%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SCT166+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 : n024.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 14:11:54 EDT 2024 % Result : Theorem 1.40s 1.55s % Output : CNFRefutation 1.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SCT166+1 : TPTP v8.2.0. Released v5.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Jun 22 09:39:09 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 1.40/1.50 %------------------------------------------- % 1.40/1.50 % File :CSE---1.7 % 1.40/1.50 % Problem :theBenchmark % 1.40/1.50 % Transform :cnf % 1.40/1.50 % Format :tptp:raw % 1.40/1.50 % Command :java -jar mcs_scs.jar %d %s % 1.40/1.50 % 1.40/1.50 % Result :Theorem 0.470000s % 1.40/1.50 % Output :CNFRefutation 0.470000s % 1.40/1.50 %------------------------------------------- % 1.40/1.50 %------------------------------------------------------------------------------ % 1.40/1.50 % File : SCT166+1 : TPTP v8.2.0. Released v5.2.0. % 1.40/1.50 % Domain : Social Choice Theory % 1.40/1.50 % Problem : Arrow's Impossibility Theorem 433663, 500 axioms selected % 1.40/1.50 % Version : Especial. % 1.40/1.50 % English : % 1.40/1.50 % 1.40/1.50 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.40/1.50 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 1.40/1.50 % Source : [Bla11] % 1.40/1.50 % Names : arrow_433663.500.p [Bla11] % 1.40/1.50 % 1.40/1.50 % Status : ContradictoryAxioms % 1.40/1.50 % Rating : 0.61 v7.5.0, 0.59 v7.4.0, 0.67 v7.3.0, 0.69 v7.1.0, 0.65 v7.0.0, 0.60 v6.4.0, 0.58 v6.3.0, 0.62 v6.2.0, 0.68 v6.1.0, 0.70 v6.0.0, 0.65 v5.5.0, 0.78 v5.4.0, 0.71 v5.3.0, 0.74 v5.2.0 % 1.40/1.50 % Syntax : Number of formulae : 533 ( 121 unt; 0 def) % 1.40/1.50 % Number of atoms : 1412 ( 332 equ) % 1.40/1.50 % Maximal formula atoms : 12 ( 2 avg) % 1.40/1.50 % Number of connectives : 1036 ( 157 ~; 26 |; 54 &) % 1.40/1.50 % ( 127 <=>; 672 =>; 0 <=; 0 <~>) % 1.40/1.50 % Maximal formula depth : 16 ( 6 avg) % 1.40/1.50 % Maximal term depth : 16 ( 2 avg) % 1.40/1.50 % Number of predicates : 35 ( 34 usr; 0 prp; 1-6 aty) % 1.40/1.50 % Number of functors : 61 ( 61 usr; 24 con; 0-6 aty) % 1.40/1.50 % Number of variables : 1535 (1523 !; 12 ?) % 1.40/1.50 % SPC : FOF_CAX_RFO_SEQ % 1.40/1.50 % 1.40/1.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 1.40/1.50 % 2011-03-01 11:30:37 % 1.40/1.50 % : Renamed from SWW168+1 % 1.40/1.50 %------------------------------------------------------------------------------ % 1.40/1.50 %----Relevant facts (491) % 1.40/1.50 fof(fact_ext,axiom, % 1.40/1.50 ! [V_g_2,V_f_2] : % 1.40/1.50 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 1.40/1.50 => V_f_2 = V_g_2 ) ). % 1.40/1.50 % 1.40/1.50 fof(fact__096a_A_126_061_Ab_096,axiom, % 1.40/1.50 v_a____ != v_b____ ). % 1.40/1.50 % 1.40/1.50 fof(fact__096c_A_126_061_Ad_096,axiom, % 1.40/1.50 v_c____ != v_d____ ). % 1.40/1.50 % 1.40/1.50 fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom, % 1.40/1.50 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____)) ). % 1.40/1.50 % 1.40/1.50 fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom, % 1.40/1.50 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____)) ). % 1.40/1.50 % 1.40/1.50 fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom, % 1.40/1.50 ~ 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____)) ). % 1.40/1.50 % 1.40/1.50 fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom, % 1.40/1.50 ~ 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____)) ). % 1.40/1.50 % 1.40/1.50 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, % 1.40/1.50 ! [B_i] : % 1.40/1.50 ( 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))) % 1.40/1.50 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.50 => 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____))) ) % 1.40/1.50 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.50 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.40/1.50 => 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____))) ) % 1.40/1.50 & ( hAPP(v_h____,B_i) != v_n____ % 1.40/1.50 => 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____))) ) ) ) ) ) ). % 1.40/1.50 % 1.40/1.50 fof(fact_in__mkbot,axiom, % 1.40/1.50 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.40/1.50 ( 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))) % 1.40/1.50 <=> ( V_y_2 != V_z_2 % 1.40/1.50 & ( V_x_2 = V_z_2 % 1.40/1.50 => V_x_2 != V_y_2 ) % 1.40/1.50 & ( V_x_2 != V_z_2 % 1.40/1.50 => 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)) ) ) ) ). % 1.40/1.50 % 1.40/1.50 fof(fact_in__mktop,axiom, % 1.40/1.51 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.40/1.51 ( 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))) % 1.40/1.51 <=> ( V_x_2 != V_z_2 % 1.40/1.51 & ( V_y_2 = V_z_2 % 1.40/1.51 => V_x_2 != V_y_2 ) % 1.40/1.51 & ( V_y_2 != V_z_2 % 1.40/1.51 => 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)) ) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom, % 1.40/1.51 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____)))) ). % 1.40/1.51 % 1.40/1.51 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, % 1.40/1.51 ! [B_i] : % 1.40/1.51 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.51 => 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____))) ) % 1.40/1.51 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.51 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.40/1.51 => 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____))) ) % 1.40/1.51 & ( hAPP(v_h____,B_i) != v_n____ % 1.40/1.51 => 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____))) ) ) ) ) % 1.40/1.51 <=> ( ( 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)))) % 1.40/1.51 => 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____)) ) % 1.40/1.51 & ( ~ 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)))) % 1.40/1.51 => 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____)) ) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact__096P_A_058_AProf_096,axiom, % 1.40/1.51 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)) ). % 1.40/1.51 % 1.40/1.51 fof(fact_equalityCE,axiom, % 1.40/1.51 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 1.40/1.51 ( V_A_2 = V_B_2 % 1.40/1.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.40/1.51 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 1.40/1.51 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.40/1.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_PW,axiom, % 1.40/1.51 ( 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____))) % 1.40/1.51 <=> 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____)))))) ) ). % 1.40/1.51 % 1.40/1.51 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, % 1.40/1.51 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____)))))) ). % 1.40/1.51 % 1.40/1.51 fof(fact_in__rel__def,axiom, % 1.40/1.51 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 1.40/1.51 ( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) % 1.40/1.51 <=> 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)) ) ). % 1.40/1.51 % 1.40/1.51 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, % 1.40/1.51 ( 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____)))))) % 1.40/1.51 <=> 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____)))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_same__fstI,axiom, % 1.40/1.51 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] : % 1.40/1.51 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.40/1.51 => ( 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))) % 1.40/1.51 => 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))) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_injh,axiom, % 1.40/1.51 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))) ). % 1.40/1.51 % 1.40/1.51 fof(fact_in__measure,axiom, % 1.40/1.51 ! [V_f_2,V_y_2,V_x_2,T_a] : % 1.40/1.51 ( 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))) % 1.40/1.51 <=> 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))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_n_I2_J,axiom, % 1.40/1.51 ! [B_m] : % 1.40/1.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),v_n____)) % 1.40/1.51 => 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____)))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_u,axiom, % 1.40/1.51 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ). % 1.40/1.51 % 1.40/1.51 fof(fact_assms_I3_J,axiom, % 1.40/1.51 c_Arrow__Order__Mirabelle_OIIA(v_F) ). % 1.40/1.51 % 1.40/1.51 fof(fact__096Lba_A_058_ALin_096,axiom, % 1.40/1.51 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)) ). % 1.40/1.51 % 1.40/1.51 fof(fact__096Lab_A_058_ALin_096,axiom, % 1.40/1.51 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)) ). % 1.40/1.51 % 1.40/1.51 fof(fact_UNIV__I,axiom, % 1.40/1.51 ! [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)))) ). % 1.40/1.51 % 1.40/1.51 fof(fact_PiProf,axiom, % 1.40/1.51 ! [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)) ). % 1.40/1.51 % 1.40/1.51 fof(fact_n_I3_J,axiom, % 1.40/1.51 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____)))) ). % 1.40/1.51 % 1.40/1.51 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, % 1.40/1.51 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)) ). % 1.40/1.51 % 1.40/1.51 fof(fact_n_I1_J,axiom, % 1.40/1.51 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))))) ). % 1.40/1.51 % 1.40/1.51 fof(fact_termination__basic__simps_I3_J,axiom, % 1.40/1.51 ! [V_z,V_y,V_x] : % 1.40/1.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) % 1.40/1.51 => 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))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_termination__basic__simps_I4_J,axiom, % 1.40/1.51 ! [V_y,V_z,V_x] : % 1.40/1.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) % 1.40/1.51 => 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))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_termination__basic__simps_I2_J,axiom, % 1.40/1.51 ! [V_y,V_z,V_x] : % 1.40/1.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 1.40/1.51 => 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))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_termination__basic__simps_I1_J,axiom, % 1.40/1.51 ! [V_z,V_y,V_x] : % 1.40/1.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.40/1.51 => 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))) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_termination__basic__simps_I5_J,axiom, % 1.40/1.51 ! [V_y,V_x] : % 1.40/1.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.40/1.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_eq__mem__trans,axiom, % 1.40/1.51 ! [V_A_2,T_a,V_ba_2,V_aa_2] : % 1.40/1.51 ( V_aa_2 = V_ba_2 % 1.40/1.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) % 1.40/1.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_eqelem__imp__iff,axiom, % 1.40/1.51 ! [V_A_2,T_a,V_y_2,V_x_2] : % 1.40/1.51 ( V_x_2 = V_y_2 % 1.40/1.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.51 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_eqset__imp__iff,axiom, % 1.40/1.51 ! [V_x_2,T_a,V_B_2,V_A_2] : % 1.40/1.51 ( V_A_2 = V_B_2 % 1.40/1.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.51 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_mem__def,axiom, % 1.40/1.51 ! [V_A_2,V_x_2,T_a] : % 1.40/1.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.51 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact__C3_C,axiom, % 1.40/1.51 ! [V_P_H_2,V_Pa_2,V_ba_2,V_aa_2] : % 1.40/1.51 ( V_aa_2 != V_ba_2 % 1.40/1.51 => ( 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)) % 1.40/1.51 => ( 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)) % 1.40/1.51 => ( ! [B_i] : % 1.40/1.51 ( 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))) % 1.40/1.51 <=> 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))) ) % 1.40/1.51 => ( 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))) % 1.40/1.51 <=> 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))) ) ) ) ) ) ). % 1.40/1.51 % 1.40/1.51 fof(fact_pairwise__neutrality,axiom, % 1.40/1.51 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.40/1.51 ( V_aa_2 != V_ba_2 % 1.40/1.51 => ( V_a_H_2 != V_b_H_2 % 1.40/1.51 => ( 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)) % 1.40/1.51 => ( 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)) % 1.40/1.51 => ( ! [B_i] : % 1.40/1.51 ( 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))) % 1.40/1.51 <=> 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))) ) % 1.40/1.51 => ( 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))) % 1.40/1.51 <=> 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))) ) ) ) ) ) ) ). % 1.40/1.51 % 1.40/1.52 fof(fact__C4_C,axiom, % 1.40/1.52 ! [V_P_H_2,V_Pa_2,V_ca_2,V_ba_2,V_aa_2] : % 1.40/1.52 ( V_aa_2 != V_ba_2 % 1.40/1.52 => ( V_ba_2 != V_ca_2 % 1.40/1.52 => ( V_aa_2 != V_ca_2 % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( ! [B_i] : % 1.40/1.52 ( 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))) % 1.40/1.52 <=> 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))) ) % 1.40/1.52 => ( 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))) % 1.40/1.52 <=> 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))) ) ) ) ) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact__C1_C,axiom, % 1.40/1.52 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.40/1.52 ( V_aa_2 != V_ba_2 % 1.40/1.52 => ( V_a_H_2 != V_b_H_2 % 1.40/1.52 => ( V_aa_2 != V_b_H_2 % 1.40/1.52 => ( V_ba_2 != V_a_H_2 % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( ! [B_i] : % 1.40/1.52 ( 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))) % 1.40/1.52 <=> 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))) ) % 1.40/1.52 => ( 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))) % 1.40/1.52 => 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))) ) ) ) ) ) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact__C2_C,axiom, % 1.40/1.52 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.40/1.52 ( V_aa_2 != V_ba_2 % 1.40/1.52 => ( V_a_H_2 != V_b_H_2 % 1.40/1.52 => ( V_aa_2 != V_b_H_2 % 1.40/1.52 => ( V_ba_2 != V_a_H_2 % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( ! [B_i] : % 1.40/1.52 ( 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))) % 1.40/1.52 <=> 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))) ) % 1.40/1.52 => ( 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))) % 1.40/1.52 <=> 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))) ) ) ) ) ) ) ) ) ). % 1.40/1.52 % 1.40/1.52 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, % 1.40/1.52 ? [B_n] : % 1.40/1.52 ( 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))))) % 1.40/1.52 & ! [B_m] : % 1.40/1.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 1.40/1.52 => 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____)))) ) % 1.40/1.52 & 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____)))) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_in__lex__prod,axiom, % 1.40/1.52 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] : % 1.40/1.52 ( 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))) % 1.40/1.52 <=> ( 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)) % 1.40/1.52 | ( V_aa_2 = V_a_H_2 % 1.40/1.52 & 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)) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inv__f__f,axiom, % 1.40/1.52 ! [V_x_2,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.52 => 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 ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inv__f__eq,axiom, % 1.40/1.52 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.52 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.40/1.52 => 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 ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inv__into__f__f,axiom, % 1.40/1.52 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.52 => 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 ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inv__into__f__eq,axiom, % 1.40/1.52 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.52 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.40/1.52 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_assms_I1_J,axiom, % 1.40/1.52 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)))) ). % 1.40/1.52 % 1.40/1.52 fof(fact_above__Lin,axiom, % 1.40/1.52 ! [V_L_2,V_y_2,V_x_2] : % 1.40/1.52 ( V_x_2 != V_y_2 % 1.40/1.52 => ( 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)) % 1.40/1.52 => 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)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_mkbot__Lin,axiom, % 1.40/1.52 ! [V_x_2,V_L_2] : % 1.40/1.52 ( 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)) % 1.40/1.52 => 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)) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_mktop__Lin,axiom, % 1.40/1.52 ! [V_x_2,V_L_2] : % 1.40/1.52 ( 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)) % 1.40/1.52 => 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)) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_notin__Lin__iff,axiom, % 1.40/1.52 ! [V_y_2,V_x_2,V_L_2] : % 1.40/1.52 ( 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)) % 1.40/1.52 => ( V_x_2 != V_y_2 % 1.40/1.52 => ( ~ 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)) % 1.40/1.52 <=> 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)) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_Lin__irrefl,axiom, % 1.40/1.52 ! [V_ba_2,V_aa_2,V_L_2] : % 1.40/1.52 ( 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)) % 1.40/1.52 => ( 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)) % 1.40/1.52 => ~ 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)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_const__Lin__Prof,axiom, % 1.40/1.52 ! [V_L_2] : % 1.40/1.52 ( 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)) % 1.40/1.52 => 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)) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_in__above,axiom, % 1.40/1.52 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.40/1.52 ( V_aa_2 != V_ba_2 % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( 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))) % 1.40/1.52 <=> ( V_x_2 != V_y_2 % 1.40/1.52 & ( V_x_2 = V_ba_2 % 1.40/1.52 => 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)) ) % 1.40/1.52 & ( V_x_2 != V_ba_2 % 1.40/1.52 => ( ( V_y_2 = V_ba_2 % 1.40/1.52 => ( V_x_2 = V_aa_2 % 1.40/1.52 | 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)) ) ) % 1.40/1.52 & ( V_y_2 != V_ba_2 % 1.40/1.52 => 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)) ) ) ) ) ) ) ) ). % 1.40/1.52 % 1.40/1.52 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, % 1.40/1.52 ~ ! [B_Lab] : % 1.40/1.52 ( 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)) % 1.40/1.52 => ~ 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)) ) ). % 1.40/1.52 % 1.40/1.52 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, % 1.40/1.52 ~ ! [B_Lba] : % 1.40/1.52 ( 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)) % 1.40/1.52 => ~ 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)) ) ). % 1.40/1.52 % 1.40/1.52 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, % 1.40/1.52 ~ ! [B_n] : % 1.40/1.52 ( 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))))) % 1.40/1.52 => ( ! [B_m] : % 1.40/1.