~P1(x10253)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10251),x10252)),f27(x10253,x10255)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10251),x10252)),f27(x10253,x10254)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10251),x10252)),f27(x10255,f86(x10253,x10255,x10254,x10251,x10252))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10251),x10252)),f27(x10254,f86(x10253,x10255,x10254,x10251,x10252))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10254),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10255),a8)) % 1.45/1.50 [1028]~P1(x10283)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10281),x10282)),f27(x10283,x10285)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10281),x10282)),f27(x10283,x10284)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10281),x10282)),f27(x10285,f86(x10283,x10284,x10285,x10281,x10282))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10281),x10282)),f27(x10284,f86(x10283,x10284,x10285,x10281,x10282))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10284),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10285),a8)) % 1.45/1.50 [1029]~P1(x10293)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10291),x10292)),f27(x10293,x10295)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10291),x10292)),f27(x10293,x10294)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10291),x10292)),f27(x10295,f86(x10293,x10295,x10294,x10291,x10292))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10291),x10292)),f27(x10294,f86(x10293,x10295,x10294,x10291,x10292))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10294),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10295),a8)) % 1.45/1.50 [998]~P12(x9983,x9984)+~P12(x9981,x9982)+~P13(x9983,x9981,x9985,x9984)+~P13(x9981,x9983,x9986,x9982)+E(f14(x9981,x9982),f14(x9983,x9984))+~P35(f27(f28(f94(x9983,a2),f36(x9981,x9983,x9986,x9982)),x9984))+~P35(f27(f28(f94(x9981,a2),f36(x9983,x9981,x9985,x9984)),x9982)) % 1.45/1.50 [992]~P12(x9923,x9924)+~P12(x9921,x9922)+~P13(x9923,x9921,x9925,x9924)+~P13(x9921,x9923,x9926,x9922)+E(f14(x9921,x9922),f14(x9923,x9924))+~P35(f27(f27(f34(f94(x9923,x9921)),x9925),f17(x9923,x9921,x9924,f27(f15(f94(x9921,a2),x9923),x9922))))+~P35(f27(f27(f34(f94(x9921,x9923)),x9926),f17(x9921,x9923,x9922,f27(f15(f94(x9923,a2),x9921),x9924)))) % 1.45/1.50 [1032]E(x10321,x10322)+E(x10323,x10324)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10323),x10324)),f27(a1,x10326)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10321),x10322)),f27(a1,x10325)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10321),x10322)),f27(x10325,f85(x10325,x10326,x10322,x10321,x10324,x10323))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10323),x10324)),f27(x10326,f85(x10325,x10326,x10322,x10321,x10324,x10323))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10325),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10326),a8)) % 1.45/1.50 [1033]E(x10331,x10332)+E(x10333,x10334)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10333),x10334)),f27(a1,x10336)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10331),x10332)),f27(a1,x10335)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10331),x10332)),f27(x10335,f85(x10336,x10335,x10334,x10333,x10332,x10331))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10333),x10334)),f27(x10336,f85(x10336,x10335,x10334,x10333,x10332,x10331))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10335),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10336),a8)) % 1.45/1.50 [1038]E(x10381,x10382)+E(x10383,x10384)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10383),x10384)),f27(a1,x10386)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10381),x10382)),f27(a1,x10385)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10381),x10382)),f27(x10385,f85(x10385,x10386,x10382,x10381,x10384,x10383))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10383),x10384)),f27(x10386,f85(x10385,x10386,x10382,x10381,x10384,x10383))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10385),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10386),a8)) % 1.45/1.50 [1039]E(x10391,x10392)+E(x10393,x10394)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10393),x10394)),f27(a1,x10396)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10391),x10392)),f27(a1,x10395)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10391),x10392)),f27(x10395,f85(x10396,x10395,x10394,x10393,x10392,x10391))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10393),x10394)),f27(x10396,f85(x10396,x10395,x10394,x10393,x10392,x10391))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10395),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10396),a8)) % 1.45/1.50 [1022]E(x10223,x10221)+E(x10221,x10222)+E(x10223,x10222)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10223),x10221)),f27(a1,x10225)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10222),x10223)),f27(a1,x10224)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10222),x10223)),f27(x10224,f84(x10225,x10224,x10221,x10223,x10222))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10223),x10221)),f27(x10225,f84(x10225,x10224,x10221,x10223,x10222))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10224),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10225),a8)) % 