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 1.40/1.52 => 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____)))) ) % 1.40/1.52 => ~ 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____)))) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_in__below,axiom, % 1.40/1.52 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.40/1.52 ( V_aa_2 != V_ba_2 % 1.40/1.52 => ( 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)) % 1.40/1.52 => ( 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))) % 1.40/1.52 <=> ( V_x_2 != V_y_2 % 1.40/1.52 & ( V_y_2 = V_aa_2 % 1.40/1.52 => 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)) ) % 1.40/1.52 & ( V_y_2 != V_aa_2 % 1.40/1.52 => ( ( V_x_2 = V_aa_2 % 1.40/1.52 => ( V_y_2 = V_ba_2 % 1.40/1.52 | 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)) ) ) % 1.40/1.52 & ( V_x_2 != V_aa_2 % 1.40/1.52 => 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)) ) ) ) ) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_less__add__one,axiom, % 1.40/1.52 ! [V_a,T_a] : % 1.40/1.52 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.52 => 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)))) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__le__less__mono,axiom, % 1.40/1.52 ! [V_d,V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.40/1.52 => 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))) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__less__le__mono,axiom, % 1.40/1.52 ! [V_d,V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.40/1.52 => 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))) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_top1I,axiom, % 1.40/1.52 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inj__fun,axiom, % 1.40/1.52 ! [T_c,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.52 => 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))) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_subsetD,axiom, % 1.40/1.52 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 1.40/1.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_subset__inj__on,axiom, % 1.40/1.52 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.52 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_pred__subset__eq2,axiom, % 1.40/1.52 ! [V_S_2,V_R_2,T_b,T_a] : % 1.40/1.52 ( 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))) % 1.40/1.52 <=> 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)) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_pred__subset__eq,axiom, % 1.40/1.52 ! [V_S_2,V_R_2,T_a] : % 1.40/1.52 ( 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))) % 1.40/1.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_psubsetD,axiom, % 1.40/1.52 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 1.40/1.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_set__mp,axiom, % 1.40/1.52 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.40/1.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_set__rev__mp,axiom, % 1.40/1.52 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.40/1.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_in__mono,axiom, % 1.40/1.52 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.40/1.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_subset__UNIV,axiom, % 1.40/1.52 ! [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)))) ). % 1.40/1.52 % 1.40/1.52 fof(fact_eq__mem,axiom, % 1.40/1.52 ! [V_y_2,V_x_2,T_a] : % 1.40/1.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 1.40/1.52 <=> V_x_2 = V_y_2 ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_linorder__neqE__linordered__idom,axiom, % 1.40/1.52 ! [V_y,V_x,T_a] : % 1.40/1.52 ( class_Rings_Olinordered__idom(T_a) % 1.40/1.52 => ( V_x != V_y % 1.40/1.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 1.40/1.52 ! [V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oab__semigroup__add(T_a) % 1.40/1.52 => 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)) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__left__cancel,axiom, % 1.40/1.52 ! [V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.40/1.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.40/1.52 => ( 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) % 1.40/1.52 <=> V_ba_2 = V_ca_2 ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__right__cancel,axiom, % 1.40/1.52 ! [V_ca_2,V_aa_2,V_ba_2,T_a] : % 1.40/1.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.40/1.52 => ( 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) % 1.40/1.52 <=> V_ba_2 = V_ca_2 ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__left__imp__eq,axiom, % 1.40/1.52 ! [V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.40/1.52 => ( 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) % 1.40/1.52 => V_b = V_c ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__imp__eq,axiom, % 1.40/1.52 ! [V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 1.40/1.52 => ( 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) % 1.40/1.52 => V_b = V_c ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__right__imp__eq,axiom, % 1.40/1.52 ! [V_c,V_a,V_b,T_a] : % 1.40/1.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.40/1.52 => ( 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) % 1.40/1.52 => V_b = V_c ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_one__reorient,axiom, % 1.40/1.52 ! [V_x_2,T_a] : % 1.40/1.52 ( class_Groups_Oone(T_a) % 1.40/1.52 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 1.40/1.52 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inj__on__def,axiom, % 1.40/1.52 ! [V_A_2,V_f_2,T_b,T_a] : % 1.40/1.52 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.52 <=> ! [B_x] : % 1.40/1.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.40/1.52 => ! [B_xa] : % 1.40/1.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 1.40/1.52 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 1.40/1.52 => B_x = B_xa ) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_pred__equals__eq,axiom, % 1.40/1.52 ! [V_S_2,V_R_2,T_a] : % 1.40/1.52 ( 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) % 1.40/1.52 <=> V_R_2 = V_S_2 ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_inj__on__id2,axiom, % 1.40/1.52 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__le__cancel__right,axiom, % 1.40/1.52 ! [V_ba_2,V_ca_2,V_aa_2,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.52 => ( 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))) % 1.40/1.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__le__cancel__left,axiom, % 1.40/1.52 ! [V_ba_2,V_aa_2,V_ca_2,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.52 => ( 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))) % 1.40/1.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__right__mono,axiom, % 1.40/1.52 ! [V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.52 => 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))) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__left__mono,axiom, % 1.40/1.52 ! [V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.52 => 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))) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__mono,axiom, % 1.40/1.52 ! [V_d,V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.40/1.52 => 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))) ) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__le__imp__le__right,axiom, % 1.40/1.52 ! [V_b,V_c,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.52 => ( 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))) % 1.40/1.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__le__imp__le__left,axiom, % 1.40/1.52 ! [V_b,V_a,V_c,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.52 => ( 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))) % 1.40/1.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__less__imp__less__left,axiom, % 1.40/1.52 ! [V_b,V_a,V_c,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.52 => ( 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))) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__less__imp__less__right,axiom, % 1.40/1.52 ! [V_b,V_c,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.52 => ( 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))) % 1.40/1.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.40/1.52 % 1.40/1.52 fof(fact_add__strict__mono,axiom, % 1.40/1.52 ! [V_d,V_c,V_b,V_a,T_a] : % 1.40/1.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.40/1.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.40/1.53 => 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))) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__strict__left__mono,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.40/1.53 => 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))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__strict__right__mono,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.40/1.53 => 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))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__less__cancel__left,axiom, % 1.40/1.53 ! [V_ba_2,V_aa_2,V_ca_2,T_a] : % 1.40/1.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.53 => ( 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))) % 1.40/1.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__less__cancel__right,axiom, % 1.40/1.53 ! [V_ba_2,V_ca_2,V_aa_2,T_a] : % 1.40/1.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.40/1.53 => ( 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))) % 1.40/1.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_inj__onD,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.40/1.53 => V_x_2 = V_y_2 ) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_inj__on__iff,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.40/1.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.40/1.53 <=> V_x_2 = V_y_2 ) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_inj__on__contraD,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.53 => ( V_x_2 != V_y_2 % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.40/1.53 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_inj__eq,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.40/1.53 <=> V_x_2 = V_y_2 ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_injD,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.53 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.40/1.53 => V_x_2 = V_y_2 ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_pred__equals__eq2,axiom, % 1.40/1.53 ! [V_S_2,V_R_2,T_b,T_a] : % 1.40/1.53 ( 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) % 1.40/1.53 <=> V_R_2 = V_S_2 ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_below__Lin,axiom, % 1.40/1.53 ! [V_L_2,V_y_2,V_x_2] : % 1.40/1.53 ( V_x_2 != V_y_2 % 1.40/1.53 => ( 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)) % 1.40/1.53 => 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)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_PiE,axiom, % 1.40/1.53 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( 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))) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_funcset__mem,axiom, % 1.40/1.53 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( 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)))) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_Pi__mem,axiom, % 1.40/1.53 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.53 ( 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))) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_Pi__UNIV,axiom, % 1.40/1.53 ! [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)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_funcset__id,axiom, % 1.40/1.53 ! [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)))) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__refl,axiom, % 1.40/1.53 ! [V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_dictatorI,axiom, % 1.40/1.53 ! [V_i_2,V_Fa_2] : % 1.40/1.53 ( 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)))) % 1.40/1.53 => ( ! [B_x] : % 1.40/1.53 ( 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)) % 1.40/1.53 => ! [B_a,B_b] : % 1.40/1.53 ( B_a != B_b % 1.40/1.53 => ( 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))) % 1.40/1.53 => 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))) ) ) ) % 1.40/1.53 => c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_mlex__leq,axiom, % 1.40/1.53 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.40/1.53 ( 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))) % 1.40/1.53 => ( 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)) % 1.40/1.53 => 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))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_mlex__less,axiom, % 1.40/1.53 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.40/1.53 ( 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))) % 1.40/1.53 => 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))) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_equalityI,axiom, % 1.40/1.53 ! [V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) % 1.40/1.53 => V_A_2 = V_B_2 ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_rev__predicate2D,axiom, % 1.40/1.53 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 1.40/1.53 => ( 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)) % 1.40/1.53 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_equalityE,axiom, % 1.40/1.53 ! [T_a,V_B_2,V_A_2] : % 1.40/1.53 ( V_A_2 = V_B_2 % 1.40/1.53 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_predicate2D,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_b,T_a] : % 1.40/1.53 ( 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)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_subset__trans,axiom, % 1.40/1.53 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_subset__psubset__trans,axiom, % 1.40/1.53 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_psubset__subset__trans,axiom, % 1.40/1.53 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_psubset__trans,axiom, % 1.40/1.53 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_predicate1D,axiom, % 1.40/1.53 ! [V_x_2,V_Q_2,V_Pa_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) % 1.40/1.53 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.40/1.53 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_psubset__imp__subset,axiom, % 1.40/1.53 ! [V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_equalityD2,axiom, % 1.40/1.53 ! [T_a,V_B_2,V_A_2] : % 1.40/1.53 ( V_A_2 = V_B_2 % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_equalityD1,axiom, % 1.40/1.53 ! [T_a,V_B_2,V_A_2] : % 1.40/1.53 ( V_A_2 = V_B_2 % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_rev__predicate1D,axiom, % 1.40/1.53 ! [V_Q_2,T_a,V_x_2,V_Pa_2] : % 1.40/1.53 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2)) % 1.40/1.53 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_subset__iff__psubset__eq,axiom, % 1.40/1.53 ! [V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.53 | V_A_2 = V_B_2 ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_set__eq__subset,axiom, % 1.40/1.53 ! [T_a,V_B_2,V_A_2] : % 1.40/1.53 ( V_A_2 = V_B_2 % 1.40/1.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__fun__def,axiom, % 1.40/1.53 ! [V_g_2,V_f_2,T_a,T_b] : % 1.40/1.53 ( class_Orderings_Oord(T_b) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.40/1.53 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_psubset__eq,axiom, % 1.40/1.53 ! [V_B_2,V_A_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.53 & V_A_2 != V_B_2 ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_subset__refl,axiom, % 1.40/1.53 ! [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)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__le__cases,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_le__funE,axiom, % 1.40/1.53 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.40/1.53 ( class_Orderings_Oord(T_b) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I6_J,axiom, % 1.40/1.53 ! [V_z,V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I5_J,axiom, % 1.40/1.53 ! [V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 => V_x = V_y ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__trans,axiom, % 1.40/1.53 ! [V_z,V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__antisym,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.40/1.53 => V_x = V_y ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I4_J,axiom, % 1.40/1.53 ! [V_c,V_a,V_b,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.40/1.53 => ( V_b = V_c % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_ord__le__eq__trans,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oord(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.53 => ( V_b = V_c % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I3_J,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( V_a = V_b % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_ord__eq__le__trans,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oord(T_a) % 1.40/1.53 => ( V_a = V_b % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__antisym__conv,axiom, % 1.40/1.53 ! [V_x_2,V_y_2,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 <=> V_x_2 = V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_le__funD,axiom, % 1.40/1.53 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.40/1.53 ( class_Orderings_Oord(T_b) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__eq__refl,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( V_x = V_y % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__eq__iff,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( V_x_2 = V_y_2 % 1.40/1.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__linear,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_le__fun__def,axiom, % 1.40/1.53 ! [V_g_2,V_f_2,T_a,T_b] : % 1.40/1.53 ( class_Orderings_Oord(T_b) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.40/1.53 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__irrefl,axiom, % 1.40/1.53 ! [V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__neq__iff,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( V_x_2 != V_y_2 % 1.40/1.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_not__less__iff__gr__or__eq,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.40/1.53 | V_x_2 = V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__less__linear,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 | V_x = V_y % 1.40/1.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__antisym__conv3,axiom, % 1.40/1.53 ! [V_x_2,V_y_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 <=> V_x_2 = V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__neqE,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( V_x != V_y % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__imp__neq,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => V_x != V_y ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__not__sym,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__imp__not__less,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__imp__not__eq,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => V_x != V_y ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__imp__not__eq2,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => V_y != V_x ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__asym_H,axiom, % 1.40/1.53 ! [V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I9_J,axiom, % 1.40/1.53 ! [V_a,V_b,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_ord__eq__less__trans,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oord(T_a) % 1.40/1.53 => ( V_a = V_b % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I1_J,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( V_a = V_b % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_ord__less__eq__trans,axiom, % 1.40/1.53 ! [V_c,V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oord(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.40/1.53 => ( V_b = V_c % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I2_J,axiom, % 1.40/1.53 ! [V_c,V_a,V_b,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.40/1.53 => ( V_b = V_c % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__trans,axiom, % 1.40/1.53 ! [V_z,V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I10_J,axiom, % 1.40/1.53 ! [V_z,V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__asym,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__cases,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => ( V_x != V_y % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_Pi__anti__mono,axiom, % 1.40/1.53 ! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2)) % 1.40/1.53 => 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))) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_Prof__def,axiom, % 1.40/1.53 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)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_dictator__def,axiom, % 1.40/1.53 ! [V_i_2,V_Fa_2] : % 1.40/1.53 ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) % 1.40/1.53 <=> ! [B_x] : % 1.40/1.53 ( 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)) % 1.40/1.53 => hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__not__less,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__not__le,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__le__less__linear,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__le,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 & V_x_2 != V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__le__not__le,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__le__less,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 | V_x_2 = V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_leI,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_not__leE,axiom, % 1.40/1.53 ! [V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__antisym__conv1,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 <=> V_x_2 = V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__neq__le__trans,axiom, % 1.40/1.53 ! [V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( V_a != V_b % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I12_J,axiom, % 1.40/1.53 ! [V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( V_a != V_b % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_leD,axiom, % 1.40/1.53 ! [V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.40/1.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__imp__le,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__antisym__conv2,axiom, % 1.40/1.53 ! [V_y_2,V_x_2,T_a] : % 1.40/1.53 ( class_Orderings_Olinorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.40/1.53 <=> V_x_2 = V_y_2 ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__le__imp__less__or__eq,axiom, % 1.40/1.53 ! [V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 | V_x = V_y ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__le__neq__trans,axiom, % 1.40/1.53 ! [V_b,V_a,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.40/1.53 => ( V_a != V_b % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I11_J,axiom, % 1.40/1.53 ! [V_a,V_b,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.40/1.53 => ( V_a != V_b % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__less__le__trans,axiom, % 1.40/1.53 ! [V_z,V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I7_J,axiom, % 1.40/1.53 ! [V_z,V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_order__le__less__trans,axiom, % 1.40/1.53 ! [V_z,V_y,V_x,T_a] : % 1.40/1.53 ( class_Orderings_Opreorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_xt1_I8_J,axiom, % 1.40/1.53 ! [V_z,V_x,V_y,T_a] : % 1.40/1.53 ( class_Orderings_Oorder(T_a) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.40/1.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_top__greatest,axiom, % 1.40/1.53 ! [V_x,T_a] : % 1.40/1.53 ( class_Orderings_Otop(T_a) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_top__apply,axiom, % 1.40/1.53 ! [V_x_2,T_b,T_a] : % 1.40/1.53 ( class_Orderings_Otop(T_a) % 1.40/1.53 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__leE,axiom, % 1.40/1.53 ! [V_n,V_k,V_m] : % 1.40/1.53 ( 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)) % 1.40/1.53 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.53 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__leD1,axiom, % 1.40/1.53 ! [V_n,V_k,V_m] : % 1.40/1.53 ( 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)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__leD2,axiom, % 1.40/1.53 ! [V_n,V_k,V_m] : % 1.40/1.53 ( 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)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__le__mono,axiom, % 1.40/1.53 ! [V_l,V_k,V_j,V_i] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) % 1.40/1.53 => 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))) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_add__le__mono1,axiom, % 1.40/1.53 ! [V_k,V_j,V_i] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.40/1.53 => 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))) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_trans__le__add2,axiom, % 1.40/1.53 ! [V_m,V_j,V_i] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.40/1.53 => 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))) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_trans__le__add1,axiom, % 1.40/1.53 ! [V_m,V_j,V_i] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.40/1.53 => 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))) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__less__cases,axiom, % 1.40/1.53 ! [V_Pa_2,V_na_2,V_m_2] : % 1.40/1.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.40/1.53 => ( ( V_m_2 = V_na_2 % 1.40/1.53 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.40/1.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.40/1.53 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 1.40/1.53 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__not__refl3,axiom, % 1.40/1.53 ! [V_t,V_s] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 1.40/1.53 => V_s != V_t ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__not__refl2,axiom, % 1.40/1.53 ! [V_m,V_n] : % 1.40/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.40/1.53 => V_m != V_n ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__irrefl__nat,axiom, % 1.40/1.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_linorder__neqE__nat,axiom, % 1.40/1.53 ! [V_y,V_x] : % 1.40/1.53 ( V_x != V_y % 1.40/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.40/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__neq__iff,axiom, % 1.40/1.53 ! [V_na_2,V_m_2] : % 1.40/1.53 ( V_m_2 != V_na_2 % 1.40/1.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_less__not__refl,axiom, % 1.40/1.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__add__commute,axiom, % 1.40/1.53 ! [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) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__add__left__commute,axiom, % 1.40/1.53 ! [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)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__add__assoc,axiom, % 1.40/1.53 ! [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)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__add__left__cancel,axiom, % 1.40/1.53 ! [V_na_2,V_m_2,V_k_2] : % 1.40/1.53 ( 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) % 1.40/1.53 <=> V_m_2 = V_na_2 ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__add__right__cancel,axiom, % 1.40/1.53 ! [V_na_2,V_k_2,V_m_2] : % 1.40/1.53 ( 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) % 1.40/1.53 <=> V_m_2 = V_na_2 ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_le__refl,axiom, % 1.40/1.53 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ). % 1.40/1.53 % 1.40/1.53 fof(fact_nat__le__linear,axiom, % 1.40/1.53 ! [V_n,V_m] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_eq__imp__le,axiom, % 1.40/1.53 ! [V_n,V_m] : % 1.40/1.53 ( V_m = V_n % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_le__trans,axiom, % 1.40/1.53 ! [V_k,V_j,V_i] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) % 1.40/1.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_le__antisym,axiom, % 1.40/1.53 ! [V_n,V_m] : % 1.40/1.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 1.40/1.53 => V_m = V_n ) ) ). % 1.40/1.53 % 1.40/1.53 fof(fact_inj__on__add__nat,axiom, % 1.40/1.54 ! [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) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__lessD1,axiom, % 1.40/1.54 ! [V_k,V_j,V_i] : % 1.40/1.54 ( 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)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__add__eq__less,axiom, % 1.40/1.54 ! [V_n,V_m,V_l,V_k] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.40/1.54 => ( 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) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__less__mono,axiom, % 1.40/1.54 ! [V_l,V_k,V_j,V_i] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.40/1.54 => 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))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__less__mono1,axiom, % 1.40/1.54 ! [V_k,V_j,V_i] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_trans__less__add2,axiom, % 1.40/1.54 ! [V_m,V_j,V_i] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_trans__less__add1,axiom, % 1.40/1.54 ! [V_m,V_j,V_i] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat__add__left__cancel__less,axiom, % 1.40/1.54 ! [V_na_2,V_m_2,V_k_2] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__add__less2,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__add__less1,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__or__eq__imp__le,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 | V_m = V_n ) % 1.40/1.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__neq__implies__less,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.54 => ( V_m != V_n % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__imp__le__nat,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__eq__less__or__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.40/1.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.54 | V_m_2 = V_na_2 ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat__less__le,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.54 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.40/1.54 & V_m_2 != V_na_2 ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__add2,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__add1,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__iff__add,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.40/1.54 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat__add__left__cancel__le,axiom, % 1.40/1.54 ! [V_na_2,V_m_2,V_k_2] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_IIA__def,axiom, % 1.40/1.54 ! [V_Fa_2] : % 1.40/1.54 ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) % 1.40/1.54 <=> ! [B_x] : % 1.40/1.54 ( 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)) % 1.40/1.54 => ! [B_xa] : % 1.40/1.54 ( 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)) % 1.40/1.54 => ! [B_a,B_b] : % 1.40/1.54 ( ! [B_i] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> 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))) ) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> 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))) ) ) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_unanimity__def,axiom, % 1.40/1.54 ! [V_Fa_2] : % 1.40/1.54 ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) % 1.40/1.54 <=> ! [B_x] : % 1.40/1.54 ( 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)) % 1.40/1.54 => ! [B_a,B_b] : % 1.40/1.54 ( ! [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))) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_iso__tuple__UNIV__I,axiom, % 1.40/1.54 ! [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)))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__inj,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( 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)))) % 1.40/1.54 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Pi__mono,axiom, % 1.40/1.54 ! [V_C_2,V_B_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( ! [B_x] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.40/1.54 => 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))) ) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__indi,axiom, % 1.40/1.54 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__bij,axiom, % 1.40/1.54 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( 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)))) % 1.40/1.54 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.54 => ( 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)))) % 1.40/1.54 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.54 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__psubset,axiom, % 1.40/1.54 ! [V_A_2,V_B_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.54 => ( 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))) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_psubset__card__mono,axiom, % 1.40/1.54 ! [V_A_2,V_B_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.54 => 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))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__mono,axiom, % 1.40/1.54 ! [V_A_2,V_B_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.54 => 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))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__seteq,axiom, % 1.40/1.54 ! [V_A_2,V_B_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.54 => ( 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))) % 1.40/1.54 => V_A_2 = V_B_2 ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( class_Finite__Set_Ofinite(T_a) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__code,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( class_Finite__Set_Ofinite(T_a) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__UNIV__unit,axiom, % 1.40/1.54 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) ). % 1.40/1.54 % 1.40/1.54 fof(fact_rev__finite__subset,axiom, % 1.40/1.54 ! [V_A_2,V_B_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__subset,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__option__UNIV,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))) % 1.40/1.54 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__Plus__UNIV__iff,axiom, % 1.40/1.54 ! [T_b,T_a] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__Prod__UNIV,axiom, % 1.40/1.54 ! [T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 1.40/1.54 => 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))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__UNIV,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Finite__Set_Ofinite(T_a) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( 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))) % 1.40/1.54 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__fun__UNIVD2,axiom, % 1.40/1.54 ! [T_b,T_a] : % 1.40/1.54 ( 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))) % 1.40/1.54 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_in__finite__psubset,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,T_a] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.54 & c_Finite__Set_Ofinite(T_a,V_B_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__Plus,axiom, % 1.40/1.54 ! [V_B_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.54 => 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)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card_Oinsert,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => 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)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Pi__I,axiom, % 1.40/1.54 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( ! [B_x] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) ) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insertCI,axiom, % 1.40/1.54 ! [V_ba_2,V_B_2,V_aa_2,T_a] : % 1.40/1.54 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) % 1.40/1.54 => V_aa_2 = V_ba_2 ) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insertE,axiom, % 1.40/1.54 ! [V_A_2,V_ba_2,V_aa_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) % 1.40/1.54 => ( V_aa_2 != V_ba_2 % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite_OinsertI,axiom, % 1.40/1.54 ! [V_aa_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__insert,axiom, % 1.40/1.54 ! [V_A_2,V_aa_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) % 1.40/1.54 <=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__absorb,axiom, % 1.40/1.54 ! [V_A_2,V_aa_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) % 1.40/1.54 => c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insertI2,axiom, % 1.40/1.54 ! [V_ba_2,V_B_2,V_aa_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__ident,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.40/1.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 1.40/1.54 => ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2) % 1.40/1.54 <=> V_A_2 = V_B_2 ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__iff,axiom, % 1.40/1.54 ! [V_A_2,V_ba_2,V_aa_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2))) % 1.40/1.54 <=> ( V_aa_2 = V_ba_2 % 1.40/1.54 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insertI1,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_subset__insertI,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_subset__insertI2,axiom, % 1.40/1.54 ! [V_ba_2,V_B_2,V_A_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__mono,axiom, % 1.40/1.54 ! [V_aa_2,V_D_2,V_C_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_D_2)) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__absorb2,axiom, % 1.40/1.54 ! [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) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__commute,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__code,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,V_y_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2)) % 1.40/1.54 <=> ( V_y_2 = V_x_2 % 1.40/1.54 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__Plus__iff,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.40/1.54 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__Plus,axiom, % 1.40/1.54 ! [V_B_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.54 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__PlusD_I1_J,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__PlusD_I2_J,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.40/1.54 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__subset,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.40/1.54 ( 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)) % 1.40/1.54 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 1.40/1.54 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_subset__insert,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.40/1.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__insert__le,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => 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)))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_UNIV__Plus__UNIV,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__Plus__conv__if,axiom, % 1.40/1.54 ! [V_B_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.40/1.54 => 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)) ) % 1.40/1.54 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.40/1.54 => 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) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_folding__image__simple_Oinsert,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.40/1.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.40/1.54 => 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)) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) % 1.40/1.54 => 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) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__zeroE,axiom, % 1.40/1.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le0,axiom, % 1.40/1.54 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_plus__nat_Oadd__0,axiom, % 1.40/1.54 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 1.40/1.54 % 1.40/1.54 fof(fact_Nat_Oadd__0__right,axiom, % 1.40/1.54 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__is__0,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__eq__self__zero,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 1.40/1.54 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 1.40/1.54 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__0__eq,axiom, % 1.40/1.54 ! [V_na_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.40/1.54 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__reorient,axiom, % 1.40/1.54 ! [V_x_2,T_a] : % 1.40/1.54 ( class_Groups_Ozero(T_a) % 1.40/1.54 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 1.40/1.54 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__neq__one,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Ozero__neq__one(T_a) % 1.40/1.54 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_one__neq__zero,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Ozero__neq__one(T_a) % 1.40/1.54 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add_Ocomm__neutral,axiom, % 1.40/1.54 ! [V_a,T_a] : % 1.40/1.54 ( class_Groups_Ocomm__monoid__add(T_a) % 1.40/1.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__0__right,axiom, % 1.40/1.54 ! [V_a,T_a] : % 1.40/1.54 ( class_Groups_Omonoid__add(T_a) % 1.40/1.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_double__zero__sym,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.40/1.54 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) % 1.40/1.54 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__0,axiom, % 1.40/1.54 ! [V_a,T_a] : % 1.40/1.54 ( class_Groups_Ocomm__monoid__add(T_a) % 1.40/1.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__0__left,axiom, % 1.40/1.54 ! [V_a,T_a] : % 1.40/1.54 ( class_Groups_Omonoid__add(T_a) % 1.40/1.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_gr0I,axiom, % 1.40/1.54 ! [V_n] : % 1.40/1.54 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_gr__implies__not0,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__nat__zero__code,axiom, % 1.40/1.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_neq0__conv,axiom, % 1.40/1.54 ! [V_na_2] : % 1.40/1.54 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__less0,axiom, % 1.40/1.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_folding__image__simple__idem_Oidem,axiom, % 1.40/1.54 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.40/1.54 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__nonneg__nonneg,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__nonneg__eq__0__iff,axiom, % 1.40/1.54 ! [V_y_2,V_x_2,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 1.40/1.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.40/1.54 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 1.40/1.54 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__increasing,axiom, % 1.40/1.54 ! [V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__increasing2,axiom, % 1.40/1.54 ! [V_a,V_b,V_c,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__nonpos__nonpos,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__pos__pos,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_pos__add__strict,axiom, % 1.40/1.54 ! [V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__neg__neg,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__one__le__zero,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.54 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__le__one,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__one__less__zero,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__less__one,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__gr__0,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 1.40/1.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__infinite,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__pos__nonneg,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__nonneg__pos,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__strict__increasing,axiom, % 1.40/1.54 ! [V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__strict__increasing2,axiom, % 1.40/1.54 ! [V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__neg__nonpos,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__nonpos__neg,axiom, % 1.40/1.54 ! [V_b,V_a,T_a] : % 1.40/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.40/1.54 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__less__two,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Olinordered__semidom(T_a) % 1.40/1.54 => 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)))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__ge__0__finite,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( 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))) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__UNIV__card__ge__0,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => 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))))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.40/1.54 => 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) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.40/1.54 => 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)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_even__less__0__iff,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Rings_Olinordered__idom(T_a) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__fun__UNIVD1,axiom, % 1.40/1.54 ! [T_b,T_a] : % 1.40/1.54 ( 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))) % 1.40/1.54 => ( 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)) % 1.40/1.54 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_double__eq__0__iff,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.40/1.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.40/1.54 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_lessI,axiom, % 1.40/1.54 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__mono,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_zero__less__Suc,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__neq__Zero,axiom, % 1.40/1.54 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Zero__neq__Suc,axiom, % 1.40/1.54 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Osimps_I3_J,axiom, % 1.40/1.54 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__not__Zero,axiom, % 1.40/1.54 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Osimps_I2_J,axiom, % 1.40/1.54 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Zero__not__Suc,axiom, % 1.40/1.54 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__less__SucD,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__lessD,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__SucE,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 1.40/1.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => V_m = V_n ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__trans__Suc,axiom, % 1.40/1.54 ! [V_k,V_j,V_i] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__lessI,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__SucI,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__antisym,axiom, % 1.40/1.54 ! [V_m,V_n] : % 1.40/1.54 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 1.40/1.54 => V_m = V_n ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__less__less__Suc__eq,axiom, % 1.40/1.54 ! [V_m_2,V_na_2] : % 1.40/1.54 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.40/1.54 <=> V_na_2 = V_m_2 ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__less__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__Suc__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.40/1.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.54 | V_m_2 = V_na_2 ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__less__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__n__not__le__n,axiom, % 1.40/1.54 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_not__less__eq__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__Suc__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.40/1.54 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.40/1.54 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__le__mono,axiom, % 1.40/1.54 ! [V_m_2,V_na_2] : % 1.40/1.54 ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),V_m_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__SucI,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__SucE,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) % 1.40/1.54 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.54 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__leD,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.40/1.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_n__not__Suc__n,axiom, % 1.40/1.54 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__n__not__n,axiom, % 1.40/1.54 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Oinject,axiom, % 1.40/1.54 ! [V_nat_H_2,V_nat_2] : % 1.40/1.54 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 1.40/1.54 <=> V_nat_2 = V_nat_H_2 ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__inject,axiom, % 1.40/1.54 ! [V_y,V_x] : % 1.40/1.54 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 1.40/1.54 => V_x = V_y ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__Suc__shift,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__Suc,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__Suc__right,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inj__Suc,axiom, % 1.40/1.54 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 1.40/1.54 % 1.40/1.54 fof(fact_gr0__conv__Suc,axiom, % 1.40/1.54 ! [V_na_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 1.40/1.54 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__Suc0,axiom, % 1.40/1.54 ! [V_na_2] : % 1.40/1.54 ( 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)))) % 1.40/1.54 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__Suc__eq__0__disj,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.40/1.54 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 | ? [B_j] : % 1.40/1.54 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 1.40/1.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_one__is__add,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( 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) % 1.40/1.54 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.40/1.54 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.40/1.54 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__is__1,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( 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)) % 1.40/1.54 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.40/1.54 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.40/1.54 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.40/1.54 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__iff__Suc__add,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 1.40/1.54 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__add__Suc2,axiom, % 1.40/1.54 ! [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)))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__add__Suc1,axiom, % 1.40/1.54 ! [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)))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__le__lessD,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__less__Suc__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.40/1.54 <=> V_na_2 = V_m_2 ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__leI,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.40/1.54 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_le__imp__less__Suc,axiom, % 1.40/1.54 ! [V_n,V_m] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__le__eq,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__Suc__eq__le,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__eq__Suc__le,axiom, % 1.40/1.54 ! [V_m_2,V_na_2] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_One__nat__def,axiom, % 1.40/1.54 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__eq__Suc__le__raw,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__insert__disjoint,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => 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)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__insert__if,axiom, % 1.40/1.54 ! [V_x_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => 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) ) % 1.40/1.54 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => 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)) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__eq__plus1__left,axiom, % 1.40/1.54 ! [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) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Suc__eq__plus1,axiom, % 1.40/1.54 ! [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)) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Osize_I2_J,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Osize_I1_J,axiom, % 1.40/1.54 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Osize_I4_J,axiom, % 1.40/1.54 ! [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))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Ints__odd__less__0,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Rings_Olinordered__idom(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat__size,axiom, % 1.40/1.54 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ). % 1.40/1.54 % 1.40/1.54 fof(fact_Ints__0,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Oring__1(T_a) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Ints__add,axiom, % 1.40/1.54 ! [V_ba_2,V_aa_2,T_a] : % 1.40/1.54 ( class_Rings_Oring__1(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Int_Oring__1__class_OInts(T_a))) % 1.40/1.54 => 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))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_nat_Osize_I3_J,axiom, % 1.40/1.54 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Ints__1,axiom, % 1.40/1.54 ! [T_a] : % 1.40/1.54 ( class_Rings_Oring__1(T_a) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Ints__double__eq__0__iff,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Int_Oring__char__0(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.40/1.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.40/1.54 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_Ints__odd__nonzero,axiom, % 1.40/1.54 ! [V_aa_2,T_a] : % 1.40/1.54 ( class_Int_Oring__char__0(T_a) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a))) % 1.40/1.54 => 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) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 1.40/1.54 ! [V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 1.40/1.54 ! [V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 1.40/1.54 ! [V_c,V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => 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) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 1.40/1.54 ! [V_d,V_c,V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => 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)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 1.40/1.54 ! [V_d,V_c,V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => 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) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 1.40/1.54 ! [V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => 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)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 1.40/1.54 ! [V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => 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) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 1.40/1.54 ! [V_d,V_c,V_b,V_a,T_a] : % 1.40/1.54 ( class_Rings_Ocomm__semiring__1(T_a) % 1.40/1.54 => 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)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_add__0__iff,axiom, % 1.40/1.54 ! [V_aa_2,V_ba_2,T_a] : % 1.40/1.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 1.40/1.54 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) % 1.40/1.54 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_ex__least__nat__less,axiom, % 1.40/1.54 ! [V_na_2,V_Pa_2] : % 1.40/1.54 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.40/1.54 => ( hBOOL(hAPP(V_Pa_2,V_na_2)) % 1.40/1.54 => ? [B_k] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2)) % 1.40/1.54 & ! [B_i] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) % 1.40/1.54 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 1.40/1.54 & 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)))) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__def,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => 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) ) % 1.40/1.54 & ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 1.40/1.54 ! [V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.40/1.54 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.40/1.54 => 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) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card_Oeq__fold__g,axiom, % 1.40/1.54 ! [V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => 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) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_surjh,axiom, % 1.40/1.54 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)))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 1.40/1.54 ! [V_na_2,V_m_2] : % 1.40/1.54 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 1.40/1.54 <=> 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)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_image__eqI,axiom, % 1.40/1.54 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_ba_2] : % 1.40/1.54 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.40/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__imageI,axiom, % 1.40/1.54 ! [V_ha_2,T_b,V_Fa_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_Fa_2) % 1.40/1.54 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inj__image__mem__iff,axiom, % 1.40/1.54 ! [V_A_2,V_aa_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_range__ex1__eq,axiom, % 1.40/1.54 ! [V_ba_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( 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))))) % 1.40/1.54 <=> ? [B_x] : % 1.40/1.54 ( V_ba_2 = hAPP(V_f_2,B_x) % 1.40/1.54 & ! [B_y] : % 1.40/1.54 ( V_ba_2 = hAPP(V_f_2,B_y) % 1.40/1.54 => B_y = B_x ) ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__surj__inj,axiom, % 1.40/1.54 ! [V_f_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( 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))) % 1.40/1.54 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_endo__inj__surj,axiom, % 1.40/1.54 ! [V_f_2,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( 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)) % 1.40/1.54 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 1.40/1.54 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__UNIV__surj__inj,axiom, % 1.40/1.54 ! [V_f_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( 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)) % 1.40/1.54 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__UNIV__inj__surj,axiom, % 1.40/1.54 ! [V_f_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => 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)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inj__image__subset__iff,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( 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))) % 1.40/1.54 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__image__le,axiom, % 1.40/1.54 ! [V_f_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => 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))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_eq__card__imp__inj__on,axiom, % 1.40/1.54 ! [V_f_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( 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) % 1.40/1.54 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inj__on__iff__eq__card,axiom, % 1.40/1.54 ! [V_f_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.54 <=> 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) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_pigeonhole,axiom, % 1.40/1.54 ! [V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( 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))) % 1.40/1.54 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_insert__image,axiom, % 1.40/1.54 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.54 => 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) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_range__eqI,axiom, % 1.40/1.54 ! [T_b,T_a,V_x_2,V_f_2,V_ba_2] : % 1.40/1.54 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.40/1.54 => 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))))) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_rangeI,axiom, % 1.40/1.54 ! [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))))) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__surj,axiom, % 1.40/1.54 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.54 => ( 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))) % 1.40/1.54 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_finite__imageD,axiom, % 1.40/1.54 ! [V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) % 1.40/1.54 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 1.40/1.54 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inj__image__eq__iff,axiom, % 1.40/1.54 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.54 => ( 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) % 1.40/1.54 <=> V_A_2 = V_B_2 ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_card__image,axiom, % 1.40/1.54 ! [V_A_2,V_f_2,T_b,T_a] : % 1.40/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.54 => 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) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inv__into__injective,axiom, % 1.40/1.54 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_b,T_a] : % 1.40/1.54 ( 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) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.40/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.40/1.54 => V_x_2 = V_y_2 ) ) ) ). % 1.40/1.54 % 1.40/1.54 fof(fact_inv__into__into,axiom, % 1.40/1.54 ! [V_A_2,V_f_2,T_b,V_x_2,T_a] : % 1.40/1.