1.45/1.50 [1023]E(x10233,x10231)+E(x10231,x10232)+E(x10233,x10232)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10233),x10231)),f27(a1,x10235)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10231),x10232)),f27(a1,x10234)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10231),x10232)),f27(x10234,f84(x10234,x10235,x10232,x10231,x10233))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10233),x10231)),f27(x10235,f84(x10234,x10235,x10232,x10231,x10233))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10234),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10235),a8)) % 1.45/1.50 [1026]E(x10263,x10261)+E(x10261,x10262)+E(x10263,x10262)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10263),x10261)),f27(a1,x10265)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10262),x10263)),f27(a1,x10264)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10262),x10263)),f27(x10264,f84(x10265,x10264,x10261,x10263,x10262))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10263),x10261)),f27(x10265,f84(x10265,x10264,x10261,x10263,x10262))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10264),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10265),a8)) % 1.45/1.50 [1027]E(x10273,x10271)+E(x10271,x10272)+E(x10273,x10272)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10273),x10271)),f27(a1,x10275)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10271),x10272)),f27(a1,x10274)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10271),x10272)),f27(x10274,f84(x10274,x10275,x10272,x10271,x10273))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10273),x10271)),f27(x10275,f84(x10274,x10275,x10272,x10271,x10273))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10274),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10275),a8)) % 1.45/1.50 [1034]E(x10344,x10343)+E(x10341,x10342)+E(x10343,x10342)+E(x10344,x10341)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10344),x10343)),f27(a1,x10346)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10342),x10341)),f27(a1,x10345)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10342),x10341)),f27(x10345,f87(x10345,x10346,x10341,x10342,x10343,x10344))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10344),x10343)),f27(x10346,f87(x10345,x10346,x10341,x10342,x10343,x10344))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10345),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10346),a8)) % 1.45/1.50 [1035]E(x10354,x10353)+E(x10351,x10352)+E(x10353,x10351)+E(x10354,x10352)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10354),x10353)),f27(a1,x10356)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10351),x10352)),f27(a1,x10355)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10351),x10352)),f27(x10355,f88(x10355,x10356,x10352,x10351,x10353,x10354))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10354),x10353)),f27(x10356,f88(x10355,x10356,x10352,x10351,x10353,x10354))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10355),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10356),a8)) % 1.45/1.50 [1036]E(x10364,x10363)+E(x10361,x10362)+E(x10363,x10361)+E(x10364,x10362)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10364),x10363)),f27(a1,x10366)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10361),x10362)),f27(a1,x10365)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10361),x10362)),f27(x10365,f88(x10366,x10365,x10363,x10364,x10362,x10361))))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10364),x10363)),f27(x10366,f88(x10366,x10365,x10363,x10364,x10362,x10361))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10365),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10366),a8)) % 1.45/1.50 [1040]E(x10404,x10403)+E(x10401,x10402)+E(x10403,x10402)+E(x10404,x10401)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10404),x10403)),f27(a1,x10406)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10402),x10401)),f27(a1,x10405)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10402),x10401)),f27(x10405,f87(x10405,x10406,x10401,x10402,x10403,x10404))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10404),x10403)),f27(x10406,f87(x10405,x10406,x10401,x10402,x10403,x10404))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10405),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10406),a8)) % 1.45/1.50 [1041]E(x10414,x10413)+E(x10411,x10412)+E(x10413,x10411)+E(x10414,x10412)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10414),x10413)),f27(a1,x10416)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10411),x10412)),f27(a1,x10415)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10411),x10412)),f27(x10415,f88(x10415,x10416,x10412,x10411,x10413,x10414))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10414),x10413)),f27(x10416,f88(x10415,x10416,x10412,x10411,x10413,x10414))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10415),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10416),a8)) % 1.45/1.50 [1042]E(x10424,x10423)+E(x10421,x10422)+E(x10423,x10421)+E(x10424,x10422)+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10424),x10423)),f27(a1,x10426)))+P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10421),x10422)),f27(a1,x10425)))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10421),x10422)),f27(x10425,f88(x10426,x10425,x10423,x10424,x10422,x10421))))+~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10424),x10423)),f27(x10426,f88(x10426,x10425,x10423,x10424,x10422,x10421))))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10425),a8))+~P35(f27(f27(f34(f94(a89,f94(f96(a90,a90),a2))),x10426),a8)) % 1.45/1.50 %EqnAxiom % 1.45/1.50 [1]E(x11,x11) % 1.45/1.50 [2]E(x22,x21)+~E(x21,x22) % 1.45/1.50 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.45/1.50 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 1.45/1.50 [5]~E(x51,x52)+E(f20(x51),f20(x52)) % 1.45/1.50 [6]~E(x61,x62)+E(f27(x61,x63),f27(x62,x63)) % 1.45/1.50 [7]~E(x71,x72)+E(f27(x73,x71),f27(x73,x72)) % 1.45/1.50 [8]~E(x81,x82)+E(f26(x81,x83),f26(x82,x83)) % 1.45/1.50 [9]~E(x91,x92)+E(f26(x93,x91),f26(x93,x92)) % 1.45/1.50 [10]~E(x101,x102)+E(f9(x101,x103,x104,x105),f9(x102,x103,x104,x105)) % 1.45/1.50 [11]~E(x111,x112)+E(f9(x113,x111,x114,x115),f9(x113,x112,x114,x115)) % 1.45/1.50 [12]~E(x121,x122)+E(f9(x123,x124,x121,x125),f9(x123,x124,x122,x125)) % 1.45/1.50 [13]~E(x131,x132)+E(f9(x133,x134,x135,x131),f9(x133,x134,x135,x132)) % 1.45/1.50 [14]~E(x141,x142)+E(f94(x141,x143),f94(x142,x143)) % 1.45/1.50 [15]~E(x151,x152)+E(f94(x153,x151),f94(x153,x152)) % 1.45/1.50 [16]~E(x161,x162)+E(f4(x161),f4(x162)) % 1.45/1.50 [17]~E(x171,x172)+E(f16(x171,x173,x174,x175,x176),f16(x172,x173,x174,x175,x176)) % 1.45/1.50 [18]~E(x181,x182)+E(f16(x183,x181,x184,x185,x186),f16(x183,x182,x184,x185,x186)) % 1.45/1.50 [19]~E(x191,x192)+E(f16(x193,x194,x191,x195,x196),f16(x193,x194,x192,x195,x196)) % 1.45/1.50 [20]~E(x201,x202)+E(f16(x203,x204,x205,x201,x206),f16(x203,x204,x205,x202,x206)) % 1.45/1.50 [21]~E(x211,x212)+E(f16(x213,x214,x215,x216,x211),f16(x213,x214,x215,x216,x212)) % 1.45/1.50 [22]~E(x221,x222)+E(f32(x221,x223),f32(x222,x223)) % 1.45/1.50 [23]~E(x231,x232)+E(f32(x233,x231),f32(x233,x232)) % 1.45/1.50 [24]~E(x241,x242)+E(f34(x241),f34(x242)) % 1.45/1.50 [25]~E(x251,x252)+E(f5(x251),f5(x252)) % 1.45/1.50 [26]~E(x261,x262)+E(f6(x261,x263,x264),f6(x262,x263,x264)) % 1.45/1.50 [27]~E(x271,x272)+E(f6(x273,x271,x274),f6(x273,x272,x274)) % 1.45/1.50 [28]~E(x281,x282)+E(f6(x283,x284,x281),f6(x283,x284,x282)) % 1.45/1.50 [29]~E(x291,x292)+E(f19(x291),f19(x292)) % 1.45/1.50 [30]~E(x301,x302)+E(f96(x301,x303),f96(x302,x303)) % 1.45/1.50 [31]~E(x311,x312)+E(f96(x313,x311),f96(x313,x312)) % 1.45/1.50 [32]~E(x321,x322)+E(f23(x321),f23(x322)) % 1.45/1.50 [33]~E(x331,x332)+E(f57(x331,x333,x334,x335),f57(x332,x333,x334,x335)) % 1.45/1.50 [34]~E(x341,x342)+E(f57(x343,x341,x344,x345),f57(x343,x342,x344,x345)) % 1.45/1.50 [35]~E(x351,x352)+E(f57(x353,x354,x351,x355),f57(x353,x354,x352,x355)) % 1.45/1.50 [36]~E(x361,x362)+E(f57(x363,x364,x365,x361),f57(x363,x364,x365,x362)) % 1.45/1.50 [37]~E(x371,x372)+E(f28(x371,x373),f28(x372,x373)) % 1.45/1.50 [38]~E(x381,x382)+E(f28(x383,x381),f28(x383,x382)) % 1.45/1.50 [39]~E(x391,x392)+E(f35(x391,x393,x394),f35(x392,x393,x394)) % 1.45/1.50 [40]~E(x401,x402)+E(f35(x403,x401,x404),f35(x403,x402,x404)) % 1.45/1.50 [41]~E(x411,x412)+E(f35(x413,x414,x411),f35(x413,x414,x412)) % 1.45/1.50 [42]~E(x421,x422)+E(f29(x421),f29(x422)) % 1.45/1.50 [43]~E(x431,x432)+E(f30(x431),f30(x432)) % 1.45/1.50 [44]~E(x441,x442)+E(f37(x441,x443,x444,x445),f37(x442,x443,x444,x445)) % 1.45/1.50 [45]~E(x451,x452)+E(f37(x453,x451,x454,x455),f37(x453,x452,x454,x455)) % 1.45/1.50 [46]~E(x461,x462)+E(f37(x463,x464,x461,x465),f37(x463,x464,x462,x465)) % 1.45/1.50 [47]~E(x471,x472)+E(f37(x473,x474,x475,x471),f37(x473,x474,x475,x472)) % 1.45/1.50 [48]~E(x481,x482)+E(f36(x481,x483,x484,x485),f36(x482,x483,x484,x485)) % 1.45/1.50 [49]~E(x491,x492)+E(f36(x493,x491,x494,x495),f36(x493,x492,x494,x495)) % 1.45/1.50 [50]~E(x501,x502)+E(f36(x503,x504,x501,x505),f36(x503,x504,x502,x505)) % 1.45/1.50 [51]~E(x511,x512)+E(f36(x513,x514,x515,x511),f36(x513,x514,x515,x512)) % 1.45/1.50 [52]~E(x521,x522)+E(f17(x521,x523,x524,x525),f17(x522,x523,x524,x525)) % 1.45/1.50 [53]~E(x531,x532)+E(f17(x533,x531,x534,x535),f17(x533,x532,x534,x535)) % 1.45/1.50 [54]~E(x541,x542)+E(f17(x543,x544,x541,x545),f17(x543,x544,x542,x545)) % 1.45/1.50 [55]~E(x551,x552)+E(f17(x553,x554,x555,x551),f17(x553,x554,x555,x552)) % 1.45/1.50 [56]~E(x561,x562)+E(f13(x561,x563,x564),f13(x562,x563,x564)) % 1.45/1.50 [57]~E(x571,x572)+E(f13(x573,x571,x574),f13(x573,x572,x574)) % 1.45/1.50 [58]~E(x581,x582)+E(f13(x583,x584,x581),f13(x583,x584,x582)) % 1.45/1.50 [59]~E(x591,x592)+E(f24(x591),f24(x592)) % 1.45/1.50 [60]~E(x601,x602)+E(f63(x601),f63(x602)) % 1.45/1.50 [61]~E(x611,x612)+E(f42(x611,x613,x614,x615),f42(x612,x613,x614,x615)) % 1.45/1.50 [62]~E(x621,x622)+E(f42(x623,x621,x624,x625),f42(x623,x622,x624,x625)) % 1.45/1.50 [63]~E(x631,x632)+E(f42(x633,x634,x631,x635),f42(x633,x634,x632,x635)) % 1.45/1.50 [64]~E(x641,x642)+E(f42(x643,x644,x645,x641),f42(x643,x644,x645,x642)) % 1.45/1.50 [65]~E(x651,x652)+E(f79(x651),f79(x652)) % 1.45/1.50 [66]~E(x661,x662)+E(f14(x661,x663),f14(x662,x663)) % 1.45/1.50 [67]~E(x671,x672)+E(f14(x673,x671),f14(x673,x672)) % 1.45/1.50 [68]~E(x681,x682)+E(f15(x681,x683),f15(x682,x683)) % 1.45/1.50 [69]~E(x691,x692)+E(f15(x693,x691),f15(x693,x692)) % 1.45/1.50 [70]~E(x701,x702)+E(f22(x701,x703,x704,x705),f22(x702,x703,x704,x705)) % 1.45/1.50 [71]~E(x711,x712)+E(f22(x713,x711,x714,x715),f22(x713,x712,x714,x715)) % 1.45/1.50 [72]~E(x721,x722)+E(f22(x723,x724,x721,x725),f22(x723,x724,x722,x725)) % 1.45/1.50 [73]~E(x731,x732)+E(f22(x733,x734,x735,x731),f22(x733,x734,x735,x732)) % 1.45/1.50 [74]~E(x741,x742)+E(f81(x741,x743),f81(x742,x743)) % 1.45/1.50 [75]~E(x751,x752)+E(f81(x753,x751),f81(x753,x752)) % 1.45/1.50 [76]~E(x761,x762)+E(f77(x761,x763,x764,x765),f77(x762,x763,x764,x765)) % 1.45/1.50 [77]~E(x771,x772)+E(f77(x773,x771,x774,x775),f77(x773,x772,x774,x775)) % 1.45/1.50 [78]~E(x781,x782)+E(f77(x783,x784,x781,x785),f77(x783,x784,x782,x785)) % 1.45/1.50 [79]~E(x791,x792)+E(f77(x793,x794,x795,x791),f77(x793,x794,x795,x792)) % 1.45/1.50 [80]~E(x801,x802)+E(f25(x801,x803,x804,x805),f25(x802,x803,x804,x805)) % 1.45/1.50 [81]~E(x811,x812)+E(f25(x813,x811,x814,x815),f25(x813,x812,x814,x815)) % 1.45/1.50 [82]~E(x821,x822)+E(f25(x823,x824,x821,x825),f25(x823,x824,x822,x825)) % 1.45/1.50 [83]~E(x831,x832)+E(f25(x833,x834,x835,x831),f25(x833,x834,x835,x832)) % 1.45/1.50 [84]~E(x841,x842)+E(f69(x841,x843),f69(x842,x843)) % 1.45/1.50 [85]~E(x851,x852)+E(f69(x853,x851),f69(x853,x852)) % 1.45/1.50 [86]~E(x861,x862)+E(f88(x861,x863,x864,x865,x866,x867),f88(x862,x863,x864,x865,x866,x867)) % 1.45/1.50 [87]~E(x871,x872)+E(f88(x873,x871,x874,x875,x876,x877),f88(x873,x872,x874,x875,x876,x877)) % 1.45/1.50 [88]~E(x881,x882)+E(f88(x883,x884,x881,x885,x886,x887),f88(x883,x884,x882,x885,x886,x887)) % 1.45/1.50 [89]~E(x891,x892)+E(f88(x893,x894,x895,x891,x896,x897),f88(x893,x894,x895,x892,x896,x897)) % 1.45/1.50 [90]~E(x901,x902)+E(f88(x903,x904,x905,x906,x901,x907),f88(x903,x904,x905,x906,x902,x907)) % 1.45/1.50 [91]~E(x911,x912)+E(f88(x913,x914,x915,x916,x917,x911),f88(x913,x914,x915,x916,x917,x912)) % 1.45/1.50 [92]~E(x921,x922)+E(f43(x921,x923,x924),f43(x922,x923,x924)) % 1.45/1.50 [93]~E(x931,x932)+E(f43(x933,x931,x934),f43(x933,x932,x934)) % 1.45/1.50 [94]~E(x941,x942)+E(f43(x943,x944,x941),f43(x943,x944,x942)) % 1.45/1.50 [95]~E(x951,x952)+E(f85(x951,x953,x954,x955,x956,x957),f85(x952,x953,x954,x955,x956,x957)) % 1.45/1.50 [96]~E(x961,x962)+E(f85(x963,x961,x964,x965,x966,x967),f85(x963,x962,x964,x965,x966,x967)) % 1.45/1.50 [97]~E(x971,x972)+E(f85(x973,x974,x971,x975,x976,x977),f85(x973,x974,x972,x975,x976,x977)) % 1.45/1.50 [98]~E(x981,x982)+E(f85(x983,x984,x985,x981,x986,x987),f85(x983,x984,x985,x982,x986,x987)) % 1.45/1.50 [99]~E(x991,x992)+E(f85(x993,x994,x995,x996,x991,x997),f85(x993,x994,x995,x996,x992,x997)) % 1.45/1.50 [100]~E(x1001,x1002)+E(f85(x1003,x1004,x1005,x1006,x1007,x1001),f85(x1003,x1004,x1005,x1006,x1007,x1002)) % 1.45/1.50 [101]~E(x1011,x1012)+E(f93(x1011),f93(x1012)) % 1.45/1.50 [102]~E(x1021,x1022)+E(f95(x1021,x1023),f95(x1022,x1023)) % 1.45/1.50 [103]~E(x1031,x1032)+E(f95(x1033,x1031),f95(x1033,x1032)) % 1.45/1.50 [104]~E(x1041,x1042)+E(f76(x1041,x1043,x1044,x1045,x1046),f76(x1042,x1043,x1044,x1045,x1046)) % 1.45/1.50 [105]~E(x1051,x1052)+E(f76(x1053,x1051,x1054,x1055,x1056),f76(x1053,x1052,x1054,x1055,x1056)) % 1.45/1.50 [106]~E(x1061,x1062)+E(f76(x1063,x1064,x1061,x1065,x1066),f76(x1063,x1064,x1062,x1065,x1066)) % 1.45/1.50 [107]~E(x1071,x1072)+E(f76(x1073,x1074,x1075,x1071,x1076),f76(x1073,x1074,x1075,x1072,x1076)) % 1.45/1.50 [108]~E(x1081,x1082)+E(f76(x1083,x1084,x1085,x1086,x1081),f76(x1083,x1084,x1085,x1086,x1082)) % 1.45/1.50 [109]~E(x1091,x1092)+E(f31(x1091,x1093,x1094),f31(x1092,x1093,x1094)) % 1.45/1.50 [110]~E(x1101,x1102)+E(f31(x1103,x1101,x1104),f31(x1103,x1102,x1104)) % 1.45/1.50 [111]~E(x1111,x1112)+E(f31(x1113,x1114,x1111),f31(x1113,x1114,x1112)) % 1.45/1.50 [112]~E(x1121,x1122)+E(f48(x1121),f48(x1122)) % 1.45/1.50 [113]~E(x1131,x1132)+E(f72(x1131,x1133,x1134,x1135),f72(x1132,x1133,x1134,x1135)) % 1.45/1.50 [114]~E(x1141,x1142)+E(f72(x1143,x1141,x1144,x1145),f72(x1143,x1142,x1144,x1145)) % 1.45/1.50 [115]~E(x1151,x1152)+E(f72(x1153,x1154,x1151,x1155),f72(x1153,x1154,x1152,x1155)) % 1.45/1.50 [116]~E(x1161,x1162)+E(f72(x1163,x1164,x1165,x1161),f72(x1163,x1164,x1165,x1162)) % 1.45/1.50 [117]~E(x1171,x1172)+E(f41(x1171),f41(x1172)) % 1.45/1.50 [118]~E(x1181,x1182)+E(f86(x1181,x1183,x1184,x1185,x1186),f86(x1182,x1183,x1184,x1185,x1186)) % 1.45/1.50 [119]~E(x1191,x1192)+E(f86(x1193,x1191,x1194,x1195,x1196),f86(x1193,x1192,x1194,x1195,x1196)) % 1.45/1.50 [120]~E(x1201,x1202)+E(f86(x1203,x1204,x1201,x1205,x1206),f86(x1203,x1204,x1202,x1205,x1206)) % 1.45/1.50 [121]~E(x1211,x1212)+E(f86(x1213,x1214,x1215,x1211,x1216),f86(x1213,x1214,x1215,x1212,x1216)) % 