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.40/1.54 => 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)) ) ). % 1.40/1.54 % 1.40/1.55 fof(fact_f__inv__into__f,axiom, % 1.40/1.55 ! [V_A_2,V_f_2,T_b,V_y_2,T_a] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.40/1.55 => 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 ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__inv__into__cancel,axiom, % 1.40/1.55 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 1.40/1.55 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_A_H_2 % 1.40/1.55 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_H_2),V_A_H_2)) % 1.40/1.55 => 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 ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__surj__f__inv__f,axiom, % 1.40/1.55 ! [V_A_2,V_f_2,T_a,T_b] : % 1.40/1.55 ( 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)) % 1.40/1.55 => 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 ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_surj__f__inv__f,axiom, % 1.40/1.55 ! [V_y_2,V_f_2,T_a,T_b] : % 1.40/1.55 ( 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)) % 1.40/1.55 => 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 ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_surj__iff__all,axiom, % 1.40/1.55 ! [V_f_2,T_a,T_b] : % 1.40/1.55 ( 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)) % 1.40/1.55 <=> ! [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 ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_inj__on__strict__subset,axiom, % 1.40/1.55 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.40/1.55 => 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))) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_rev__image__eqI,axiom, % 1.40/1.55 ! [T_b,V_f_2,V_ba_2,V_A_2,V_x_2,T_a] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.55 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.40/1.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_imageI,axiom, % 1.40/1.55 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.40/1.55 => 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))) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__iff,axiom, % 1.40/1.55 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.40/1.55 <=> ? [B_x] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 1.40/1.55 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__insert,axiom, % 1.40/1.55 ! [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)) ). % 1.40/1.55 % 1.40/1.55 fof(fact_range__composition,axiom, % 1.40/1.55 ! [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)))) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__ident,axiom, % 1.40/1.55 ! [V_Y_2,T_a] : c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2 ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__image,axiom, % 1.40/1.55 ! [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) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__mono,axiom, % 1.40/1.55 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 1.40/1.55 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.40/1.55 => 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))) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_subset__image__iff,axiom, % 1.40/1.55 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.40/1.55 ( 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))) % 1.40/1.55 <=> ? [B_AA] : % 1.40/1.55 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2)) % 1.40/1.55 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_nat__case__Suc,axiom, % 1.40/1.55 ! [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) ). % 1.40/1.55 % 1.40/1.55 fof(fact_nat__case__0,axiom, % 1.40/1.55 ! [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 ). % 1.40/1.55 % 1.40/1.55 fof(fact_finite__range__imageI,axiom, % 1.40/1.55 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 1.40/1.55 ( 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)))) % 1.40/1.55 => 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)))) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_inv__into__image__cancel,axiom, % 1.40/1.55 ! [V_S_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.55 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_S_2),V_A_2)) % 1.40/1.55 => 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 ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_inj__on__inv__into,axiom, % 1.40/1.55 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.40/1.55 ( 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))) % 1.40/1.55 => 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) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_inj__imp__surj__inv,axiom, % 1.40/1.55 ! [V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.55 => 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)) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__inv__f__f,axiom, % 1.40/1.55 ! [V_A_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.55 => 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 ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_inv__image__comp,axiom, % 1.40/1.55 ! [V_X_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.40/1.55 => 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 ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_surj__imp__inj__inv,axiom, % 1.40/1.55 ! [V_f_2,T_a,T_b] : % 1.40/1.55 ( 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)) % 1.40/1.55 => 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))) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_funcset__image,axiom, % 1.40/1.55 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( 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)))) % 1.40/1.55 => 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)) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_card__bij__eq,axiom, % 1.40/1.55 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.55 => ( 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)) % 1.40/1.55 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.40/1.55 => ( 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)) % 1.40/1.55 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.55 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.55 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_card__inj__on__le,axiom, % 1.40/1.55 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.40/1.55 => ( 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)) % 1.40/1.55 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.55 => 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))) ) ) ) ). % 1.40/1.55 % 1.40/1.55 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, % 1.40/1.55 ~ ! [B_h] : % 1.40/1.55 ( 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))) % 1.40/1.55 => 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)))) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_inj__on__iff__card__le,axiom, % 1.40/1.55 ! [V_B_2,T_b,V_A_2,T_a] : % 1.40/1.55 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.40/1.55 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.40/1.55 => ( ? [B_f] : % 1.40/1.55 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 1.40/1.55 & 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)) ) % 1.40/1.55 <=> 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))) ) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_finite__atLeastLessThan,axiom, % 1.40/1.55 ! [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)) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__Suc__atLeastLessThan,axiom, % 1.40/1.55 ! [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)) ). % 1.40/1.55 % 1.40/1.55 fof(fact_image__add__atLeastLessThan,axiom, % 1.40/1.55 ! [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)) ). % 1.40/1.55 % 1.40/1.55 fof(fact_finite__nat__set__iff__bounded,axiom, % 1.40/1.55 ! [V_N_2] : % 1.40/1.55 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.40/1.55 <=> ? [B_m] : % 1.40/1.55 ! [B_x] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.40/1.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 1.40/1.55 ! [V_N_2] : % 1.40/1.55 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.40/1.55 <=> ? [B_m] : % 1.40/1.55 ! [B_x] : % 1.40/1.55 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.40/1.55 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x),B_m)) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_atLeastLessThan__eq__iff,axiom, % 1.40/1.55 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.40/1.55 ( class_Orderings_Olinorder(T_a) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2)) % 1.40/1.55 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2) % 1.40/1.55 <=> ( V_aa_2 = V_ca_2 % 1.40/1.55 & V_ba_2 = V_da_2 ) ) ) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 1.40/1.55 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.40/1.55 ( class_Orderings_Olinorder(T_a) % 1.40/1.55 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2)) % 1.40/1.55 => V_aa_2 = V_ca_2 ) ) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 1.40/1.55 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] : % 1.40/1.55 ( class_Orderings_Olinorder(T_a) % 1.40/1.55 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.40/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2)) % 1.40/1.55 => V_ba_2 = V_da_2 ) ) ) ) ). % 1.40/1.55 % 1.40/1.55 fof(fact_subset__card__intvl__is__intvl,axiom, % 1.40/1.55 ! [V_k_2,V_A_2] : % 1.40/1.55 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))))) % 1.40/1.55 => V_A_2 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))) ) ). % 1.40/1.55 % 1.40/1.55 %----Arity declarations (33) % 1.40/1.55 fof(arity_fun__Orderings_Opreorder,axiom, % 1.40/1.55 ! [T_2,T_1] : % 1.40/1.55 ( class_Orderings_Opreorder(T_1) % 1.40/1.55 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_fun__Finite__Set_Ofinite,axiom, % 1.40/1.55 ! [T_1,T_2] : % 1.40/1.55 ( ( class_Finite__Set_Ofinite(T_2) % 1.40/1.55 & class_Finite__Set_Ofinite(T_1) ) % 1.40/1.55 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_fun__Orderings_Oorder,axiom, % 1.40/1.55 ! [T_2,T_1] : % 1.40/1.55 ( class_Orderings_Oorder(T_1) % 1.40/1.55 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_fun__Orderings_Otop,axiom, % 1.40/1.55 ! [T_2,T_1] : % 1.40/1.55 ( class_Orderings_Otop(T_1) % 1.40/1.55 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_fun__Orderings_Oord,axiom, % 1.40/1.55 ! [T_2,T_1] : % 1.40/1.55 ( class_Orderings_Oord(T_1) % 1.40/1.55 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 1.40/1.55 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 1.40/1.55 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 1.40/1.55 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 1.40/1.55 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 1.40/1.55 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 1.40/1.55 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 1.40/1.55 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 1.40/1.55 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 1.40/1.55 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 1.40/1.55 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 1.40/1.55 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 1.40/1.55 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 1.40/1.55 class_Orderings_Opreorder(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 1.40/1.55 class_Orderings_Olinorder(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 1.40/1.55 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 1.40/1.55 class_Orderings_Oorder(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 1.40/1.55 class_Orderings_Oord(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 1.40/1.55 class_Groups_Ozero(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Nat__Onat__Groups_Oone,axiom, % 1.40/1.55 class_Groups_Oone(tc_Nat_Onat) ). % 1.40/1.55 % 1.40/1.55 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 1.40/1.55 class_Orderings_Opreorder(tc_HOL_Obool) ). % 1.40/1.55 % 1.40/1.55 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 1.40/1.55 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 1.40/1.55 % 1.40/1.55 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 1.40/1.55 class_Orderings_Oorder(tc_HOL_Obool) ). % 1.40/1.55 % 1.40/1.55 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 1.40/1.55 class_Orderings_Otop(tc_HOL_Obool) ). % 1.40/1.55 % 1.40/1.55 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 1.40/1.55 class_Orderings_Oord(tc_HOL_Obool) ). % 1.40/1.55 % 1.40/1.55 fof(arity_sum__Finite__Set_Ofinite,axiom, % 1.40/1.55 ! [T_1,T_2] : % 1.40/1.55 ( ( class_Finite__Set_Ofinite(T_2) % 1.40/1.55 & class_Finite__Set_Ofinite(T_1) ) % 1.40/1.55 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 1.40/1.55 ! [T_1] : % 1.40/1.55 ( class_Finite__Set_Ofinite(T_1) % 1.40/1.55 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_prod__Finite__Set_Ofinite,axiom, % 1.40/1.55 ! [T_1,T_2] : % 1.40/1.55 ( ( class_Finite__Set_Ofinite(T_2) % 1.40/1.55 & class_Finite__Set_Ofinite(T_1) ) % 1.40/1.55 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 1.40/1.55 % 1.40/1.55 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 1.40/1.55 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 1.40/1.55 % 1.40/1.55 %----Helper facts (8) % 1.40/1.55 fof(help_c__COMBI__1,axiom, % 1.40/1.55 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 1.40/1.55 % 1.40/1.55 fof(help_c__COMBK__1,axiom, % 1.40/1.55 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 1.40/1.55 % 1.40/1.55 fof(help_c__COMBB__1,axiom, % 1.40/1.55 ! [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)) ). % 1.40/1.55 % 1.40/1.55 fof(help_c__COMBC__1,axiom, % 1.40/1.55 ! [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) ). % 1.40/1.55 % 1.40/1.55 fof(help_c__COMBS__1,axiom, % 1.40/1.55 ! [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)) ). % 1.40/1.55 % 1.40/1.55 fof(help_c__fequal__1,axiom, % 1.40/1.55 ! [V_y_2,V_x_2] : % 1.40/1.55 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 1.40/1.55 | V_x_2 = V_y_2 ) ). % 1.40/1.55 % 1.40/1.55 fof(help_c__fequal__2,axiom, % 1.40/1.55 ! [V_y_2,V_x_2] : % 1.40/1.55 ( V_x_2 != V_y_2 % 1.40/1.55 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 1.40/1.55 % 1.40/1.55 fof(help_c__fFalse__1,axiom, % 1.40/1.55 ~ hBOOL(c_fFalse) ). % 1.40/1.55 % 1.40/1.55 %----Conjectures (1) % 1.40/1.55 fof(conj_0,conjecture, % 1.40/1.55 ! [B_i] : % 1.40/1.55 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.55 => 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____))) ) % 1.40/1.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.55 => ( ( hAPP(v_h____,B_i) = v_n____ % 1.40/1.55 => 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____))) ) % 1.40/1.55 & ( hAPP(v_h____,B_i) != v_n____ % 1.40/1.55 => 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____))) ) ) ) ) % 1.40/1.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.55 => 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____)) ) % 1.40/1.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____)) % 1.40/1.55 => 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____)) ) ) ) ). % 1.40/1.55 % 1.40/1.55 %------------------------------------------------------------------------------ % 1.40/1.55 %------------------------------------------- % 1.40/1.55 % Proof found % 1.40/1.55 % SZS status Theorem for theBenchmark % 1.40/1.55 % SZS output start Proof % 1.40/1.55 %ClaNum:1052(EqnAxiom:261) % 1.40/1.55 %VarNum:5267(SingletonVarNum:1735) % 1.40/1.55 %MaxLitNum:10 % 1.40/1.55 %MaxfuncDepth:12 % 1.40/1.55 %SharedTerms:284 % 1.40/1.55 %goalClause: 859 897 936 974 % 1.40/1.55 [262]P1(a1) % 1.40/1.55 [263]P2(a1) % 1.40/1.55 [264]P4(a2) % 1.40/1.55 [265]P5(a2) % 1.40/1.55 [266]P6(a2) % 1.40/1.55 [267]P13(a2) % 1.40/1.55 [268]P14(a2) % 1.40/1.55 [269]P15(a2) % 1.40/1.55 [270]P19(a2) % 1.40/1.55 [271]P20(a2) % 1.40/1.55 [272]P21(a2) % 1.40/1.55 [273]P21(a3) % 1.40/1.55 [274]P22(a2) % 1.40/1.55 [275]P22(a3) % 1.40/1.55 [276]P23(a2) % 1.40/1.55 [277]P27(a2) % 1.40/1.55 [278]P27(a3) % 1.40/1.55 [279]P28(a3) % 1.40/1.55 [280]P7(a3) % 1.40/1.55 [281]P7(a92) % 1.40/1.55 [282]P24(a2) % 1.40/1.55 [283]P31(a2) % 1.40/1.55 [284]P16(a2) % 1.40/1.55 [285]P17(a2) % 1.40/1.55 [286]P25(a2) % 1.40/1.55 [287]P29(a2) % 1.40/1.55 [288]P33(a2) % 1.40/1.55 [372]~E(a102,a100) % 1.40/1.55 [373]~E(a104,a103) % 1.40/1.55 [374]~P34(a40) % 1.40/1.55 [289]E(f21(f4(a2)),f4(a2)) % 1.40/1.55 [291]E(f28(a22,f4(a2)),f5(a2)) % 1.40/1.55 [297]P8(a90,f31(f94(a90,a3))) % 1.40/1.55 [328]P9(a90,a2,a97,f31(f94(a90,a3))) % 1.40/1.55 [329]P9(a90,a2,a45,f31(f94(a90,a3))) % 1.40/1.55 [298]E(f15(a92,f31(f94(a92,a3))),f5(a2)) % 1.40/1.55 [330]P34(f28(f28(f30(a2),a106),f15(a90,f31(f94(a90,a3))))) % 1.40/1.55 [331]P34(f28(f28(f30(a2),a77),f15(a90,f31(f94(a90,a3))))) % 1.40/1.55 [332]P34(f28(f28(f30(a2),a46),f15(a90,f31(f94(a90,a3))))) % 1.40/1.55 [339]E(f32(a2,f4(a2),f15(a90,f31(f94(a90,a3)))),f37(a90,a2,a97,f31(f94(a90,a3)))) % 1.40/1.55 [340]E(f32(a2,f4(a2),f15(a90,f31(f94(a90,a3)))),f37(a90,a2,a45,f31(f94(a90,a3)))) % 1.40/1.55 [344]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a98),a8)) % 1.40/1.55 [345]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a99),a8)) % 1.40/1.55 [346]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a88),a8)) % 1.40/1.55 [347]P34(f28(f28(f35(f94(f96(a91,a91),a3)),a89),a8)) % 1.40/1.55 [350]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98)) % 1.40/1.55 [351]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a88)) % 1.40/1.55 [352]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a99)) % 1.40/1.55 [353]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a89)) % 1.40/1.55 [391]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [392]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a98)) % 1.40/1.55 [355]E(f18(a90,f94(f96(a91,a91),a3),f31(f94(a90,a3)),f28(f16(f94(f94(f96(a91,a91),a3),a3),a90),a8)),a9) % 1.40/1.55 [358]P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),a101),a9)) % 1.40/1.55 [364]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,f28(f23(a90,a2,f31(f94(a90,a3)),a97),a106)))) % 1.40/1.55 [365]P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),a1),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8)))) % 1.40/1.55 [367]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a106),f5(a2))))),a98)),a99)))) % 1.40/1.55 [368]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a77),f5(a2))))),a98)),a99)))) % 1.40/1.55 [369]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),f28(f28(f20(a2),a46),f5(a2))))),a98)),a99)))) % 1.40/1.55 [370]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105)))))) % 1.40/1.55 [371]P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105)))),a9)) % 1.40/1.55 [319]P9(a2,a2,a22,x3191) % 1.40/1.55 [290]E(f27(a2,x2901),x2901) % 1.40/1.55 [376]~E(f28(a22,x3761),x3761) % 1.40/1.55 [382]~E(f28(a22,x3821),f4(a2)) % 1.40/1.55 [294]E(f28(f28(f20(a2),x2941),f4(a2)),x2941) % 1.40/1.55 [295]E(f29(a2,f28(a22,x2951)),f28(f30(a2),x2951)) % 1.40/1.55 [299]E(f28(f28(f20(a2),x2991),f5(a2)),f28(a22,x2991)) % 1.40/1.55 [301]P34(f28(f29(a2,x3011),x3011)) % 1.40/1.55 [309]P34(f28(f28(f30(a2),x3091),f28(a22,x3091))) % 1.40/1.55 [310]P34(f28(f28(f30(a2),f4(a2)),f28(a22,x3101))) % 1.40/1.55 [387]~P34(f28(f28(f30(a2),x3871),f4(a2))) % 1.40/1.55 [296]E(f28(f28(f20(a2),f4(a2)),x2961),x2961) % 1.40/1.55 [300]E(f28(f28(f20(a2),f5(a2)),x3001),f28(a22,x3001)) % 1.40/1.55 [303]P34(f28(f29(a2,f4(a2)),x3031)) % 1.40/1.55 [306]E(f28(f28(f20(a2),f21(x3061)),f28(a22,f4(a2))),f21(f28(a22,x3061))) % 1.40/1.55 [311]E(f28(f28(f20(a2),f27(a2,x3111)),f28(a22,f4(a2))),f27(a2,f28(a22,x3111))) % 1.40/1.55 [384]~P34(f28(f28(f30(a2),x3841),x3841)) % 1.40/1.55 [388]~P34(f28(f29(a2,f28(a22,x3881)),x3881)) % 1.40/1.55 [366]P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x3661))),a98)),a99)),a9)) % 1.40/1.55 [307]P8(a2,f32(a2,x3071,x3072)) % 1.40/1.55 [321]P9(x3211,x3211,f6(x3211),x3212) % 1.40/1.55 [293]E(f28(f6(x2931),x2932),x2932) % 1.40/1.55 [322]E(f37(x3221,x3221,f6(x3221),x3222),x3222) % 1.40/1.55 [338]E(f37(a2,a2,a22,f32(a2,x3381,x3382)),f32(a2,f28(a22,x3381),f28(a22,x3382))) % 1.40/1.55 [304]E(f28(f28(f20(a2),x3041),x3042),f28(f28(f20(a2),x3042),x3041)) % 1.40/1.55 [308]P34(f28(f31(f94(x3081,a3)),x3082)) % 1.40/1.55 [312]E(f28(f28(f20(a2),f28(a22,x3121)),x3122),f28(f28(f20(a2),x3121),f28(a22,x3122))) % 1.40/1.55 [314]P34(f28(f29(f94(x3141,a3),x3142),x3142)) % 1.40/1.55 [317]P34(f28(f28(f35(x3171),x3172),f31(f94(x3171,a3)))) % 1.40/1.55 [326]P34(f28(f29(f94(x3261,a3),x3262),f31(f94(x3261,a3)))) % 1.40/1.55 [337]E(f38(x3371,x3372,f31(f94(x3371,a3)),f31(f94(x3372,a3))),f31(f94(f95(x3371,x3372),a3))) % 1.40/1.55 [349]P9(a2,a2,f28(f28(f7(a2,a2,a2),f20(a2)),x3491),x3492) % 1.40/1.55 [313]E(f28(f28(f20(a2),x3131),f28(a22,x3132)),f28(a22,f28(f28(f20(a2),x3131),x3132))) % 1.40/1.55 [315]E(f28(f28(f20(a2),f28(a22,x3151)),x3152),f28(a22,f28(f28(f20(a2),x3151),x3152))) % 1.40/1.55 [323]P34(f28(f29(a2,x3231),f28(f28(f20(a2),x3232),x3231))) % 1.40/1.55 [324]P34(f28(f29(a2,x3241),f28(f28(f20(a2),x3241),x3242))) % 1.40/1.55 [341]P34(f28(f28(f30(a2),x3411),f28(a22,f28(f28(f20(a2),x3412),x3411)))) % 1.40/1.55 [342]P34(f28(f28(f30(a2),x3421),f28(a22,f28(f28(f20(a2),x3421),x3422)))) % 1.40/1.55 [361]P34(f28(f28(f35(f94(x3611,x3611)),f6(x3611)),f18(x3611,x3611,x3612,f28(f16(f94(x3611,a3),x3611),x3612)))) % 1.40/1.55 [389]~P34(f28(f28(f30(a2),f28(f28(f20(a2),x3891),x3892)),x3892)) % 1.40/1.55 [390]~P34(f28(f28(f30(a2),f28(f28(f20(a2),x3901),x3902)),x3901)) % 1.40/1.55 [318]E(f36(x3181,x3182,f36(x3181,x3182,x3183)),f36(x3181,x3182,x3183)) % 1.40/1.55 [320]E(f26(x3201,x3202,x3203,f4(a2)),x3202) % 1.40/1.55 [333]P34(f28(f28(f35(x3331),x3332),f36(x3331,x3332,x3333))) % 1.40/1.55 [336]P34(f28(f29(f94(x3361,a3),x3362),f36(x3361,x3363,x3362))) % 1.40/1.55 [325]E(f28(f28(f20(a2),x3251),f28(f28(f20(a2),x3252),x3253)),f28(f28(f20(a2),x3252),f28(f28(f20(a2),x3251),x3253))) % 1.40/1.55 [348]E(f18(x3481,x3482,x3483,f28(f16(f94(x3482,a3),x3481),f31(f94(x3482,a3)))),f31(f94(f94(x3481,x3482),a3))) % 1.40/1.55 [356]E(f37(a2,a2,f28(f28(f7(a2,a2,a2),f20(a2)),x3561),f32(a2,x3562,x3563)),f32(a2,f28(f28(f20(a2),x3562),x3561),f28(f28(f20(a2),x3563),x3561))) % 1.40/1.55 [335]E(f28(f28(f20(a2),f28(f28(f20(a2),x3351),x3352)),x3353),f28(f28(f20(a2),x3351),f28(f28(f20(a2),x3352),x3353))) % 1.40/1.55 [327]E(f26(x3271,x3272,x3273,f28(a22,x3274)),f28(x3273,x3274)) % 1.40/1.55 [334]E(f36(x3341,x3342,f36(x3341,x3343,x3344)),f36(x3341,x3343,f36(x3341,x3342,x3344))) % 1.40/1.55 [305]E(f28(f28(f16(x3051,x3052),x3053),x3054),x3053) % 1.40/1.55 [359]P34(f28(f28(f35(x3591),f28(x3592,x3593)),f37(x3594,x3591,x3592,f31(f94(x3594,a3))))) % 1.40/1.55 [354]E(f37(x3541,x3542,x3543,f36(x3541,x3544,x3545)),f36(x3542,f28(x3543,x3544),f37(x3541,x3542,x3543,x3545))) % 1.40/1.55 [362]E(f37(x3621,x3622,f28(f10(x3623,x3622,x3621,x3624),x3625),f31(f94(x3621,a3))),f37(x3623,x3622,x3624,f37(x3621,x3623,x3625,f31(f94(x3621,a3))))) % 1.40/1.55 [363]E(f28(f17(x3631,x3632,x3633,x3634,x3635),x3636),f28(f28(x3634,x3636),f28(x3635,x3636))) % 1.40/1.55 [357]E(f28(f28(f10(x3571,x3572,x3573,x3574),x3575),x3576),f28(x3574,f28(x3575,x3576))) % 1.40/1.55 [360]E(f37(x3601,x3602,x3603,f37(x3604,x3601,x3605,x3606)),f37(x3604,x3602,f28(f10(x3601,x3602,x3604,x3603),x3605),x3606)) % 1.40/1.55 [343]E(f28(f28(f28(f7(x3431,x3432,x3433),x3434),x3435),x3436),f28(f28(x3434,x3436),x3435)) % 1.40/1.55 [1049]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,a101)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105)))))) % 1.40/1.55 [1050]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,a101)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a1,f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a11),a101)),a105)),f17(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3),f17(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,a39),a97)),a106)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f28(f7(a90,a91,f94(a91,f94(f96(a91,a91),a3))),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(a91,f94(f96(a91,a91),a3))),a90,a12),a101)),a103)),a105)),f28(f28(f7(a90,a91,f94(f96(a91,a91),a3)),f28(f10(f94(f96(a91,a91),a3),f94(a91,f94(f96(a91,a91),a3)),a90,a13),a101)),a105)))))) % 1.40/1.55 [393]~P7(x3931)+P7(f93(x3931)) % 1.40/1.55 [395]~P31(x3951)+~E(f5(x3951),f4(x3951)) % 1.40/1.55 [452]~P4(x4521)+P34(f28(f29(x4521,f4(x4521)),f5(x4521))) % 1.40/1.55 [457]E(x4571,f4(a2))+~P34(f28(f29(a2,x4571),f4(a2))) % 1.40/1.55 [466]~P32(x4661)+P34(f28(f28(f35(x4661),f5(x4661)),f25(x4661))) % 1.40/1.55 [467]~P32(x4671)+P34(f28(f28(f35(x4671),f4(x4671)),f25(x4671))) % 1.40/1.55 [468]~P4(x4681)+P34(f28(f28(f30(x4681),f4(x4681)),f5(x4681))) % 1.40/1.55 [507]~P4(x5071)+~P34(f28(f29(x5071,f5(x5071)),f4(x5071))) % 1.40/1.55 [536]~P4(x5361)+~P34(f28(f28(f30(x5361),f5(x5361)),f4(x5361))) % 1.40/1.55 [445]E(x4451,f4(a2))+P34(f28(f28(f30(a2),f4(a2)),x4451)) % 1.40/1.55 [503]E(f28(a22,f57(x5031)),x5031)+~P34(f28(f28(f30(a2),f4(a2)),x5031)) % 1.40/1.55 [515]~P8(x5151,f31(f94(x5151,a3)))+P8(f93(x5151),f31(f94(f93(x5151),a3))) % 1.40/1.55 [522]P8(x5221,f31(f94(x5221,a3)))+~P8(f93(x5221),f31(f94(f93(x5221),a3))) % 1.40/1.55 [543]E(x5431,f4(a2))+~P34(f28(f28(f30(a2),x5431),f28(a22,f4(a2)))) % 1.40/1.55 [649]~P4(x6491)+P34(f28(f28(f30(x6491),f4(x6491)),f28(f28(f20(x6491),f5(x6491)),f5(x6491)))) % 1.40/1.55 [822]P1(x8221)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f59(x8221)),a9)) % 1.40/1.55 [823]P2(x8231)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f60(x8231)),a9)) % 1.40/1.55 [824]P2(x8241)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f61(x8241)),a9)) % 1.40/1.55 [839]P1(x8391)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f58(x8391)),f65(x8391))),f28(x8391,f59(x8391)))) % 1.40/1.55 [670]~P8(x6701,f31(f94(x6701,a3)))+P34(f28(f28(f30(a2),f4(a2)),f15(x6701,f31(f94(x6701,a3))))) % 1.40/1.55 [911]~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9111),a8))+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f28(f16(f94(f96(a91,a91),a3),a90),x9111)),a9)) % 1.40/1.55 [1046]~P34(f28(f29(a2,x10461),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x10461))),a98)),a99)))) % 1.40/1.55 [1047]~P34(f28(f29(a2,x10471),a77))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x10471))),a98)),a99)))) % 1.40/1.55 [1048]~P34(f28(f29(a2,x10481),a46))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),f28(a1,f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f96(a91,a91),a3)),f28(f28(f7(a90,f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),f28(f10(a3,f94(f94(f96(a91,a91),a3),f94(f94(f96(a91,a91),a3),f94(f96(a91,a91),a3))),a90,f24(f94(f96(a91,a91),a3))),f28(f28(f7(a90,a2,a3),f28(f10(a2,f94(a2,a3),a90,f30(a2)),a97)),x10481))),a98)),a99)))) % 1.40/1.55 [397]~P7(x3971)+P8(x3971,x3972) % 1.40/1.55 [399]P8(x3991,x3992)+E(f15(x3991,x3992),f4(a2)) % 1.40/1.55 [400]~P21(x4002)+P21(f94(x4001,x4002)) % 1.40/1.55 [401]~P22(x4012)+P22(f94(x4011,x4012)) % 1.40/1.55 [402]~P27(x4022)+P27(f94(x4021,x4022)) % 1.40/1.55 [403]~P28(x4032)+P28(f94(x4031,x4032)) % 1.40/1.55 [405]E(x4051,x4052)+~E(f28(a22,x4051),f28(a22,x4052)) % 1.40/1.55 [410]~P16(x4101)+E(f28(f28(f20(x4101),x4102),f4(x4101)),x4102) % 1.40/1.55 [411]~P17(x4111)+E(f28(f28(f20(x4111),x4112),f4(x4111)),x4112) % 1.40/1.55 [412]~P29(x4121)+E(f28(f28(f20(x4121),x4122),f4(x4121)),x4122) % 1.40/1.55 [421]~E(x4211,x4212)+P34(f28(f28(a39,x4211),x4212)) % 1.40/1.55 [424]~E(x4241,x4242)+P34(f28(f29(a2,x4241),x4242)) % 1.40/1.55 [429]~P21(x4291)+P34(f28(f29(x4291,x4292),x4292)) % 1.40/1.55 [441]~P28(x4411)+P34(f28(f29(x4411,x4412),f31(x4411))) % 1.40/1.55 [451]E(x4511,x4512)+~P34(f28(f28(a39,x4511),x4512)) % 1.40/1.55 [453]E(x4531,x4532)+~E(f28(x4531,f47(x4532,x4531)),f28(x4532,f47(x4532,x4531))) % 1.40/1.55 [458]P3(x4581,x4582)+~E(f28(x4581,f48(x4582,x4581)),f28(f48(x4582,x4581),x4582)) % 1.40/1.55 [460]~E(x4601,x4602)+P34(f28(f28(f30(a2),x4601),f28(a22,x4602))) % 1.40/1.55 [463]~E(x4631,f4(a2))+P34(f28(f28(f30(a2),x4631),f28(a22,x4632))) % 1.40/1.55 [475]P34(f28(f29(a2,x4752),x4751))+P34(f28(f29(a2,x4751),x4752)) % 1.40/1.55 [506]E(f28(f28(f20(a2),x5061),f55(x5062,x5061)),x5062)+~P34(f28(f29(a2,x5061),x5062)) % 1.40/1.55 [540]~P34(f28(f29(a2,x5401),x5402))+P34(f28(f29(a2,x5401),f28(a22,x5402))) % 1.40/1.55 [564]~P34(f28(f29(a2,x5641),x5642))+P34(f28(f28(f30(a2),x5641),f28(a22,x5642))) % 1.40/1.55 [565]P8(x5651,x5652)+~P34(f28(f28(f30(a2),f4(a2)),f15(x5651,x5652))) % 1.40/1.55 [584]P34(f28(f29(a2,x5841),x5842))+~P34(f28(f28(f30(a2),x5841),f28(a22,x5842))) % 1.40/1.55 [609]~P34(f28(f29(a2,x6091),x6092))+P34(f28(f29(a2,f28(a22,x6091)),f28(a22,x6092))) % 1.40/1.55 [648]P34(f28(f29(a2,x6481),x6482))+~P34(f28(f29(a2,f28(a22,x6481)),f28(a22,x6482))) % 1.40/1.55 [982]~P8(x9821,x9822)+E(f19(a2,x9821,f20(a2),f28(f16(a2,x9821),f5(a2)),f4(a2),x9822),f15(x9821,x9822)) % 1.40/1.55 [416]~P16(x4161)+E(f28(f28(f20(x4161),f4(x4161)),x4162),x4162) % 1.40/1.55 [417]~P17(x4171)+E(f28(f28(f20(x4171),f4(x4171)),x4172),x4172) % 1.40/1.55 [418]~P29(x4181)+E(f28(f28(f20(x4181),f4(x4181)),x4182),x4182) % 1.40/1.55 [420]E(x4201,f4(a2))+~E(f28(f28(f20(a2),x4202),x4201),x4202) % 1.40/1.55 [425]E(x4251,f4(a2))+~E(f28(f28(f20(a2),x4252),x4251),f4(a2)) % 1.40/1.55 [426]E(x4261,f4(a2))+~E(f28(f28(f20(a2),x4261),x4262),f4(a2)) % 1.40/1.55 [454]~E(x4541,f28(a22,x4542))+P34(f28(f28(f30(a2),f4(a2)),x4541)) % 1.40/1.55 [474]~E(x4741,x4742)+~P34(f28(f28(f30(a2),x4741),x4742)) % 1.40/1.55 [476]~E(x4761,f4(a2))+~P34(f28(f28(f30(a2),x4762),x4761)) % 1.40/1.55 [488]~P21(x4881)+~P34(f28(f28(f30(x4881),x4882),x4882)) % 1.40/1.55 [517]P8(a2,x5171)+P34(f28(f28(f35(a2),f78(x5171,x5172)),x5171)) % 1.40/1.55 [518]P8(a2,x5181)+P34(f28(f28(f35(a2),f82(x5181,x5182)),x5181)) % 1.40/1.55 [535]P34(f28(f29(a2,x5351),x5352))+~P34(f28(f28(f30(a2),x5351),x5352)) % 1.40/1.55 [537]P34(f28(f28(f30(a2),x5372),f28(a22,x5371)))+P34(f28(f28(f30(a2),x5371),x5372)) % 1.40/1.55 [544]P34(f28(f29(a2,x5441),x5442))+P34(f28(f29(a2,f28(a22,x5442)),x5441)) % 1.40/1.55 [579]P34(f28(f28(f30(a2),x5791),f28(a22,x5792)))+~P34(f28(f28(f30(a2),x5791),x5792)) % 1.40/1.55 [583]P8(a2,x5831)+~P34(f28(f29(a2,f82(x5831,x5832)),x5832)) % 1.40/1.55 [585]E(f28(a22,f28(f28(f20(a2),x5851),f71(x5852,x5851))),x5852)+~P34(f28(f28(f30(a2),x5851),x5852)) % 1.40/1.55 [598]~P34(f28(f28(f30(a2),x5981),x5982))+P34(f28(f29(a2,f28(a22,x5981)),x5982)) % 1.40/1.55 [605]P8(a2,x6051)+~P34(f28(f28(f30(a2),f78(x6051,x6052)),x6052)) % 1.40/1.55 [611]P34(f28(f29(a2,x6111),x6112))+~P34(f28(f29(a2,f28(a22,x6111)),x6112)) % 1.40/1.55 [613]~P4(x6131)+P34(f28(f28(f30(x6131),x6132),f28(f28(f20(x6131),x6132),f5(x6131)))) % 1.40/1.55 [627]P34(f28(f28(f30(a2),x6271),x6272))+~P34(f28(f29(a2,f28(a22,x6271)),x6272)) % 1.40/1.55 [628]~P34(f28(f28(f30(a2),x6282),f28(a22,x6281)))+~P34(f28(f28(f30(a2),x6281),x6282)) % 1.40/1.55 [629]P8(x6291,f31(f94(x6291,a3)))+~P8(f94(x6292,x6291),f31(f94(f94(x6292,x6291),a3))) % 1.40/1.55 [630]P8(x6301,f31(f94(x6301,a3)))+~P8(f95(x6302,x6301),f31(f94(f95(x6302,x6301),a3))) % 1.40/1.55 [631]P8(x6311,f31(f94(x6311,a3)))+~P8(f95(x6311,x6312),f31(f94(f95(x6311,x6312),a3))) % 1.40/1.55 [637]P34(f28(f28(f30(a2),f28(a22,x6371)),f28(a22,x6372)))+~P34(f28(f28(f30(a2),x6371),x6372)) % 1.40/1.55 [638]~P34(f28(f29(a2,x6381),x6382))+~P34(f28(f29(a2,f28(a22,x6382)),x6381)) % 1.40/1.55 [639]P34(f28(f28(f30(a2),x6391),x6392))+~P34(f28(f28(f30(a2),f28(a22,x6391)),x6392)) % 1.40/1.55 [668]~P34(f28(f28(f30(a2),f28(a22,x6681)),f28(a22,x6682)))+P34(f28(f28(f30(a2),x6681),x6682)) % 1.40/1.55 [750]P34(f26(a3,a40,f29(a2,x7501),x7502))+~P34(f28(f29(a2,f28(a22,x7501)),x7502)) % 1.40/1.55 [783]~P34(f26(a3,a40,f29(a2,x7831),x7832))+P34(f28(f29(a2,f28(a22,x7831)),x7832)) % 1.40/1.55 [805]P1(x8051)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f58(x8051)),f65(x8051))),f28(f59(x8051),x8052))) % 1.40/1.55 [828]P3(x8281,x8282)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f48(x8282,x8281)),a9)) % 1.40/1.55 [831]E(f32(a2,x8311,f28(f28(f20(a2),x8311),f15(a2,x8312))),x8312)+~P34(f28(f29(f94(a2,a3),x8312),f32(a2,x8311,f28(f28(f20(a2),x8311),f15(a2,x8312))))) % 1.40/1.55 [844]P34(f28(f28(f35(f94(f96(a91,a91),a3)),f28(f28(a11,x8441),x8442)),a8))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8441),a8)) % 1.40/1.55 [845]P34(f28(f28(f35(f94(f96(a91,a91),a3)),f28(f28(a13,x8451),x8452)),a8))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8451),a8)) % 1.40/1.55 [462]~P8(x4621,x4623)+P8(x4621,f36(x4621,x4622,x4623)) % 1.40/1.55 [516]P8(x5161,x5162)+~P8(x5161,f36(x5161,x5163,x5162)) % 1.40/1.55 [478]~E(x4782,x4783)+P34(f28(f28(f35(x4781),x4782),f28(a39,x4783))) % 1.40/1.55 [541]E(x5411,x5412)+~P34(f28(f28(f35(x5413),x5411),f28(a39,x5412))) % 1.40/1.55 [963]P8(x9631,x9632)+~P34(f28(f28(f35(f96(f94(x9631,a3),f94(x9631,a3))),f28(f28(f33(f94(x9631,a3),f94(x9631,a3)),x9633),x9632)),f42(x9631))) % 1.40/1.55 [427]~P28(x4272)+E(f28(f31(f94(x4271,x4272)),x4273),f31(x4272)) % 1.40/1.55 [446]~P29(x4461)+E(f28(f28(f20(x4461),x4462),x4463),f28(f28(f20(x4461),x4463),x4462)) % 1.40/1.55 [464]E(x4641,x4642)+~E(f28(f28(f20(a2),x4643),x4641),f28(f28(f20(a2),x4643),x4642)) % 1.40/1.55 [465]E(x4651,x4652)+~E(f28(f28(f20(a2),x4651),x4653),f28(f28(f20(a2),x4652),x4653)) % 1.40/1.55 [469]~E(x4692,f28(f28(f20(a2),x4691),x4693))+P34(f28(f29(a2,x4691),x4692)) % 1.40/1.55 [477]~P34(f28(x4773,x4772))+P34(f28(f28(f35(x4771),x4772),x4773)) % 1.40/1.55 [489]~E(x4893,x4892)+P34(f28(f29(f94(x4891,a3),x4892),x4893)) % 1.40/1.55 [495]~E(x4952,x4953)+P34(f28(f29(f94(x4951,a3),x4952),x4953)) % 1.40/1.55 [513]P34(f28(x5131,x5132))+~P34(f28(f28(f35(x5133),x5132),x5131)) % 1.40/1.55 [530]E(f36(x5301,x5302,x5303),x5303)+~P34(f28(f28(f35(x5301),x5302),x5303)) % 1.40/1.55 [719]~P8(x7191,x7192)+P34(f28(f29(a2,f15(x7191,x7192)),f15(x7191,f36(x7191,x7193,x7192)))) % 1.40/1.55 [801]E(x8011,x8012)+~E(f28(f28(f7(x8013,f94(x8013,a3),a3),f35(x8013)),x8011),f28(f28(f7(x8013,f94(x8013,a3),a3),f35(x8013)),x8012)) % 1.40/1.55 [827]~P9(x8272,x8271,x8273,f31(f94(x8272,a3)))+E(f37(x8271,x8272,f23(x8272,x8271,f31(f94(x8272,a3)),x8273),f31(f94(x8271,a3))),f31(f94(x8272,a3))) % 1.40/1.55 [829]P9(x8291,x8292,f23(x8292,x8291,f31(f94(x8292,a3)),x8293),f31(f94(x8291,a3)))+~E(f37(x8292,x8291,x8293,f31(f94(x8292,a3))),f31(f94(x8291,a3))) % 1.40/1.55 [875]~E(f28(x8753,f28(f23(x8751,x8752,f31(f94(x8751,a3)),x8753),f73(x8753,x8752,x8751))),f73(x8753,x8752,x8751))+E(f37(x8751,x8752,x8753,f31(f94(x8751,a3))),f31(f94(x8752,a3))) % 1.40/1.55 [560]~E(x5602,f28(a22,f28(f28(f20(a2),x5601),x5603)))+P34(f28(f28(f30(a2),x5601),x5602)) % 1.40/1.55 [633]~P34(f28(f29(a2,x6331),x6333))+P34(f28(f29(a2,x6331),f28(f28(f20(a2),x6332),x6333))) % 1.40/1.55 [635]~P34(f28(f29(a2,x6351),x6352))+P34(f28(f29(a2,x6351),f28(f28(f20(a2),x6352),x6353))) % 1.40/1.55 [657]~P34(f28(f28(f30(a2),x6571),x6573))+P34(f28(f28(f30(a2),x6571),f28(f28(f20(a2),x6572),x6573))) % 1.40/1.55 [659]~P34(f28(f28(f30(a2),x6591),x6592))+P34(f28(f28(f30(a2),x6591),f28(f28(f20(a2),x6592),x6593))) % 1.40/1.55 [669]~E(x6691,x6692)+~P34(f28(f28(f30(f94(x6693,a3)),x6691),x6692)) % 1.40/1.55 [709]P34(f28(f29(f94(x7091,a3),x7092),x7093))+~P34(f28(f28(f30(f94(x7091,a3)),x7092),x7093)) % 1.40/1.55 [732]~P34(f28(f29(a2,x7322),x7323))+P34(f28(f29(a2,f28(f28(f20(a2),x7321),x7322)),f28(f28(f20(a2),x7321),x7323))) % 1.40/1.55 [733]~P34(f28(f29(a2,x7331),x7333))+P34(f28(f29(a2,f28(f28(f20(a2),x7331),x7332)),f28(f28(f20(a2),x7333),x7332))) % 1.40/1.55 [744]~P34(f28(f28(f30(a2),x7442),x7443))+P34(f28(f28(f30(a2),f28(f28(f20(a2),x7441),x7442)),f28(f28(f20(a2),x7441),x7443))) % 1.40/1.55 [745]~P34(f28(f28(f30(a2),x7451),x7453))+P34(f28(f28(f30(a2),f28(f28(f20(a2),x7451),x7452)),f28(f28(f20(a2),x7453),x7452))) % 1.40/1.55 [790]P34(f28(f29(a2,x7901),x7902))+~P34(f28(f29(a2,f28(f28(f20(a2),x7903),x7901)),f28(f28(f20(a2),x7903),x7902))) % 1.40/1.55 [800]P34(f28(f28(f30(a2),x8001),x8002))+~P34(f28(f28(f30(a2),f28(f28(f20(a2),x8003),x8001)),f28(f28(f20(a2),x8003),x8002))) % 1.40/1.55 [950]~P34(f28(f29(f94(x9501,a3),x9502),x9503))+P34(f28(f29(f94(x9501,a3),f28(f28(f7(x9501,f94(x9501,a3),a3),f35(x9501)),x9502)),f28(f28(f7(x9501,f94(x9501,a3),a3),f35(x9501)),x9503))) % 1.40/1.55 [971]~P34(f28(f28(f35(f96(f94(x9711,a3),f94(x9711,a3))),f28(f28(f33(f94(x9711,a3),f94(x9711,a3)),x9712),x9713)),f42(x9711)))+P34(f28(f28(f30(f94(x9711,a3)),x9712),x9713)) % 1.40/1.55 [991]P34(f28(f29(f94(x9911,a3),x9912),x9913))+~P34(f28(f29(f94(x9911,a3),f28(f28(f7(x9911,f94(x9911,a3),a3),f35(x9911)),x9912)),f28(f28(f7(x9911,f94(x9911,a3),a3),f35(x9911)),x9913))) % 1.40/1.55 [737]P34(f28(f29(a2,x7371),x7372))+~P34(f28(f29(a2,f28(f28(f20(a2),x7373),x7371)),x7372)) % 1.40/1.55 [738]P34(f28(f29(a2,x7381),x7382))+~P34(f28(f29(a2,f28(f28(f20(a2),x7381),x7383)),x7382)) % 1.40/1.55 [752]P34(f28(f28(f30(a2),x7521),x7522))+~P34(f28(f28(f30(a2),f28(f28(f20(a2),x7521),x7523)),x7522)) % 1.40/1.55 [685]~P8(x6852,x6854)+P8(x6851,f37(x6852,x6851,x6853,x6854)) % 1.40/1.55 [759]P8(x7591,x7592)+~P8(f95(x7593,x7591),f38(x7593,x7591,x7594,x7592)) % 1.40/1.55 [760]P8(x7601,x7602)+~P8(f95(x7601,x7603),f38(x7601,x7603,x7602,x7604)) % 1.40/1.55 [788]P9(x7881,x7882,x7883,x7884)+~E(f49(x7884,x7883,x7882,x7881),f50(x7884,x7883,x7882,x7881)) % 1.40/1.55 [554]~E(x5542,x5544)+P34(f28(f36(x5541,x5542,x5543),x5544)) % 1.40/1.55 [582]~P34(f28(x5823,x5824))+P34(f28(f36(x5821,x5822,x5823),x5824)) % 1.40/1.55 [604]~E(x6042,x6043)+P34(f28(f28(f35(x6041),x6042),f36(x6041,x6043,x6044))) % 1.40/1.55 [696]P8(x6962,x6964)+E(f15(f95(x6961,x6962),f38(x6961,x6962,x6963,x6964)),f4(a2)) % 1.40/1.55 [697]P8(x6971,x6973)+E(f15(f95(x6971,x6972),f38(x6971,x6972,x6973,x6974)),f4(a2)) % 1.40/1.55 [773]~P9(x7732,x7731,x7733,x7734)+E(f15(x7731,f37(x7732,x7731,x7733,x7734)),f15(x7732,x7734)) % 1.40/1.55 [803]~P9(x8031,x8032,x8033,f31(f94(x8031,a3)))+E(f28(f23(x8031,x8032,f31(f94(x8031,a3)),x8033),f28(x8033,x8034)),x8034) % 1.40/1.55 [818]P9(x8184,x8183,x8181,x8182)+E(f28(x8181,f49(x8182,x8181,x8183,x8184)),f28(x8181,f50(x8182,x8181,x8183,x8184))) % 1.40/1.55 [830]P34(f28(f28(f35(f96(x8301,x8301)),f28(f28(f33(x8301,x8301),x8302),x8303)),f41(x8301,x8304)))+~P34(f28(f28(f30(a2),f28(x8304,x8302)),f28(x8304,x8303))) % 1.40/1.55 [841]~P9(x8412,x8411,x8413,f31(f94(x8412,a3)))+E(f37(x8411,x8412,f23(x8412,x8411,f31(f94(x8412,a3)),x8413),f37(x8412,x8411,x8413,x8414)),x8414) % 