1.45/1.50 [122]~E(x1221,x1222)+E(f86(x1223,x1224,x1225,x1226,x1221),f86(x1223,x1224,x1225,x1226,x1222)) % 1.45/1.50 [123]~E(x1231,x1232)+E(f65(x1231),f65(x1232)) % 1.45/1.50 [124]~E(x1241,x1242)+E(f40(x1241,x1243),f40(x1242,x1243)) % 1.45/1.50 [125]~E(x1251,x1252)+E(f40(x1253,x1251),f40(x1253,x1252)) % 1.45/1.50 [126]~E(x1261,x1262)+E(f62(x1261),f62(x1262)) % 1.45/1.50 [127]~E(x1271,x1272)+E(f47(x1271),f47(x1272)) % 1.45/1.50 [128]~E(x1281,x1282)+E(f78(x1281,x1283),f78(x1282,x1283)) % 1.45/1.50 [129]~E(x1291,x1292)+E(f78(x1293,x1291),f78(x1293,x1292)) % 1.45/1.50 [130]~E(x1301,x1302)+E(f83(x1301),f83(x1302)) % 1.45/1.50 [131]~E(x1311,x1312)+E(f54(x1311,x1313),f54(x1312,x1313)) % 1.45/1.50 [132]~E(x1321,x1322)+E(f54(x1323,x1321),f54(x1323,x1322)) % 1.45/1.50 [133]~E(x1331,x1332)+E(f87(x1331,x1333,x1334,x1335,x1336,x1337),f87(x1332,x1333,x1334,x1335,x1336,x1337)) % 1.45/1.50 [134]~E(x1341,x1342)+E(f87(x1343,x1341,x1344,x1345,x1346,x1347),f87(x1343,x1342,x1344,x1345,x1346,x1347)) % 1.45/1.50 [135]~E(x1351,x1352)+E(f87(x1353,x1354,x1351,x1355,x1356,x1357),f87(x1353,x1354,x1352,x1355,x1356,x1357)) % 1.45/1.50 [136]~E(x1361,x1362)+E(f87(x1363,x1364,x1365,x1361,x1366,x1367),f87(x1363,x1364,x1365,x1362,x1366,x1367)) % 1.45/1.50 [137]~E(x1371,x1372)+E(f87(x1373,x1374,x1375,x1376,x1371,x1377),f87(x1373,x1374,x1375,x1376,x1372,x1377)) % 1.45/1.50 [138]~E(x1381,x1382)+E(f87(x1383,x1384,x1385,x1386,x1387,x1381),f87(x1383,x1384,x1385,x1386,x1387,x1382)) % 1.45/1.50 [139]~E(x1391,x1392)+E(f74(x1391,x1393,x1394,x1395),f74(x1392,x1393,x1394,x1395)) % 1.45/1.50 [140]~E(x1401,x1402)+E(f74(x1403,x1401,x1404,x1405),f74(x1403,x1402,x1404,x1405)) % 1.45/1.50 [141]~E(x1411,x1412)+E(f74(x1413,x1414,x1411,x1415),f74(x1413,x1414,x1412,x1415)) % 1.45/1.50 [142]~E(x1421,x1422)+E(f74(x1423,x1424,x1425,x1421),f74(x1423,x1424,x1425,x1422)) % 1.45/1.50 [143]~E(x1431,x1432)+E(f46(x1431),f46(x1432)) % 1.45/1.50 [144]~E(x1441,x1442)+E(f56(x1441,x1443),f56(x1442,x1443)) % 1.45/1.50 [145]~E(x1451,x1452)+E(f56(x1453,x1451),f56(x1453,x1452)) % 1.45/1.50 [146]~E(x1461,x1462)+E(f58(x1461,x1463),f58(x1462,x1463)) % 1.45/1.50 [147]~E(x1471,x1472)+E(f58(x1473,x1471),f58(x1473,x1472)) % 1.45/1.50 [148]~E(x1481,x1482)+E(f55(x1481,x1483),f55(x1482,x1483)) % 1.45/1.50 [149]~E(x1491,x1492)+E(f55(x1493,x1491),f55(x1493,x1492)) % 1.45/1.50 [150]~E(x1501,x1502)+E(f61(x1501,x1503),f61(x1502,x1503)) % 1.45/1.50 [151]~E(x1511,x1512)+E(f61(x1513,x1511),f61(x1513,x1512)) % 1.45/1.50 [152]~E(x1521,x1522)+E(f18(x1521,x1523,x1524,x1525,x1526,x1527),f18(x1522,x1523,x1524,x1525,x1526,x1527)) % 1.45/1.50 [153]~E(x1531,x1532)+E(f18(x1533,x1531,x1534,x1535,x1536,x1537),f18(x1533,x1532,x1534,x1535,x1536,x1537)) % 1.45/1.50 [154]~E(x1541,x1542)+E(f18(x1543,x1544,x1541,x1545,x1546,x1547),f18(x1543,x1544,x1542,x1545,x1546,x1547)) % 1.45/1.50 [155]~E(x1551,x1552)+E(f18(x1553,x1554,x1555,x1551,x1556,x1557),f18(x1553,x1554,x1555,x1552,x1556,x1557)) % 1.45/1.50 [156]~E(x1561,x1562)+E(f18(x1563,x1564,x1565,x1566,x1561,x1567),f18(x1563,x1564,x1565,x1566,x1562,x1567)) % 1.45/1.50 [157]~E(x1571,x1572)+E(f18(x1573,x1574,x1575,x1576,x1577,x1571),f18(x1573,x1574,x1575,x1576,x1577,x1572)) % 1.45/1.50 [158]~E(x1581,x1582)+E(f84(x1581,x1583,x1584,x1585,x1586),f84(x1582,x1583,x1584,x1585,x1586)) % 1.45/1.50 [159]~E(x1591,x1592)+E(f84(x1593,x1591,x1594,x1595,x1596),f84(x1593,x1592,x1594,x1595,x1596)) % 1.45/1.50 [160]~E(x1601,x1602)+E(f84(x1603,x1604,x1601,x1605,x1606),f84(x1603,x1604,x1602,x1605,x1606)) % 1.45/1.50 [161]~E(x1611,x1612)+E(f84(x1613,x1614,x1615,x1611,x1616),f84(x1613,x1614,x1615,x1612,x1616)) % 1.45/1.50 [162]~E(x1621,x1622)+E(f84(x1623,x1624,x1625,x1626,x1621),f84(x1623,x1624,x1625,x1626,x1622)) % 1.45/1.50 [163]~E(x1631,x1632)+E(f49(x1631,x1633,x1634,x1635),f49(x1632,x1633,x1634,x1635)) % 1.45/1.50 [164]~E(x1641,x1642)+E(f49(x1643,x1641,x1644,x1645),f49(x1643,x1642,x1644,x1645)) % 1.45/1.50 [165]~E(x1651,x1652)+E(f49(x1653,x1654,x1651,x1655),f49(x1653,x1654,x1652,x1655)) % 1.45/1.50 [166]~E(x1661,x1662)+E(f49(x1663,x1664,x1665,x1661),f49(x1663,x1664,x1665,x1662)) % 1.45/1.50 [167]~E(x1671,x1672)+E(f75(x1671,x1673,x1674,x1675,x1676),f75(x1672,x1673,x1674,x1675,x1676)) % 1.45/1.50 [168]~E(x1681,x1682)+E(f75(x1683,x1681,x1684,x1685,x1686),f75(x1683,x1682,x1684,x1685,x1686)) % 1.45/1.50 [169]~E(x1691,x1692)+E(f75(x1693,x1694,x1691,x1695,x1696),f75(x1693,x1694,x1692,x1695,x1696)) % 1.45/1.50 [170]~E(x1701,x1702)+E(f75(x1703,x1704,x1705,x1701,x1706),f75(x1703,x1704,x1705,x1702,x1706)) % 1.45/1.50 [171]~E(x1711,x1712)+E(f75(x1713,x1714,x1715,x1716,x1711),f75(x1713,x1714,x1715,x1716,x1712)) % 1.45/1.50 [172]~E(x1721,x1722)+E(f64(x1721,x1723,x1724,x1725),f64(x1722,x1723,x1724,x1725)) % 1.45/1.50 [173]~E(x1731,x1732)+E(f64(x1733,x1731,x1734,x1735),f64(x1733,x1732,x1734,x1735)) % 1.45/1.50 [174]~E(x1741,x1742)+E(f64(x1743,x1744,x1741,x1745),f64(x1743,x1744,x1742,x1745)) % 1.45/1.50 [175]~E(x1751,x1752)+E(f64(x1753,x1754,x1755,x1751),f64(x1753,x1754,x1755,x1752)) % 1.45/1.50 [176]~E(x1761,x1762)+E(f80(x1761,x1763,x1764,x1765),f80(x1762,x1763,x1764,x1765)) % 1.45/1.50 [177]~E(x1771,x1772)+E(f80(x1773,x1771,x1774,x1775),f80(x1773,x1772,x1774,x1775)) % 1.45/1.50 [178]~E(x1781,x1782)+E(f80(x1783,x1784,x1781,x1785),f80(x1783,x1784,x1782,x1785)) % 1.45/1.50 [179]~E(x1791,x1792)+E(f80(x1793,x1794,x1795,x1791),f80(x1793,x1794,x1795,x1792)) % 1.45/1.50 [180]~E(x1801,x1802)+E(f68(x1801,x1803,x1804,x1805,x1806),f68(x1802,x1803,x1804,x1805,x1806)) % 1.45/1.50 [181]~E(x1811,x1812)+E(f68(x1813,x1811,x1814,x1815,x1816),f68(x1813,x1812,x1814,x1815,x1816)) % 1.45/1.50 [182]~E(x1821,x1822)+E(f68(x1823,x1824,x1821,x1825,x1826),f68(x1823,x1824,x1822,x1825,x1826)) % 1.45/1.50 [183]~E(x1831,x1832)+E(f68(x1833,x1834,x1835,x1831,x1836),f68(x1833,x1834,x1835,x1832,x1836)) % 1.45/1.50 [184]~E(x1841,x1842)+E(f68(x1843,x1844,x1845,x1846,x1841),f68(x1843,x1844,x1845,x1846,x1842)) % 1.45/1.50 [185]~E(x1851,x1852)+E(f70(x1851,x1853),f70(x1852,x1853)) % 1.45/1.50 [186]~E(x1861,x1862)+E(f70(x1863,x1861),f70(x1863,x1862)) % 1.45/1.50 [187]~E(x1871,x1872)+E(f53(x1871,x1873),f53(x1872,x1873)) % 1.45/1.50 [188]~E(x1881,x1882)+E(f53(x1883,x1881),f53(x1883,x1882)) % 1.45/1.50 [189]~E(x1891,x1892)+E(f59(x1891,x1893,x1894,x1895),f59(x1892,x1893,x1894,x1895)) % 1.45/1.50 [190]~E(x1901,x1902)+E(f59(x1903,x1901,x1904,x1905),f59(x1903,x1902,x1904,x1905)) % 1.45/1.50 [191]~E(x1911,x1912)+E(f59(x1913,x1914,x1911,x1915),f59(x1913,x1914,x1912,x1915)) % 1.45/1.50 [192]~E(x1921,x1922)+E(f59(x1923,x1924,x1925,x1921),f59(x1923,x1924,x1925,x1922)) % 1.45/1.50 [193]~E(x1931,x1932)+E(f71(x1931,x1933),f71(x1932,x1933)) % 1.45/1.50 [194]~E(x1941,x1942)+E(f71(x1943,x1941),f71(x1943,x1942)) % 1.45/1.50 [195]~E(x1951,x1952)+E(f67(x1951,x1953,x1954,x1955,x1956),f67(x1952,x1953,x1954,x1955,x1956)) % 1.45/1.50 [196]~E(x1961,x1962)+E(f67(x1963,x1961,x1964,x1965,x1966),f67(x1963,x1962,x1964,x1965,x1966)) % 1.45/1.50 [197]~E(x1971,x1972)+E(f67(x1973,x1974,x1971,x1975,x1976),f67(x1973,x1974,x1972,x1975,x1976)) % 1.45/1.50 [198]~E(x1981,x1982)+E(f67(x1983,x1984,x1985,x1981,x1986),f67(x1983,x1984,x1985,x1982,x1986)) % 1.45/1.50 [199]~E(x1991,x1992)+E(f67(x1993,x1994,x1995,x1996,x1991),f67(x1993,x1994,x1995,x1996,x1992)) % 1.45/1.50 [200]~E(x2001,x2002)+E(f60(x2001),f60(x2002)) % 1.45/1.50 [201]~E(x2011,x2012)+E(f73(x2011,x2013,x2014),f73(x2012,x2013,x2014)) % 1.45/1.50 [202]~E(x2021,x2022)+E(f73(x2023,x2021,x2024),f73(x2023,x2022,x2024)) % 1.45/1.50 [203]~E(x2031,x2032)+E(f73(x2033,x2034,x2031),f73(x2033,x2034,x2032)) % 1.45/1.50 [204]~E(x2041,x2042)+E(f66(x2041,x2043),f66(x2042,x2043)) % 1.45/1.50 [205]~E(x2051,x2052)+E(f66(x2053,x2051),f66(x2053,x2052)) % 1.45/1.50 [206]~E(x2061,x2062)+E(f82(x2061),f82(x2062)) % 1.45/1.50 [207]~E(x2071,x2072)+E(f33(x2071,x2073,x2074,x2075),f33(x2072,x2073,x2074,x2075)) % 1.45/1.50 [208]~E(x2081,x2082)+E(f33(x2083,x2081,x2084,x2085),f33(x2083,x2082,x2084,x2085)) % 1.45/1.50 [209]~E(x2091,x2092)+E(f33(x2093,x2094,x2091,x2095),f33(x2093,x2094,x2092,x2095)) % 1.45/1.50 [210]~E(x2101,x2102)+E(f33(x2103,x2104,x2105,x2101),f33(x2103,x2104,x2105,x2102)) % 1.45/1.50 [211]~P1(x2111)+P1(x2112)+~E(x2111,x2112) % 1.45/1.50 [212]~P2(x2121)+P2(x2122)+~E(x2121,x2122) % 1.45/1.50 [213]~P4(x2131)+P4(x2132)+~E(x2131,x2132) % 1.45/1.50 [214]~P5(x2141)+P5(x2142)+~E(x2141,x2142) % 1.45/1.50 [215]~P35(x2151)+P35(x2152)+~E(x2151,x2152) % 1.45/1.50 [216]~P6(x2161)+P6(x2162)+~E(x2161,x2162) % 1.45/1.50 [217]~P27(x2171)+P27(x2172)+~E(x2171,x2172) % 1.45/1.50 [218]P12(x2182,x2183)+~E(x2181,x2182)+~P12(x2181,x2183) % 1.45/1.50 [219]P12(x2193,x2192)+~E(x2191,x2192)+~P12(x2193,x2191) % 1.45/1.50 [220]~P28(x2201)+P28(x2202)+~E(x2201,x2202) % 1.45/1.50 [221]~P23(x2211)+P23(x2212)+~E(x2211,x2212) % 1.45/1.50 [222]~P29(x2221)+P29(x2222)+~E(x2221,x2222) % 1.45/1.50 [223]~P7(x2231)+P7(x2232)+~E(x2231,x2232) % 1.45/1.50 [224]~P8(x2241)+P8(x2242)+~E(x2241,x2242) % 1.45/1.50 [225]~P9(x2251)+P9(x2252)+~E(x2251,x2252) % 1.45/1.50 [226]~P10(x2261)+P10(x2262)+~E(x2261,x2262) % 1.45/1.50 [227]~P18(x2271)+P18(x2272)+~E(x2271,x2272) % 1.45/1.50 [228]~P22(x2281)+P22(x2282)+~E(x2281,x2282) % 1.45/1.50 [229]~P26(x2291)+P26(x2292)+~E(x2291,x2292) % 1.45/1.50 [230]~P11(x2301)+P11(x2302)+~E(x2301,x2302) % 1.45/1.50 [231]P13(x2312,x2313,x2314,x2315)+~E(x2311,x2312)+~P13(x2311,x2313,x2314,x2315) % 1.45/1.50 [232]P13(x2323,x2322,x2324,x2325)+~E(x2321,x2322)+~P13(x2323,x2321,x2324,x2325) % 1.45/1.50 [233]P13(x2333,x2334,x2332,x2335)+~E(x2331,x2332)+~P13(x2333,x2334,x2331,x2335) % 1.45/1.50 [234]P13(x2343,x2344,x2345,x2342)+~E(x2341,x2342)+~P13(x2343,x2344,x2345,x2341) % 1.45/1.50 [235]~P24(x2351)+P24(x2352)+~E(x2351,x2352) % 1.45/1.50 [236]~P32(x2361)+P32(x2362)+~E(x2361,x2362) % 1.45/1.50 [237]~P19(x2371)+P19(x2372)+~E(x2371,x2372) % 1.45/1.50 [238]~P20(x2381)+P20(x2382)+~E(x2381,x2382) % 1.45/1.50 [239]~P25(x2391)+P25(x2392)+~E(x2391,x2392) % 1.45/1.50 [240]~P30(x2401)+P30(x2402)+~E(x2401,x2402) % 1.45/1.50 [241]~P34(x2411)+P34(x2412)+~E(x2411,x2412) % 1.45/1.50 [242]P17(x2422,x2423)+~E(x2421,x2422)+~P17(x2421,x2423) % 1.45/1.50 [243]P17(x2433,x2432)+~E(x2431,x2432)+~P17(x2433,x2431) % 1.45/1.50 [244]P3(x2442,x2443)+~E(x2441,x2442)+~P3(x2441,x2443) % 1.45/1.50 [245]P3(x2453,x2452)+~E(x2451,x2452)+~P3(x2453,x2451) % 1.45/1.50 [246]~P21(x2461)+P21(x2462)+~E(x2461,x2462) % 1.45/1.50 [247]P14(x2472,x2473,x2474,x2475,x2476)+~E(x2471,x2472)+~P14(x2471,x2473,x2474,x2475,x2476) % 1.45/1.50 [248]P14(x2483,x2482,x2484,x2485,x2486)+~E(x2481,x2482)+~P14(x2483,x2481,x2484,x2485,x2486) % 1.45/1.50 [249]P14(x2493,x2494,x2492,x2495,x2496)+~E(x2491,x2492)+~P14(x2493,x2494,x2491,x2495,x2496) % 1.45/1.50 [250]P14(x2503,x2504,x2505,x2502,x2506)+~E(x2501,x2502)+~P14(x2503,x2504,x2505,x2501,x2506) % 1.45/1.50 [251]P14(x2513,x2514,x2515,x2516,x2512)+~E(x2511,x2512)+~P14(x2513,x2514,x2515,x2516,x2511) % 1.45/1.50 [252]~P31(x2521)+P31(x2522)+~E(x2521,x2522) % 1.45/1.50 [253]~P33(x2531)+P33(x2532)+~E(x2531,x2532) % 1.45/1.50 [254]P16(x2542,x2543,x2544,x2545,x2546,x2547)+~E(x2541,x2542)+~P16(x2541,x2543,x2544,x2545,x2546,x2547) % 1.45/1.50 [255]P16(x2553,x2552,x2554,x2555,x2556,x2557)+~E(x2551,x2552)+~P16(x2553,x2551,x2554,x2555,x2556,x2557) % 1.45/1.50 [256]P16(x2563,x2564,x2562,x2565,x2566,x2567)+~E(x2561,x2562)+~P16(x2563,x2564,x2561,x2565,x2566,x2567) % 1.45/1.50 [257]P16(x2573,x2574,x2575,x2572,x2576,x2577)+~E(x2571,x2572)+~P16(x2573,x2574,x2575,x2571,x2576,x2577) % 1.45/1.50 [258]P16(x2583,x2584,x2585,x2586,x2582,x2587)+~E(x2581,x2582)+~P16(x2583,x2584,x2585,x2586,x2581,x2587) % 1.45/1.50 [259]P16(x2593,x2594,x2595,x2596,x2597,x2592)+~E(x2591,x2592)+~P16(x2593,x2594,x2595,x2596,x2597,x2591) % 1.45/1.50 [260]P15(x2602,x2603,x2604,x2605,x2606,x2607)+~E(x2601,x2602)+~P15(x2601,x2603,x2604,x2605,x2606,x2607) % 1.45/1.50 [261]P15(x2613,x2612,x2614,x2615,x2616,x2617)+~E(x2611,x2612)+~P15(x2613,x2611,x2614,x2615,x2616,x2617) % 1.45/1.50 [262]P15(x2623,x2624,x2622,x2625,x2626,x2627)+~E(x2621,x2622)+~P15(x2623,x2624,x2621,x2625,x2626,x2627) % 1.45/1.50 [263]P15(x2633,x2634,x2635,x2632,x2636,x2637)+~E(x2631,x2632)+~P15(x2633,x2634,x2635,x2631,x2636,x2637) % 1.45/1.50 [264]P15(x2643,x2644,x2645,x2646,x2642,x2647)+~E(x2641,x2642)+~P15(x2643,x2644,x2645,x2646,x2641,x2647) % 1.45/1.50 [265]P15(x2653,x2654,x2655,x2656,x2657,x2652)+~E(x2651,x2652)+~P15(x2653,x2654,x2655,x2656,x2657,x2651) % 1.45/1.50 % 1.45/1.50 %------------------------------------------- % 1.45/1.50 cnf(1070,plain, % 1.45/1.50 (P35(f27(f27(f34(x10702),x10701),f27(a38,x10701)))), % 1.45/1.50 inference(equality_inference,[],[484])). % 1.45/1.50 cnf(1079,plain, % 1.45/1.50 (P35(f27(f35(x10792,x10791,x10793),x10791))), % 1.45/1.50 inference(equality_inference,[],[560])). % 1.45/1.50 cnf(1087,plain, % 1.45/1.50 (~P35(f27(f27(f29(f94(x10872,a2)),x10871),x10871))), % 1.45/1.50 inference(equality_inference,[],[675])). % 1.45/1.50 cnf(1098,plain, % 1.45/1.50 (~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x10982),x10981)),f27(f27(a12,x10983),x10981)))), % 1.45/1.50 inference(equality_inference,[],[834])). % 1.45/1.50 cnf(1101,plain, % 1.45/1.50 (E(f36(x11011,x11012,x11013,f36(x11012,x11011,f22(x11011,x11012,x11014,x11013),x11015)),x11015)+~P35(f27(f28(f94(x11012,a2),x11015),f36(x11011,x11012,x11013,x11014)))), % 1.45/1.50 inference(equality_inference,[],[862])). % 1.45/1.50 cnf(1130,plain, % 1.45/1.50 (P35(f27(f28(f94(x11301,a2),x11302),f35(x11301,x11303,x11302)))), % 1.45/1.50 inference(rename_variables,[],[340])). % 1.45/1.50 cnf(1137,plain, % 1.45/1.50 (~P35(f27(f28(a91,f27(a21,x11371)),x11371))), % 1.45/1.50 inference(rename_variables,[],[393])). % 1.45/1.50 cnf(1140,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),x11401),f3(a91)))), % 1.45/1.50 inference(rename_variables,[],[392])). % 1.45/1.50 cnf(1143,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),f27(f27(f19(a91),x11431),x11432)),x11432))), % 1.45/1.50 inference(rename_variables,[],[394])). % 1.45/1.50 cnf(1146,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),f27(f27(f19(a91),x11461),x11462)),x11462))), % 1.45/1.50 inference(rename_variables,[],[394])). % 1.45/1.50 cnf(1157,plain, % 1.45/1.50 (P35(f27(f27(f29(a91),x11571),f27(a21,x11571)))), % 1.45/1.50 inference(rename_variables,[],[313])). % 1.45/1.50 cnf(1164,plain, % 1.45/1.50 (~P35(f27(f28(a91,f27(a21,x11641)),x11641))), % 1.45/1.50 inference(rename_variables,[],[393])). % 1.45/1.50 cnf(1169,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),f27(f27(f19(a91),x11691),x11692)),x11692))), % 1.45/1.50 inference(rename_variables,[],[394])). % 1.45/1.50 cnf(1178,plain, % 1.45/1.50 (P35(f27(f28(a91,x11781),f27(f27(f19(a91),x11782),x11781)))), % 1.45/1.50 inference(rename_variables,[],[327])). % 1.45/1.50 cnf(1181,plain, % 1.45/1.50 (P35(f27(f28(a91,x11811),f27(f27(f19(a91),x11812),x11811)))), % 1.45/1.50 inference(rename_variables,[],[327])). % 1.45/1.50 cnf(1186,plain, % 1.45/1.50 (~P35(f27(f28(a91,f27(a21,x11861)),x11861))), % 1.45/1.50 inference(rename_variables,[],[393])). % 1.45/1.50 cnf(1189,plain, % 1.45/1.50 (~P35(f27(f28(a91,f27(a21,x11891)),x11891))), % 1.45/1.50 inference(rename_variables,[],[393])). % 1.45/1.50 cnf(1197,plain, % 1.45/1.50 (P35(f27(f27(f29(a91),x11971),f27(a21,f27(f27(f19(a91),x11972),x11971))))), % 1.45/1.50 inference(rename_variables,[],[345])). % 1.45/1.50 cnf(1200,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),f27(f27(f19(a91),x12001),x12002)),x12002))), % 1.45/1.50 inference(rename_variables,[],[394])). % 1.45/1.50 cnf(1203,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),f27(f27(f19(a91),x12031),x12032)),x12032))), % 1.45/1.50 inference(rename_variables,[],[394])). % 1.45/1.50 cnf(1212,plain, % 1.45/1.50 (P35(f27(f28(a91,x12121),f27(f27(f19(a91),x12122),x12121)))), % 1.45/1.50 inference(rename_variables,[],[327])). % 1.45/1.50 cnf(1230,plain, % 1.45/1.50 (~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x12301),x12302)),f27(f27(a12,x12303),x12302)))), % 1.45/1.50 inference(rename_variables,[],[1098])). % 1.45/1.50 cnf(1239,plain, % 1.45/1.50 (P35(f27(f27(f29(a91),x12391),f27(a21,x12391)))), % 1.45/1.50 inference(rename_variables,[],[313])). % 1.45/1.50 cnf(1242,plain, % 1.45/1.50 (P35(f27(f27(f29(a91),x12421),f27(a21,x12421)))), % 1.45/1.50 inference(rename_variables,[],[313])). % 1.45/1.50 cnf(1249,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),x12491),x12491))), % 1.45/1.50 inference(rename_variables,[],[389])). % 1.45/1.50 cnf(1254,plain, % 1.45/1.50 (P35(f27(f28(f94(x12541,a2),x12542),x12542))), % 1.45/1.50 inference(rename_variables,[],[318])). % 1.45/1.50 cnf(1257,plain, % 1.45/1.50 (P35(f27(f27(f34(x12571),x12572),f30(f94(x12571,a2))))), % 1.45/1.50 inference(rename_variables,[],[321])). % 1.45/1.50 cnf(1262,plain, % 1.45/1.50 (P35(f27(f27(f34(x12621),x12622),f27(a38,x12622)))), % 1.45/1.50 inference(rename_variables,[],[1070])). % 1.45/1.50 cnf(1265,plain, % 1.45/1.50 (P35(f27(f28(f94(x12651,a2),x12652),f35(x12651,x12653,x12652)))), % 1.45/1.50 inference(rename_variables,[],[340])). % 1.45/1.50 cnf(1270,plain, % 1.45/1.50 (P35(f27(f28(f94(x12701,a2),x12702),x12702))), % 1.45/1.50 inference(rename_variables,[],[318])). % 1.45/1.50 cnf(1277,plain, % 1.45/1.50 (P35(f27(f28(f94(x12771,a2),x12772),x12772))), % 1.45/1.50 inference(rename_variables,[],[318])). % 1.45/1.50 cnf(1300,plain, % 1.45/1.50 (P35(f27(f28(f94(x13001,a2),x13002),f35(x13001,x13003,x13002)))), % 1.45/1.50 inference(rename_variables,[],[340])). % 1.45/1.50 cnf(1305,plain, % 1.45/1.50 (P13(x13051,x13051,f5(x13051),x13052)), % 1.45/1.50 inference(rename_variables,[],[325])). % 1.45/1.50 cnf(1308,plain, % 1.45/1.50 (~P35(f27(f27(f34(f96(a90,a90)),f27(f27(f32(a90,a90),x13081),x13082)),f27(f27(a12,x13083),x13082)))), % 1.45/1.50 inference(rename_variables,[],[1098])). % 1.45/1.50 cnf(1330,plain, % 1.45/1.50 (~P35(f27(f27(f29(a91),f27(f27(f19(a91),x13301),x13302)),x13301))), % 1.45/1.50 inference(rename_variables,[],[395])). % 1.45/1.50 cnf(1352,plain, % 1.45/1.50 (P35(f27(f28(f94(x13521,a2),x13522),f35(x13521,x13523,x13522)))), % 1.45/1.50 inference(rename_variables,[],[340])). % 1.45/1.50 cnf(1361,plain, % 1.45/1.50 (P35(f27(f27(f34(x13611),x13612),f27(a38,x13612)))), % 1.45/1.50 inference(rename_variables,[],[1070])). % 1.45/1.50 cnf(1372,plain, % 1.45/1.50 (P35(f27(f28(f94(x13721,a2),x13722),f30(f94(x13721,a2))))), % 1.45/1.50 inference(rename_variables,[],[330])). % 1.45/1.50 cnf(1377,plain, % 1.45/1.50 (P35(f27(f28(f94(x13771,a2),x13772),f35(x13771,x13773,x13772)))), % 1.45/1.50 inference(rename_variables,[],[340])). % 1.45/1.50 cnf(1378,plain, % 1.45/1.50 (P35(f27(f28(f94(x13781,a2),x13782),f30(f94(x13781,a2))))), % 1.45/1.50 inference(rename_variables,[],[330])). % 1.45/1.50 cnf(1382,plain, % 1.45/1.50 (P35(f27(f28(f94(x13821,a2),x13822),f35(x13821,x13823,x13822)))), % 1.45/1.50 inference(rename_variables,[],[340])). % 1.45/1.50 cnf(1388,plain, % 1.45/1.50 (P35(f27(f28(f94(x13881,a2),x13882),x13882))), % 1.45/1.50 inference(rename_variables,[],[318])). % 1.45/1.50 cnf(1391,plain, % 1.45/1.50 (P35(f27(f27(f34(x13911),x13912),f27(a38,x13912)))), % 1.45/1.50 inference(rename_variables,[],[1070])). % 1.45/1.50 cnf(1397,plain, % 1.45/1.50 (E(f26(a91,x13971),x13971)), % 1.45/1.50 inference(rename_variables,[],[294])). % 1.45/1.50 cnf(1402,plain, % 1.45/1.50 ($false), % 1.45/1.51 inference(scs_inference,[],[398,1079,1087,1098,1230,1308,1070,1262,1361,1391,301,337,340,1130,1265,1300,1352,1377,1382,305,313,1157,1239,1242,314,392,1140,318,1254,1270,1277,1388,389,1249,321,1257,330,1372,1378,393,1137,1164,1186,1189,363,327,1178,1181,1212,328,336,335,334,365,394,1143,1146,1169,1200,1203,395,1330,345,1197,348,362,369,325,1305,294,1397,381,387,270,271,272,275,282,284,326,367,304,1048,483,519,536,795,889,403,447,460,466,469,475,480,481,482,509,512,541,546,566,570,585,591,604,617,633,634,639,641,643,644,645,663,665,674,681,716,739,740,752,754,784,785,792,797,798,807,829,833,838,846,847,850,857,873,874,879,883,904,927,954,972,976,1101,2,6,7,411,426,459,470,832,840,875,630,694,868,871,872,913,215,437,439,487,507,508,518,527,562,564,565,573,579,592,595,598,599,608,612,623,624,625,647,686,690,696,728,787,791,802,811,824,844,848]), % 1.45/1.51 ['proof']). % 1.45/1.51 % SZS output end Proof % 1.45/1.51 % Total time :0.430000s %------------------------------------------------------------------------------