1.40/1.55 [848]~P34(f28(f28(f35(f96(x8484,x8484)),f28(f28(f33(x8484,x8484),x8482),x8483)),f41(x8484,x8481)))+P34(f28(f28(f30(a2),f28(x8481,x8482)),f28(x8481,x8483))) % 1.40/1.55 [944]~P8(x9442,x9444)+P34(f28(f29(a2,f15(x9441,f37(x9442,x9441,x9443,x9444))),f15(x9442,x9444))) % 1.40/1.55 [988]~P9(x9881,x9882,x9883,x9884)+~P34(f28(f28(f30(a2),f15(x9882,f37(x9881,x9882,x9883,x9884))),f15(x9881,x9884))) % 1.40/1.55 [675]P34(f28(f28(f35(x6751),x6752),f36(x6751,x6753,x6754)))+~P34(f28(f28(f35(x6751),x6752),x6754)) % 1.40/1.55 [714]P34(f28(f29(f94(x7141,a3),x7142),f36(x7141,x7143,x7144)))+~P34(f28(f29(f94(x7141,a3),x7142),x7144)) % 1.40/1.55 [793]P34(f28(f28(f35(x7931),x7932),x7933))+~P34(f28(f29(f94(x7931,a3),f36(x7931,x7932,x7934)),x7933)) % 1.40/1.55 [795]P34(f28(f29(f94(x7951,a3),f36(x7951,x7952,x7953)),f36(x7951,x7952,x7954)))+~P34(f28(f29(f94(x7951,a3),x7953),x7954)) % 1.40/1.55 [804]~P34(f28(f29(f94(x8041,a3),f36(x8041,x8044,x8042)),x8043))+P34(f28(f29(f94(x8041,a3),x8042),x8043)) % 1.40/1.55 [832]~E(x8321,x8322)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8323),x8321)),f28(f28(a13,x8324),x8322))) % 1.40/1.55 [833]~E(x8331,x8332)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8331),x8333)),f28(f28(a11,x8334),x8332))) % 1.40/1.55 [850]~P9(x8501,x8503,x8504,f31(f94(x8501,a3)))+P9(x8501,f94(x8502,x8503),f28(f10(x8503,f94(x8502,x8503),x8501,f16(x8503,x8502)),x8504),f31(f94(x8501,a3))) % 1.40/1.55 [860]P9(x8601,x8602,x8603,x8604)+P34(f28(f28(f35(x8601),f49(x8604,x8603,x8602,x8601)),x8604)) % 1.40/1.55 [861]P9(x8611,x8612,x8613,x8614)+P34(f28(f28(f35(x8611),f50(x8614,x8613,x8612,x8611)),x8614)) % 1.40/1.55 [595]~P29(x5951)+E(f28(f28(f20(x5951),x5952),f28(f28(f20(x5951),x5953),x5954)),f28(f28(f20(x5951),x5953),f28(f28(f20(x5951),x5952),x5954))) % 1.40/1.55 [653]~P6(x6531)+E(f28(f28(f20(x6531),f28(f28(f20(x6531),x6532),x6533)),x6534),f28(f28(f20(x6531),x6532),f28(f28(f20(x6531),x6533),x6534))) % 1.40/1.55 [654]~P29(x6541)+E(f28(f28(f20(x6541),f28(f28(f20(x6541),x6542),x6543)),x6544),f28(f28(f20(x6541),x6542),f28(f28(f20(x6541),x6543),x6544))) % 1.40/1.55 [683]~P29(x6831)+E(f28(f28(f20(x6831),f28(f28(f20(x6831),x6832),x6833)),x6834),f28(f28(f20(x6831),f28(f28(f20(x6831),x6832),x6834)),x6833)) % 1.40/1.55 [838]~E(f37(x8382,x8383,x8381,f31(f94(x8382,a3))),f31(f94(x8383,a3)))+E(f28(x8381,f28(f23(x8382,x8383,f31(f94(x8382,a3)),x8381),x8384)),x8384) % 1.40/1.55 [867]~E(f37(x8671,x8672,x8673,f31(f94(x8671,a3))),f31(f94(x8672,a3)))+E(f37(x8671,x8672,x8673,f37(x8672,x8671,f23(x8671,x8672,f31(f94(x8671,a3)),x8673),x8674)),x8674) % 1.40/1.55 [1038]E(x10381,x10382)+~E(f28(f28(f7(x10383,f94(f96(x10383,x10384),a3),f94(x10384,a3)),f28(f10(f94(x10384,f94(f94(f96(x10383,x10384),a3),a3)),f94(f94(f96(x10383,x10384),a3),f94(x10384,a3)),x10383,f7(x10384,f94(f96(x10383,x10384),a3),a3)),f28(f10(f94(x10384,f96(x10383,x10384)),f94(x10384,f94(f94(f96(x10383,x10384),a3),a3)),x10383,f10(f96(x10383,x10384),f94(f94(f96(x10383,x10384),a3),a3),x10384,f35(f96(x10383,x10384)))),f33(x10383,x10384)))),x10381),f28(f28(f7(x10383,f94(f96(x10383,x10384),a3),f94(x10384,a3)),f28(f10(f94(x10384,f94(f94(f96(x10383,x10384),a3),a3)),f94(f94(f96(x10383,x10384),a3),f94(x10384,a3)),x10383,f7(x10384,f94(f96(x10383,x10384),a3),a3)),f28(f10(f94(x10384,f96(x10383,x10384)),f94(x10384,f94(f94(f96(x10383,x10384),a3),a3)),x10383,f10(f96(x10383,x10384),f94(f94(f96(x10383,x10384),a3),a3),x10384,f35(f96(x10383,x10384)))),f33(x10383,x10384)))),x10382)) % 1.40/1.55 [1044]~P34(f28(f29(f94(f96(x10441,x10442),a3),x10443),x10444))+P34(f28(f29(f94(x10441,f94(x10442,a3)),f28(f28(f7(x10441,f94(f96(x10441,x10442),a3),f94(x10442,a3)),f28(f10(f94(x10442,f94(f94(f96(x10441,x10442),a3),a3)),f94(f94(f96(x10441,x10442),a3),f94(x10442,a3)),x10441,f7(x10442,f94(f96(x10441,x10442),a3),a3)),f28(f10(f94(x10442,f96(x10441,x10442)),f94(x10442,f94(f94(f96(x10441,x10442),a3),a3)),x10441,f10(f96(x10441,x10442),f94(f94(f96(x10441,x10442),a3),a3),x10442,f35(f96(x10441,x10442)))),f33(x10441,x10442)))),x10443)),f28(f28(f7(x10441,f94(f96(x10441,x10442),a3),f94(x10442,a3)),f28(f10(f94(x10442,f94(f94(f96(x10441,x10442),a3),a3)),f94(f94(f96(x10441,x10442),a3),f94(x10442,a3)),x10441,f7(x10442,f94(f96(x10441,x10442),a3),a3)),f28(f10(f94(x10442,f96(x10441,x10442)),f94(x10442,f94(f94(f96(x10441,x10442),a3),a3)),x10441,f10(f96(x10441,x10442),f94(f94(f96(x10441,x10442),a3),a3),x10442,f35(f96(x10441,x10442)))),f33(x10441,x10442)))),x10444))) % 1.40/1.55 [1045]P34(f28(f29(f94(f96(x10451,x10452),a3),x10453),x10454))+~P34(f28(f29(f94(x10451,f94(x10452,a3)),f28(f28(f7(x10451,f94(f96(x10451,x10452),a3),f94(x10452,a3)),f28(f10(f94(x10452,f94(f94(f96(x10451,x10452),a3),a3)),f94(f94(f96(x10451,x10452),a3),f94(x10452,a3)),x10451,f7(x10452,f94(f96(x10451,x10452),a3),a3)),f28(f10(f94(x10452,f96(x10451,x10452)),f94(x10452,f94(f94(f96(x10451,x10452),a3),a3)),x10451,f10(f96(x10451,x10452),f94(f94(f96(x10451,x10452),a3),a3),x10452,f35(f96(x10451,x10452)))),f33(x10451,x10452)))),x10453)),f28(f28(f7(x10451,f94(f96(x10451,x10452),a3),f94(x10452,a3)),f28(f10(f94(x10452,f94(f94(f96(x10451,x10452),a3),a3)),f94(f94(f96(x10451,x10452),a3),f94(x10452,a3)),x10451,f7(x10452,f94(f96(x10451,x10452),a3),a3)),f28(f10(f94(x10452,f96(x10451,x10452)),f94(x10452,f94(f94(f96(x10451,x10452),a3),a3)),x10451,f10(f96(x10451,x10452),f94(f94(f96(x10451,x10452),a3),a3),x10452,f35(f96(x10451,x10452)))),f33(x10451,x10452)))),x10454))) % 1.40/1.55 [836]P34(f28(f28(f35(f96(x8361,x8361)),f28(f28(f33(x8361,x8361),x8362),x8363)),f44(x8361,x8364,x8365)))+~P34(f28(f28(f30(a2),f28(x8364,x8362)),f28(x8364,x8363))) % 1.40/1.55 [856]E(f28(x8561,f72(x8562,x8561,x8563,x8564)),x8564)+~P34(f28(f28(f35(x8565),x8564),f37(x8563,x8565,x8561,x8562))) % 1.40/1.55 [874]P9(x8741,x8742,f23(x8742,x8741,x8743,x8744),x8745)+~P34(f28(f29(f94(x8741,a3),x8745),f37(x8742,x8741,x8744,x8743))) % 1.40/1.55 [948]E(f37(x9481,x9482,x9483,f76(x9484,x9483,x9481,x9485,x9482)),x9485)+~P34(f28(f29(f94(x9482,a3),x9485),f37(x9481,x9482,x9483,x9484))) % 1.40/1.55 [782]E(f36(x7821,f28(x7822,x7823),f37(x7824,x7821,x7822,x7825)),f37(x7824,x7821,x7822,x7825))+~P34(f28(f28(f35(x7824),x7823),x7825)) % 1.40/1.55 [826]P34(f28(f28(f35(x8261),f28(x8262,x8263)),f37(x8264,x8261,x8262,x8265)))+~P34(f28(f28(f35(x8264),x8263),x8265)) % 1.40/1.55 [878]E(f28(x8781,f28(f23(x8782,x8783,x8784,x8781),x8785)),x8785)+~P34(f28(f28(f35(x8783),x8785),f37(x8782,x8783,x8781,x8784))) % 1.40/1.55 [900]P34(f28(f29(f94(x9001,a3),f37(x9002,x9001,x9003,x9004)),f37(x9002,x9001,x9003,x9005)))+~P34(f28(f29(f94(x9002,a3),x9004),x9005)) % 1.40/1.55 [916]~P8(x9163,f37(x9162,x9163,x9165,f31(f94(x9162,a3))))+P8(x9161,f37(x9162,x9161,f28(f10(x9163,x9161,x9162,x9164),x9165),f31(f94(x9162,a3)))) % 1.40/1.55 [923]P34(f28(f29(f94(f94(x9231,x9232),a3),f18(x9231,x9232,x9233,x9234)),f18(x9231,x9232,x9235,x9234)))+~P34(f28(f29(f94(x9231,a3),x9235),x9233)) % 1.40/1.55 [933]~P34(f28(f28(f35(x9335),x9334),f37(x9331,x9335,x9333,x9332)))+P34(f28(f28(f35(x9331),f72(x9332,x9333,x9331,x9334)),x9332)) % 1.40/1.55 [1009]P34(f28(f28(f35(f94(x10091,x10094)),x10093),f18(x10091,x10094,x10095,x10092)))+P34(f28(f28(f35(x10091),f66(x10092,x10093,x10094,x10095,x10091)),x10095)) % 1.40/1.55 [1010]~P34(f28(f29(f94(x10105,a3),x10104),f37(x10101,x10105,x10103,x10102)))+P34(f28(f29(f94(x10101,a3),f76(x10102,x10103,x10101,x10104,x10105)),x10102)) % 1.40/1.55 [1013]P34(f28(f29(f94(f94(x10131,x10134),a3),f18(x10131,x10134,x10135,x10133)),f18(x10131,x10134,x10135,x10132)))+P34(f28(f28(f35(x10131),f67(x10132,x10133,x10134,x10135,x10131)),x10135)) % 1.40/1.55 [1031]P34(f28(f28(f35(f94(x10311,x10312)),x10313),f18(x10311,x10312,x10314,x10315)))+~P34(f28(f28(f35(x10312),f28(x10313,f66(x10315,x10313,x10312,x10314,x10311))),f28(x10315,f66(x10315,x10313,x10312,x10314,x10311)))) % 1.40/1.55 [1032]P34(f28(f29(f94(f94(x10321,x10322),a3),f18(x10321,x10322,x10323,x10324)),f18(x10321,x10322,x10323,x10325)))+~P34(f28(f29(f94(x10322,a3),f28(x10324,f67(x10325,x10324,x10322,x10323,x10321))),f28(x10325,f67(x10325,x10324,x10322,x10323,x10321)))) % 1.40/1.55 [729]~P29(x7291)+E(f28(f28(f20(x7291),f28(f28(f20(x7291),x7292),x7293)),f28(f28(f20(x7291),x7294),x7295)),f28(f28(f20(x7291),f28(f28(f20(x7291),x7292),x7294)),f28(f28(f20(x7291),x7293),x7295))) % 1.40/1.55 [825]~E(x8252,f28(x8254,x8255))+P34(f28(f28(f35(x8251),x8252),f37(x8253,x8251,x8254,f31(f94(x8253,a3))))) % 1.40/1.55 [979]~P34(f28(f28(f35(x9792),x9795),f37(x9791,x9792,x9794,x9793)))+P34(f28(f28(f35(x9791),f28(f23(x9791,x9792,x9793,x9794),x9795)),x9793)) % 1.40/1.55 [881]P10(x8811,x8812,x8813,x8814,x8815)+~P34(f28(f28(f35(f96(x8811,x8812)),f28(f28(f33(x8811,x8812),x8814),x8815)),x8813)) % 1.40/1.55 [886]~P10(x8861,x8862,x8865,x8863,x8864)+P34(f28(f28(f35(f96(x8861,x8862)),f28(f28(f33(x8861,x8862),x8863),x8864)),x8865)) % 1.40/1.55 [969]P34(f28(f29(f94(x9691,a3),f37(x9692,x9691,x9693,x9694)),x9695))+~P34(f28(f28(f35(f94(x9692,x9691)),x9693),f18(x9692,x9691,x9694,f28(f16(f94(x9691,a3),x9692),x9695)))) % 1.40/1.55 [1000]~P11(x10003,x10004,x10001,x10005,x10006,x10007)+E(f28(f28(x10001,x10002),x10002),x10002) % 1.40/1.55 [1006]P34(f28(f28(f35(f96(f96(x10061,x10062),f96(x10061,x10062))),f28(f28(f33(f96(x10061,x10062),f96(x10061,x10062)),f28(f28(f33(x10061,x10062),x10063),x10064)),f28(f28(f33(x10061,x10062),x10065),x10066))),f43(x10061,x10062,x10067,x10068)))+~P34(f28(f28(f35(f96(x10061,x10061)),f28(f28(f33(x10061,x10061),x10063),x10065)),x10067)) % 1.40/1.55 [859]~P34(f28(f28(f30(a2),f28(a97,a84)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a105),a104)),f28(f28(a11,f28(a101,a84)),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a98)) % 1.40/1.55 [858]P2(x8581)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x8581)),f63(x8581))),f28(x8581,f61(x8581))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x8581)),f63(x8581))),f28(x8581,f60(x8581)))) % 1.40/1.55 [910]P2(x9101)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x9101)),f63(x9101))),f28(x9101,f61(x9101))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x9101)),f63(x9101))),f28(x9101,f60(x9101)))) % 1.40/1.55 [884]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8841)))+~P34(f28(f28(f30(a2),f28(a97,x8841)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x8841)),a105))) % 1.40/1.55 [890]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8901)))+~P34(f28(f28(f30(a2),f28(a97,x8901)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x8901)),a105))) % 1.40/1.55 [406]~P7(x4062)+~P7(x4061)+P7(f96(x4061,x4062)) % 1.40/1.55 [407]~P7(x4072)+~P7(x4071)+P7(f94(x4071,x4072)) % 1.40/1.55 [408]~P7(x4082)+~P7(x4081)+P7(f95(x4081,x4082)) % 1.40/1.55 [542]E(x5421,x5422)+~P34(f28(f29(a2,x5422),x5421))+~P34(f28(f29(a2,x5421),x5422)) % 1.40/1.55 [567]E(x5671,f4(a2))+E(f28(a22,f69(x5672,x5671)),x5671)+~P34(f28(f28(f30(a2),x5671),f28(a22,x5672))) % 1.40/1.55 [575]E(x5751,f28(a22,x5752))+P34(f28(f29(a2,x5751),x5752))+~P34(f28(f29(a2,x5751),f28(a22,x5752))) % 1.40/1.55 [612]E(x6121,x6122)+~P34(f28(f29(a2,x6122),x6121))+~P34(f28(f28(f30(a2),x6121),f28(a22,x6122))) % 1.40/1.55 [713]~P18(x7131)+~P34(f28(f29(x7131,x7132),f4(x7131)))+P34(f28(f29(x7131,f28(f28(f20(x7131),x7132),x7132)),f4(x7131))) % 1.40/1.55 [727]~P30(x7271)+~P34(f28(f28(f30(x7271),x7272),f4(x7271)))+P34(f28(f28(f30(x7271),f28(f28(f20(x7271),x7272),x7272)),f4(x7271))) % 1.40/1.55 [728]~P18(x7281)+~P34(f28(f28(f30(x7281),x7282),f4(x7281)))+P34(f28(f28(f30(x7281),f28(f28(f20(x7281),x7282),x7282)),f4(x7281))) % 1.40/1.55 [765]~P18(x7651)+~P34(f28(f29(x7651,f28(f28(f20(x7651),x7652),x7652)),f4(x7651)))+P34(f28(f29(x7651,x7652),f4(x7651))) % 1.40/1.55 [778]~P30(x7781)+~P34(f28(f28(f30(x7781),f28(f28(f20(x7781),x7782),x7782)),f4(x7781)))+P34(f28(f28(f30(x7781),x7782),f4(x7781))) % 1.40/1.55 [779]~P18(x7791)+~P34(f28(f28(f30(x7791),f28(f28(f20(x7791),x7792),x7792)),f4(x7791)))+P34(f28(f28(f30(x7791),x7792),f4(x7791))) % 1.40/1.55 [409]~E(x4092,f4(a2))+~E(x4091,f4(a2))+E(f28(f28(f20(a2),x4091),x4092),f4(a2)) % 1.40/1.55 [415]~P18(x4151)+~E(x4152,f4(x4151))+E(f28(f28(f20(x4151),x4152),x4152),f4(x4151)) % 1.40/1.55 [436]~E(x4362,f4(a2))+~E(x4361,f28(a22,f4(a2)))+E(f28(f28(f20(a2),x4361),x4362),f28(a22,f4(a2))) % 1.40/1.55 [437]~E(x4371,f4(a2))+~E(x4372,f28(a22,f4(a2)))+E(f28(f28(f20(a2),x4371),x4372),f28(a22,f4(a2))) % 1.40/1.55 [440]~P18(x4402)+E(x4401,f4(x4402))+~E(f28(f28(f20(x4402),x4401),x4401),f4(x4402)) % 1.40/1.55 [443]E(x4431,f4(a2))+E(x4432,f4(a2))+~E(f28(f28(f20(a2),x4432),x4431),f28(a22,f4(a2))) % 1.40/1.55 [449]E(x4491,f4(a2))+E(x4491,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4492),x4491),f28(a22,f4(a2))) % 1.40/1.55 [450]E(x4501,f4(a2))+E(x4501,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4501),x4502),f28(a22,f4(a2))) % 1.40/1.55 [456]E(x4561,f28(a22,f4(a2)))+E(x4562,f28(a22,f4(a2)))+~E(f28(f28(f20(a2),x4561),x4562),f28(a22,f4(a2))) % 1.40/1.55 [505]E(x5051,x5052)+P34(f28(f28(f30(a2),x5052),x5051))+P34(f28(f28(f30(a2),x5051),x5052)) % 1.40/1.55 [521]E(x5211,x5212)+~P34(f28(f29(a2,x5211),x5212))+P34(f28(f28(f30(a2),x5211),x5212)) % 1.40/1.55 [559]~P8(a2,x5592)+P34(f28(f29(a2,x5591),f83(x5592)))+~P34(f28(f28(f35(a2),x5591),x5592)) % 1.40/1.55 [561]E(x5611,f31(f94(x5612,a3)))+~P8(x5612,f31(f94(x5612,a3)))+~E(f15(x5612,x5611),f15(x5612,f31(f94(x5612,a3)))) % 1.40/1.55 [573]~P8(a2,x5732)+P34(f28(f28(f30(a2),x5731),f79(x5732)))+~P34(f28(f28(f35(a2),x5731),x5732)) % 1.40/1.55 [576]~P34(f28(x5761,x5762))+P34(f28(x5761,f4(a2)))+P34(f28(f28(f30(a2),f70(x5762,x5761)),x5762)) % 1.40/1.55 [602]E(x6021,x6022)+~P34(f28(f28(f30(a2),x6021),f28(a22,x6022)))+P34(f28(f28(f30(a2),x6021),x6022)) % 1.40/1.55 [620]E(f28(a22,x6201),x6202)+~P34(f28(f28(f30(a2),x6201),x6202))+P34(f28(f28(f30(a2),f28(a22,x6201)),x6202)) % 1.40/1.55 [642]~P8(x6422,f31(f94(x6422,a3)))+~P8(x6421,f31(f94(x6421,a3)))+P8(f96(x6421,x6422),f31(f94(f96(x6421,x6422),a3))) % 1.40/1.55 [643]~P8(x6432,f31(f94(x6432,a3)))+~P8(x6431,f31(f94(x6431,a3)))+P8(f95(x6431,x6432),f31(f94(f95(x6431,x6432),a3))) % 1.40/1.55 [655]E(x6551,f4(a2))+~P34(f28(f28(f30(a2),x6551),f28(a22,x6552)))+P34(f28(f28(f30(a2),f69(x6552,x6551)),x6552)) % 1.40/1.55 [666]P8(x6662,f31(f94(x6662,a3)))+E(f15(x6661,f31(f94(x6661,a3))),f28(a22,f4(a2)))+~P8(f94(x6662,x6661),f31(f94(f94(x6662,x6661),a3))) % 1.40/1.55 [676]~P34(f28(x6761,x6762))+P34(f28(x6761,f4(a2)))+P34(f28(x6761,f28(f28(f20(a2),f70(x6762,x6761)),f5(a2)))) % 1.40/1.55 [770]~P9(x7701,x7701,x7702,f31(f94(x7701,a3)))+~P8(x7701,f31(f94(x7701,a3)))+E(f37(x7701,x7701,x7702,f31(f94(x7701,a3))),f31(f94(x7701,a3))) % 1.40/1.55 [775]P9(x7751,x7751,x7752,f31(f94(x7751,a3)))+~P8(x7751,f31(f94(x7751,a3)))+~E(f37(x7751,x7751,x7752,f31(f94(x7751,a3))),f31(f94(x7751,a3))) % 1.40/1.55 [882]P2(x8821)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x8821)),f63(x8821))),f28(f61(x8821),x8822)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x8821)),f63(x8821))),f28(f60(x8821),x8822))) % 1.40/1.55 [883]P2(x8831)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x8831)),f63(x8831))),f28(f60(x8831),x8832)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f62(x8831)),f63(x8831))),f28(f61(x8831),x8832))) % 1.40/1.55 [672]~P18(x6721)+~P34(f28(f29(x6721,f4(x6721)),x6722))+P34(f28(f29(x6721,f4(x6721)),f28(f28(f20(x6721),x6722),x6722))) % 1.40/1.55 [695]~P18(x6951)+~P34(f28(f28(f30(x6951),f4(x6951)),x6952))+P34(f28(f28(f30(x6951),f4(x6951)),f28(f28(f20(x6951),x6952),x6952))) % 1.40/1.55 [704]~P18(x7041)+P34(f28(f29(x7041,f4(x7041)),x7042))+~P34(f28(f29(x7041,f4(x7041)),f28(f28(f20(x7041),x7042),x7042))) % 1.40/1.55 [716]P34(f28(f28(f30(a2),f4(a2)),x7162))+P34(f28(f28(f30(a2),f4(a2)),x7161))+~P34(f28(f28(f30(a2),f4(a2)),f28(f28(f20(a2),x7162),x7161))) % 1.40/1.55 [717]~P18(x7171)+P34(f28(f28(f30(x7171),f4(x7171)),x7172))+~P34(f28(f28(f30(x7171),f4(x7171)),f28(f28(f20(x7171),x7172),x7172))) % 1.40/1.55 [718]~P26(x7181)+~P34(f28(f28(f35(x7181),x7182),f25(x7181)))+~E(f28(f28(f20(x7181),f28(f28(f20(x7181),f5(x7181)),x7182)),x7182),f4(x7181)) % 1.40/1.55 [1019]P3(x10191,x10192)+~E(f52(x10192,x10191),f53(x10192,x10191))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10191),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8)))) % 1.40/1.55 [1020]P3(x10201,x10202)+P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),f54(x10202,x10201)),a9))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10201),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8)))) % 1.40/1.55 [1021]P3(x10211,x10212)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f53(x10212,x10211)),f52(x10212,x10211))),f28(f54(x10212,x10211),x10212)))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10211),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8)))) % 1.40/1.55 [1022]P3(x10221,x10222)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),f53(x10222,x10221)),f52(x10222,x10221))),f28(x10221,f54(x10222,x10221))))+~P34(f28(f28(f35(f94(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3))),x10221),f18(f94(a90,f94(f96(a91,a91),a3)),f94(f96(a91,a91),a3),a9,f28(f16(f94(f94(f96(a91,a91),a3),a3),f94(a90,f94(f96(a91,a91),a3))),a8)))) % 1.40/1.55 [431]~E(x4312,x4313)+~P21(x4311)+P34(f28(f29(x4311,x4312),x4313)) % 1.40/1.55 [433]~E(x4332,x4333)+~P27(x4331)+P34(f28(f29(x4331,x4332),x4333)) % 1.40/1.55 [481]~P23(x4811)+P34(f28(f29(x4811,x4813),x4812))+P34(f28(f29(x4811,x4812),x4813)) % 1.40/1.55 [594]~P34(f28(f29(a2,x5941),x5943))+P34(f28(f29(a2,x5941),x5942))+~P34(f28(f29(a2,x5943),x5942)) % 1.40/1.55 [853]~P8(x8531,x8533)+P9(x8531,x8531,x8532,x8533)+~P34(f28(f29(f94(x8531,a3),x8533),f37(x8531,x8531,x8532,x8533))) % 1.40/1.55 [413]~P33(x4131)+~E(x4133,f4(x4131))+E(f28(f28(f20(x4131),x4132),x4133),x4132) % 1.40/1.55 [438]~P33(x4382)+E(x4381,f4(x4382))+~E(f28(f28(f20(x4382),x4383),x4381),x4383) % 1.40/1.55 [501]~E(x5011,x5012)+~P23(x5013)+~P34(f28(f28(f30(x5013),x5011),x5012)) % 1.40/1.55 [502]~E(x5021,x5022)+~P27(x5023)+~P34(f28(f28(f30(x5023),x5021),x5022)) % 1.40/1.55 [512]~P23(x5121)+P34(f28(f29(x5121,x5122),x5123))+P34(f28(f28(f30(x5121),x5123),x5122)) % 1.40/1.55 [556]~P21(x5561)+P34(f28(f29(x5561,x5562),x5563))+~P34(f28(f28(f30(x5561),x5562),x5563)) % 1.40/1.55 [558]~P27(x5581)+P34(f28(f29(x5581,x5582),x5583))+~P34(f28(f28(f30(x5581),x5582),x5583)) % 1.40/1.55 [581]~P8(x5811,x5813)+E(f15(x5811,f36(x5811,x5812,x5813)),f28(a22,f15(x5811,x5813)))+P34(f28(f28(f35(x5811),x5812),x5813)) % 1.40/1.55 [586]~P21(x5861)+~P34(f28(f29(x5861,x5862),x5863))+~P34(f28(f28(f30(x5861),x5863),x5862)) % 1.40/1.55 [589]~P23(x5891)+~P34(f28(f29(x5891,x5892),x5893))+~P34(f28(f28(f30(x5891),x5893),x5892)) % 1.40/1.55 [592]P8(x5921,x5922)+~P8(x5921,x5923)+~P34(f28(f29(f94(x5921,a3),x5922),x5923)) % 1.40/1.55 [593]~E(x5931,f28(a22,x5933))+P34(f28(f28(f30(a2),x5931),f28(a22,x5932)))+~P34(f28(f28(f30(a2),x5933),x5932)) % 1.40/1.55 [606]~P8(x6061,x6063)+E(f15(x6061,f36(x6061,x6062,x6063)),f15(x6061,x6063))+~P34(f28(f28(f35(x6061),x6062),x6063)) % 1.40/1.55 [608]~P8(x6081,x6083)+E(f15(x6081,f36(x6081,x6082,x6083)),f28(f28(f20(a2),f5(a2)),f15(x6081,x6083)))+P34(f28(f28(f35(x6081),x6082),x6083)) % 1.40/1.55 [617]~P21(x6171)+~P34(f28(f28(f30(x6171),x6173),x6172))+~P34(f28(f28(f30(x6171),x6172),x6173)) % 1.40/1.55 [618]~P23(x6181)+~P34(f28(f28(f30(x6181),x6183),x6182))+~P34(f28(f28(f30(x6181),x6182),x6183)) % 1.40/1.55 [619]~P27(x6191)+~P34(f28(f28(f30(x6191),x6193),x6192))+~P34(f28(f28(f30(x6191),x6192),x6193)) % 1.40/1.55 [671]~P34(f28(f28(f30(a2),x6711),x6713))+~P34(f28(f28(f30(a2),x6713),x6712))+P34(f28(f28(f30(a2),f28(a22,x6711)),x6712)) % 1.40/1.55 [684]~P8(x6841,x6843)+P34(f28(f29(a2,f15(x6841,x6842)),f15(x6841,x6843)))+~P34(f28(f29(f94(x6841,a3),x6842),x6843)) % 1.40/1.55 [694]E(x6941,x6942)+~P34(f28(f29(f94(x6943,a3),x6941),x6942))+~P34(f28(f29(f94(x6943,a3),x6942),x6941)) % 1.40/1.55 [699]E(x6991,x6992)+~P34(f28(f29(f94(x6993,a3),x6991),x6992))+P34(f28(f28(f30(f94(x6993,a3)),x6991),x6992)) % 1.40/1.55 [730]~P8(x7301,x7303)+P34(f28(f28(f30(a2),f15(x7301,x7302)),f15(x7301,x7303)))+~P34(f28(f28(f30(f94(x7301,a3)),x7302),x7303)) % 1.40/1.55 [926]~P8(x9261,x9263)+P34(f28(f28(f35(f96(f94(x9261,a3),f94(x9261,a3))),f28(f28(f33(f94(x9261,a3),f94(x9261,a3)),x9262),x9263)),f42(x9261)))+~P34(f28(f28(f30(f94(x9261,a3)),x9262),x9263)) % 1.40/1.55 [849]E(x8491,x8492)+P34(f28(f28(f35(f94(f96(a91,a91),a3)),f14(x8493,x8491,x8492)),a8))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8493),a8)) % 1.40/1.55 [857]E(x8571,x8572)+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8573),a8))+P34(f28(f28(f35(f94(f96(a91,a91),a3)),f28(f28(f28(a12,x8573),x8571),x8572)),a8)) % 1.40/1.55 [928]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9283),x9282)),x9281))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9282),x9283)),x9281))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9281),a8)) % 1.40/1.55 [852]~P3(x8521,x8523)+E(f28(x8521,x8522),f28(x8522,x8523))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x8522),a9)) % 1.40/1.55 [701]~P8(x7012,x7014)+~P8(x7011,x7013)+P8(f95(x7011,x7012),f38(x7011,x7012,x7013,x7014)) % 1.40/1.55 [812]P8(x8121,x8122)+~P9(x8121,x8123,x8124,x8122)+~P8(x8123,f37(x8121,x8123,x8124,x8122)) % 1.40/1.55 [651]E(x6511,x6512)+P34(f28(x6513,x6512))+~P34(f28(f36(x6514,x6511,x6513),x6512)) % 1.40/1.55 [723]~P8(x7232,x7234)+~P8(x7231,x7233)+E(f15(f95(x7231,x7232),f38(x7231,x7232,x7233,x7234)),f28(f28(f20(a2),f15(x7231,x7233)),f15(x7232,x7234))) % 1.40/1.55 [797]~P8(x7971,x7974)+P9(x7971,x7972,x7973,x7974)+~E(f15(x7972,f37(x7971,x7972,x7973,x7974)),f15(x7971,x7974)) % 1.40/1.55 [483]~P13(x4833)+E(x4831,x4832)+~E(f28(f28(f20(x4833),x4834),x4831),f28(f28(f20(x4833),x4834),x4832)) % 1.40/1.55 [484]~P14(x4843)+E(x4841,x4842)+~E(f28(f28(f20(x4843),x4844),x4841),f28(f28(f20(x4843),x4844),x4842)) % 1.40/1.55 [486]~P13(x4863)+E(x4861,x4862)+~E(f28(f28(f20(x4863),x4861),x4864),f28(f28(f20(x4863),x4862),x4864)) % 1.40/1.55 [624]P34(f28(x6241,x6242))+~P34(f28(x6243,x6242))+~P34(f28(f29(f94(x6244,a3),x6243),x6241)) % 1.40/1.55 [641]~E(f28(f28(f20(a2),x6413),x6412),f28(f28(f20(a2),x6411),x6414))+~P34(f28(f28(f30(a2),x6413),x6414))+P34(f28(f28(f30(a2),x6411),x6412)) % 1.40/1.55 [692]P34(f28(f28(f35(x6921),x6922),x6923))+~P34(f28(f28(f35(x6921),x6922),x6924))+~P34(f28(f29(f94(x6921,a3),x6924),x6923)) % 1.40/1.55 [706]E(x7061,x7062)+~P34(f28(f28(f35(x7063),x7061),f36(x7063,x7062,x7064)))+P34(f28(f28(f35(x7063),x7061),x7064)) % 1.40/1.55 [726]~P34(f28(f29(f94(x7261,a3),x7262),x7264))+~P34(f28(f29(f94(x7261,a3),x7264),x7263))+P34(f28(f29(f94(x7261,a3),x7262),x7263)) % 1.40/1.55 [764]~P34(f28(f29(f94(x7641,a3),x7643),f36(x7641,x7642,x7644)))+P34(f28(f28(f35(x7641),x7642),x7643))+P34(f28(f29(f94(x7641,a3),x7643),x7644)) % 1.40/1.55 [789]~P34(f28(f28(f35(x7891),x7892),x7894))+~P34(f28(f29(f94(x7891,a3),x7893),x7894))+P34(f28(f29(f94(x7891,a3),f36(x7891,x7892,x7893)),x7894)) % 1.40/1.55 [834]~E(x8341,x8342)+~E(x8341,x8343)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8342),x8341)),f28(f28(a11,x8344),x8343))) % 1.40/1.55 [835]~E(x8351,x8352)+~E(x8351,x8353)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8351),x8352)),f28(f28(a13,x8354),x8353))) % 1.40/1.55 [1005]~P22(x10052)+~P34(f28(f29(x10052,f28(x10053,f51(x10054,x10053,x10051,x10052))),f28(x10054,f51(x10054,x10053,x10051,x10052))))+P34(f28(f29(f94(x10051,x10052),x10053),x10054)) % 1.40/1.55 [720]~P22(x7202)+P34(f28(f29(f94(x7201,x7202),x7203),x7204))+~P34(f28(f28(f30(f94(x7201,x7202)),x7203),x7204)) % 1.40/1.55 [731]P34(f28(f28(f35(x7311),x7312),x7313))+~P34(f28(f28(f35(x7311),x7312),x7314))+~P34(f28(f28(f30(f94(x7311,a3)),x7314),x7313)) % 1.40/1.55 [748]~P22(x7481)+~P34(f28(f29(f94(x7482,x7481),x7483),x7484))+~P34(f28(f28(f30(f94(x7482,x7481)),x7484),x7483)) % 1.40/1.55 [753]~P19(x7531)+~P34(f28(f29(x7531,x7533),x7534))+P34(f28(f29(x7531,f28(f28(f20(x7531),x7532),x7533)),f28(f28(f20(x7531),x7532),x7534))) % 1.40/1.55 [754]~P20(x7541)+~P34(f28(f29(x7541,x7543),x7544))+P34(f28(f29(x7541,f28(f28(f20(x7541),x7542),x7543)),f28(f28(f20(x7541),x7542),x7544))) % 1.40/1.55 [755]~P19(x7551)+~P34(f28(f29(x7551,x7552),x7554))+P34(f28(f29(x7551,f28(f28(f20(x7551),x7552),x7553)),f28(f28(f20(x7551),x7554),x7553))) % 1.40/1.55 [756]~P20(x7561)+~P34(f28(f29(x7561,x7562),x7564))+P34(f28(f29(x7561,f28(f28(f20(x7561),x7562),x7563)),f28(f28(f20(x7561),x7564),x7563))) % 1.40/1.55 [761]~P34(f28(f29(a2,x7612),x7614))+~P34(f28(f29(a2,x7611),x7613))+P34(f28(f29(a2,f28(f28(f20(a2),x7611),x7612)),f28(f28(f20(a2),x7613),x7614))) % 1.40/1.55 [766]~P5(x7661)+~P34(f28(f28(f30(x7661),x7663),x7664))+P34(f28(f28(f30(x7661),f28(f28(f20(x7661),x7662),x7663)),f28(f28(f20(x7661),x7662),x7664))) % 1.40/1.55 [767]~P19(x7671)+~P34(f28(f28(f30(x7671),x7673),x7674))+P34(f28(f28(f30(x7671),f28(f28(f20(x7671),x7672),x7673)),f28(f28(f20(x7671),x7672),x7674))) % 1.40/1.55 [768]~P5(x7681)+~P34(f28(f28(f30(x7681),x7682),x7684))+P34(f28(f28(f30(x7681),f28(f28(f20(x7681),x7682),x7683)),f28(f28(f20(x7681),x7684),x7683))) % 1.40/1.55 [769]~P19(x7691)+~P34(f28(f28(f30(x7691),x7692),x7694))+P34(f28(f28(f30(x7691),f28(f28(f20(x7691),x7692),x7693)),f28(f28(f20(x7691),x7694),x7693))) % 1.40/1.55 [776]~P34(f28(f28(f30(a2),x7762),x7764))+~P34(f28(f28(f30(a2),x7761),x7763))+P34(f28(f28(f30(a2),f28(f28(f20(a2),x7761),x7762)),f28(f28(f20(a2),x7763),x7764))) % 1.40/1.55 [784]~P34(f28(f29(f94(x7841,a3),x7844),x7843))+~P34(f28(f28(f30(f94(x7841,a3)),x7842),x7844))+P34(f28(f28(f30(f94(x7841,a3)),x7842),x7843)) % 1.40/1.55 [785]~P34(f28(f29(f94(x7851,a3),x7852),x7854))+~P34(f28(f28(f30(f94(x7851,a3)),x7854),x7853))+P34(f28(f28(f30(f94(x7851,a3)),x7852),x7853)) % 1.40/1.55 [808]~P19(x8081)+P34(f28(f29(x8081,x8082),x8083))+~P34(f28(f29(x8081,f28(f28(f20(x8081),x8084),x8082)),f28(f28(f20(x8081),x8084),x8083))) % 1.40/1.55 [810]~P19(x8101)+P34(f28(f29(x8101,x8102),x8103))+~P34(f28(f29(x8101,f28(f28(f20(x8101),x8102),x8104)),f28(f28(f20(x8101),x8103),x8104))) % 1.40/1.55 [811]~P34(f28(f28(f30(f94(x8111,a3)),x8112),x8114))+P34(f28(f28(f30(f94(x8111,a3)),x8112),x8113))+~P34(f28(f28(f30(f94(x8111,a3)),x8114),x8113)) % 1.40/1.55 [814]~P19(x8141)+P34(f28(f28(f30(x8141),x8142),x8143))+~P34(f28(f28(f30(x8141),f28(f28(f20(x8141),x8144),x8142)),f28(f28(f20(x8141),x8144),x8143))) % 1.40/1.55 [816]~P19(x8161)+P34(f28(f28(f30(x8161),x8162),x8163))+~P34(f28(f28(f30(x8161),f28(f28(f20(x8161),x8162),x8164)),f28(f28(f20(x8161),x8163),x8164))) % 1.40/1.55 [889]~P9(x8894,x8893,x8891,f31(f94(x8894,a3)))+E(f28(x8891,f74(x8892,x8891,x8893,x8894)),x8892)+~P34(f28(f28(f35(x8893),x8892),f37(x8894,x8893,x8891,f31(f94(x8894,a3))))) % 1.40/1.55 [871]E(x8711,x8712)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8713),x8711)),f28(f28(a11,x8714),x8712)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8713),x8711)),x8714)) % 1.40/1.55 [872]E(x8721,x8722)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8721),x8723)),f28(f28(a13,x8724),x8722)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8721),x8723)),x8724)) % 1.40/1.55 [682]E(x6821,x6822)+~E(f28(x6823,x6821),f28(x6823,x6822))+~P9(x6824,x6825,x6823,f31(f94(x6824,a3))) % 1.40/1.55 [817]E(x8171,x8172)+~E(f37(x8173,x8174,x8175,x8171),f37(x8173,x8174,x8175,x8172))+~P9(x8173,x8174,x8175,f31(f94(x8173,a3))) % 1.40/1.55 [846]P8(x8461,x8462)+~P8(x8463,x8464)+~P34(f28(f29(f94(x8461,a3),x8462),f37(x8463,x8461,x8465,x8464))) % 1.40/1.55 [688]~P22(x6881)+P34(f28(f29(x6881,f28(x6882,x6883)),f28(x6884,x6883)))+~P34(f28(f29(f94(x6885,x6881),x6882),x6884)) % 1.40/1.55 [774]P9(x7741,x7742,x7743,x7744)+~P9(x7741,x7742,x7743,x7745)+~P34(f28(f29(f94(x7741,a3),x7744),x7745)) % 1.40/1.55 [799]~P9(x7991,x7992,x7994,x7993)+E(f28(f23(x7991,x7992,x7993,x7994),f28(x7994,x7995)),x7995)+~P34(f28(f28(f35(x7991),x7995),x7993)) % 1.40/1.55 [847]~P9(x8472,x8471,x8474,x8473)+E(f37(x8471,x8472,f23(x8472,x8471,x8473,x8474),f37(x8472,x8471,x8474,x8475)),x8475)+~P34(f28(f29(f94(x8472,a3),x8475),x8473)) % 1.40/1.55 [868]~P9(x8681,x8684,x8685,f31(f94(x8681,a3)))+~P34(f28(f28(f35(x8684),f28(x8685,x8682)),f37(x8681,x8684,x8685,x8683)))+P34(f28(f28(f35(x8681),x8682),x8683)) % 1.40/1.55 [973]~P9(x9731,x9734,x9735,f31(f94(x9731,a3)))+~P34(f28(f29(f94(x9734,a3),f37(x9731,x9734,x9735,x9732)),f37(x9731,x9734,x9735,x9733)))+P34(f28(f29(f94(x9731,a3),x9732),x9733)) % 1.40/1.55 [802]~E(f28(x8023,x8025),x8024)+~P9(x8021,x8022,x8023,f31(f94(x8021,a3)))+E(f28(f23(x8021,x8022,f31(f94(x8021,a3)),x8023),x8024),x8025) % 1.40/1.55 [942]~P9(x9422,x9421,x9423,x9425)+P34(f28(f28(f30(f94(x9421,a3)),f37(x9422,x9421,x9423,x9424)),f37(x9422,x9421,x9423,x9425)))+~P34(f28(f28(f30(f94(x9422,a3)),x9424),x9425)) % 1.40/1.55 [894]P34(f28(f28(f35(f96(x8941,x8941)),f28(f28(f33(x8941,x8941),x8942),x8943)),f44(x8941,x8944,x8945)))+~P34(f28(f29(a2,f28(x8944,x8942)),f28(x8944,x8943)))+~P34(f28(f28(f35(f96(x8941,x8941)),f28(f28(f33(x8941,x8941),x8942),x8943)),x8945)) % 1.40/1.55 [821]~E(x8212,f28(x8214,x8216))+P34(f28(f28(f35(x8211),x8212),f37(x8213,x8211,x8214,x8215)))+~P34(f28(f28(f35(x8213),x8216),x8215)) % 1.40/1.55 [842]~E(x8422,f37(x8423,x8421,x8424,x8426))+P34(f28(f29(f94(x8421,a3),x8422),f37(x8423,x8421,x8424,x8425)))+~P34(f28(f29(f94(x8423,a3),x8426),x8425)) % 1.40/1.55 [862]~E(f37(x8621,x8622,x8623,x8624),x8626)+E(f37(x8621,x8622,x8623,f37(x8622,x8621,f23(x8621,x8622,x8624,x8623),x8625)),x8625)+~P34(f28(f29(f94(x8622,a3),x8625),x8626)) % 1.40/1.55 [870]~P34(f28(f28(f35(f94(x8705,x8701)),x8702),f18(x8705,x8701,x8706,x8704)))+P34(f28(f28(f35(x8701),f28(x8702,x8703)),f28(x8704,x8703)))+~P34(f28(f28(f35(x8705),x8703),x8706)) % 1.40/1.55 [747]P34(f28(f28(x7471,x7472),x7473))+~P34(f28(f28(x7474,x7472),x7473))+~P34(f28(f29(f94(x7475,f94(x7476,a3)),x7474),x7471)) % 1.40/1.55 [909]P34(f28(f28(f35(x9091),f28(x9092,x9093)),x9094))+~P34(f28(f28(f35(x9095),x9093),x9096))+~P34(f28(f28(f35(f94(x9095,x9091)),x9092),f18(x9095,x9091,x9096,f28(f16(f94(x9091,a3),x9095),x9094)))) % 1.40/1.55 [1015]~P8(x10154,x10152)+~P12(x10153,x10154,x10155,x10157,x10156,x10151)+E(f28(x10151,x10152),f19(x10153,x10154,x10155,x10156,x10157,x10152)) % 1.40/1.55 [1008]~P34(f28(x10086,x10083))+~P34(f28(f28(f35(f96(x10082,x10082)),f28(f28(f33(x10082,x10082),x10084),x10085)),f28(x10087,x10083)))+P34(f28(f28(f35(f96(f96(x10081,x10082),f96(x10081,x10082))),f28(f28(f33(f96(x10081,x10082),f96(x10081,x10082)),f28(f28(f33(x10081,x10082),x10083),x10084)),f28(f28(f33(x10081,x10082),x10083),x10085))),f34(x10081,x10082,x10086,x10087))) % 1.40/1.55 [1001]~P8(x10012,x10014)+~P11(x10017,x10012,x10015,x10018,x10016,x10011)+E(f28(x10011,f36(x10012,x10013,x10014)),f28(f28(x10015,f28(x10016,x10013)),f28(x10011,x10014))) % 1.40/1.55 [1007]~E(x10073,x10075)+P34(f28(f28(f35(f96(f96(x10071,x10072),f96(x10071,x10072))),f28(f28(f33(f96(x10071,x10072),f96(x10071,x10072)),f28(f28(f33(x10071,x10072),x10073),x10074)),f28(f28(f33(x10071,x10072),x10075),x10076))),f43(x10071,x10072,x10077,x10078)))+~P34(f28(f28(f35(f96(x10072,x10072)),f28(f28(f33(x10072,x10072),x10074),x10076)),x10078)) % 1.40/1.55 [1014]E(x10141,x10142)+~P34(f28(f28(f35(f96(f96(x10143,x10145),f96(x10143,x10145))),f28(f28(f33(f96(x10143,x10145),f96(x10143,x10145)),f28(f28(f33(x10143,x10145),x10141),x10146)),f28(f28(f33(x10143,x10145),x10142),x10147))),f43(x10143,x10145,x10144,x10148)))+P34(f28(f28(f35(f96(x10143,x10143)),f28(f28(f33(x10143,x10143),x10141),x10142)),x10144)) % 1.40/1.55 [1018]~P34(f28(f28(f35(f96(f96(x10181,x10185),f96(x10181,x10185))),f28(f28(f33(f96(x10181,x10185),f96(x10181,x10185)),f28(f28(f33(x10181,x10185),x10182),x10186)),f28(f28(f33(x10181,x10185),x10183),x10187))),f43(x10181,x10185,x10184,x10188)))+P34(f28(f28(f35(f96(x10181,x10181)),f28(f28(f33(x10181,x10181),x10182),x10183)),x10184))+P34(f28(f28(f35(f96(x10185,x10185)),f28(f28(f33(x10185,x10185),x10186),x10187)),x10188)) % 1.40/1.55 [897]E(f28(a97,a84),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a105),a104)),f28(f28(a13,f28(a101,a84)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a99))+P34(f28(f28(f30(a2),f28(a97,a84)),a106)) % 1.40/1.55 [936]~E(f28(a97,a84),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a105),a104)),f28(f28(f28(a12,f28(a101,a84)),a103),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a99))+P34(f28(f28(f30(a2),f28(a97,a84)),a106)) % 1.40/1.55 [974]~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a105),a104)),f28(f28(f28(a12,f28(a101,a84)),a103),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a105),a104)),f28(f28(a13,f28(a101,a84)),a105)))+P34(f28(f28(f30(a2),f28(a97,a84)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a102),a100)),a99)) % 1.40/1.55 [880]E(f28(a97,x8801),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8801)))+P34(f28(f28(f30(a2),f28(a97,x8801)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x8801)),a105))) % 1.40/1.55 [888]E(f28(a97,x8881),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8881)))+P34(f28(f28(f30(a2),f28(a97,x8881)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x8881)),a105))) % 1.40/1.55 [949]E(f28(a97,x9491),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9491)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x9491)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x9491)),a105))) % 1.40/1.55 [892]~E(f28(a97,x8921),a106)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x8921)))+P34(f28(f28(f30(a2),f28(a97,x8921)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x8921)),a103),a105))) % 1.40/1.55 [899]~P34(f28(f28(f30(a2),f28(a97,x8991)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f30(a2),f28(a97,x8991)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x8991)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98)) % 1.40/1.55 [912]~E(f28(a97,x9121),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9121)))+P34(f28(f28(f30(a2),f28(a97,x9121)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9121)),a103),a105))) % 1.40/1.55 [966]~E(f28(a97,x9661),a106)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9661)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x9661)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9661)),a103),a105))) % 1.40/1.55 [970]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9701)))+P34(f28(f28(f30(a2),f28(a97,x9701)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x9701)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9701)),a103),a105))) % 1.40/1.55 [990]P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(a101,x9901)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a13,f28(a101,x9901)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(a11,f28(a101,x9901)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a104)),f28(f28(f28(a12,f28(a101,x9901)),a103),a105))) % 1.40/1.55 [887]~P30(x8871)+~P34(f28(f28(f35(x8871),x8872),f25(x8871)))+P34(f28(f28(f30(x8871),f28(f28(f20(x8871),f28(f28(f20(x8871),f5(x8871)),x8872)),x8872)),f4(x8871)))+~P34(f28(f28(f30(x8871),x8872),f4(x8871))) % 1.40/1.55 [946]~P30(x9461)+~P34(f28(f28(f35(x9461),x9462),f25(x9461)))+~P34(f28(f28(f30(x9461),f28(f28(f20(x9461),f28(f28(f20(x9461),f5(x9461)),x9462)),x9462)),f4(x9461)))+P34(f28(f28(f30(x9461),x9462),f4(x9461))) % 1.40/1.55 [562]~P26(x5621)+~E(x5622,f4(x5621))+E(f28(f28(f20(x5621),x5622),x5622),f4(x5621))+~P34(f28(f28(f35(x5621),x5622),f25(x5621))) % 1.40/1.55 [577]~P26(x5772)+E(x5771,f4(x5772))+~E(f28(f28(f20(x5772),x5771),x5771),f4(x5772))+~P34(f28(f28(f35(x5772),x5771),f25(x5772))) % 1.40/1.55 [571]E(x5711,x5712)+~P27(x5713)+~P34(f28(f29(x5713,x5712),x5711))+~P34(f28(f29(x5713,x5711),x5712)) % 1.40/1.55 [610]~P34(f28(x6101,x6102))+~P34(f28(x6101,x6103))+~P34(f28(f29(a2,x6103),f70(x6102,x6101)))+P34(f28(x6101,f4(a2))) % 1.40/1.55 [751]~P25(x7511)+~P34(f28(f29(x7511,x7513),f4(x7511)))+~P34(f28(f29(x7511,x7512),f4(x7511)))+P34(f28(f29(x7511,f28(f28(f20(x7511),x7512),x7513)),f4(x7511))) % 1.40/1.55 [762]~P25(x7621)+~P34(f28(f29(x7621,x7623),f4(x7621)))+~P34(f28(f28(f30(x7621),x7622),f4(x7621)))+P34(f28(f28(f30(x7621),f28(f28(f20(x7621),x7622),x7623)),f4(x7621))) % 1.40/1.55 [763]~P25(x7631)+~P34(f28(f29(x7631,x7632),f4(x7631)))+~P34(f28(f28(f30(x7631),x7633),f4(x7631)))+P34(f28(f28(f30(x7631),f28(f28(f20(x7631),x7632),x7633)),f4(x7631))) % 1.40/1.55 [771]~P32(x7711)+~P34(f28(f28(f35(x7711),x7713),f25(x7711)))+~P34(f28(f28(f35(x7711),x7712),f25(x7711)))+P34(f28(f28(f35(x7711),f28(f28(f20(x7711),x7712),x7713)),f25(x7711))) % 1.40/1.55 [772]~P25(x7721)+~P34(f28(f28(f30(x7721),x7723),f4(x7721)))+~P34(f28(f28(f30(x7721),x7722),f4(x7721)))+P34(f28(f28(f30(x7721),f28(f28(f20(x7721),x7722),x7723)),f4(x7721))) % 1.40/1.55 [514]~E(x5142,x5143)+~P23(x5141)+P34(f28(f29(x5141,x5142),x5143))+P34(f28(f28(f30(x5141),x5142),x5143)) % 1.40/1.55 [523]~P30(x5233)+E(x5231,x5232)+P34(f28(f28(f30(x5233),x5232),x5231))+P34(f28(f28(f30(x5233),x5231),x5232)) % 1.40/1.55 [529]~P23(x5293)+E(x5291,x5292)+P34(f28(f28(f30(x5293),x5292),x5291))+P34(f28(f28(f30(x5293),x5291),x5292)) % 1.40/1.55 [545]~P27(x5453)+E(x5451,x5452)+~P34(f28(f29(x5453,x5452),x5451))+P34(f28(f28(f30(x5453),x5452),x5451)) % 1.40/1.55 [547]~P23(x5473)+E(x5471,x5472)+~P34(f28(f29(x5473,x5471),x5472))+P34(f28(f28(f30(x5473),x5471),x5472)) % 1.40/1.55 [553]~P27(x5533)+E(x5531,x5532)+~P34(f28(f29(x5533,x5531),x5532))+P34(f28(f28(f30(x5533),x5531),x5532)) % 1.40/1.55 [607]~P21(x6071)+~P34(f28(f29(x6071,x6073),x6072))+P34(f28(f29(x6071,x6072),x6073))+P34(f28(f28(f30(x6071),x6073),x6072)) % 1.40/1.55 [715]E(x7151,x7152)+~P8(x7153,x7151)+~P34(f28(f29(a2,f15(x7153,x7151)),f15(x7153,x7152)))+~P34(f28(f29(f94(x7153,a3),x7152),x7151)) % 1.40/1.55 [938]~P8(x9381,x9383)+~P9(x9381,x9381,x9382,x9383)+E(f37(x9381,x9381,x9382,x9383),x9383)+~P34(f28(f29(f94(x9381,a3),f37(x9381,x9381,x9382,x9383)),x9383)) % 1.40/1.55 [734]~P25(x7341)+~P34(f28(f28(f30(x7341),f4(x7341)),x7343))+~P34(f28(f28(f30(x7341),f4(x7341)),x7342))+P34(f28(f28(f30(x7341),f4(x7341)),f28(f28(f20(x7341),x7342),x7343))) % 1.40/1.55 [781]~P8(x7811,x7813)+~P34(f28(f28(f30(a2),f15(x7811,x7812)),f15(x7811,x7813)))+~P34(f28(f29(f94(x7811,a3),x7812),x7813))+P34(f28(f28(f30(f94(x7811,a3)),x7812),x7813)) % 1.40/1.55 [877]E(x8771,x8772)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8771),x8772)),x8773))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8772),x8771)),x8773))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8773),a8)) % 1.40/1.55 [621]~P27(x6211)+~P34(f28(f29(x6211,x6214),x6213))+P34(f28(f29(x6211,x6212),x6213))+~P34(f28(f29(x6211,x6212),x6214)) % 1.40/1.55 [622]~P21(x6221)+~P34(f28(f29(x6221,x6222),x6224))+P34(f28(f29(x6221,x6222),x6223))+~P34(f28(f29(x6221,x6224),x6223)) % 1.40/1.55 [806]~P8(x8062,x8063)+~P8(x8061,x8064)+P9(x8061,x8062,f80(x8063,x8062,x8064,x8061),x8064)+~P34(f28(f29(a2,f15(x8061,x8064)),f15(x8062,x8063))) % 1.40/1.55 [640]E(x6401,x6402)+~E(f36(x6403,x6404,x6401),f36(x6403,x6404,x6402))+P34(f28(f28(f35(x6403),x6404),x6402))+P34(f28(f28(f35(x6403),x6404),x6401)) % 1.40/1.55 [644]~P27(x6441)+~P34(f28(f29(x6441,x6442),x6444))+~P34(f28(f28(f30(x6441),x6444),x6443))+P34(f28(f28(f30(x6441),x6442),x6443)) % 1.40/1.55 [645]~P27(x6451)+~P34(f28(f29(x6451,x6454),x6453))+~P34(f28(f28(f30(x6451),x6452),x6454))+P34(f28(f28(f30(x6451),x6452),x6453)) % 1.40/1.55 [646]~P21(x6461)+~P34(f28(f29(x6461,x6464),x6463))+~P34(f28(f28(f30(x6461),x6462),x6464))+P34(f28(f28(f30(x6461),x6462),x6463)) % 1.40/1.55 [647]~P21(x6471)+~P34(f28(f29(x6471,x6472),x6474))+~P34(f28(f28(f30(x6471),x6474),x6473))+P34(f28(f28(f30(x6471),x6472),x6473)) % 1.40/1.55 [662]~P27(x6621)+~P34(f28(f28(f30(x6621),x6624),x6623))+P34(f28(f28(f30(x6621),x6622),x6623))+~P34(f28(f28(f30(x6621),x6622),x6624)) % 1.40/1.55 [663]~P21(x6631)+~P34(f28(f28(f30(x6631),x6632),x6634))+P34(f28(f28(f30(x6631),x6632),x6633))+~P34(f28(f28(f30(x6631),x6634),x6633)) % 1.40/1.55 [791]~E(x7913,x7911)+E(x7911,x7912)+E(x7913,x7912)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x7912),x7913)),f28(f28(a11,x7914),x7911))) % 1.40/1.55 [792]~E(x7923,x7921)+E(x7921,x7922)+E(x7923,x7922)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x7923),x7922)),f28(f28(a13,x7924),x7921))) % 1.40/1.55 [702]~P25(x7021)+~P34(f28(f29(x7021,x7022),x7023))+~P34(f28(f29(x7021,f4(x7021)),x7024))+P34(f28(f29(x7021,x7022),f28(f28(f20(x7021),x7023),x7024))) % 1.40/1.55 [703]~P25(x7031)+~P34(f28(f29(x7031,x7032),x7034))+~P34(f28(f29(x7031,f4(x7031)),x7033))+P34(f28(f29(x7031,x7032),f28(f28(f20(x7031),x7033),x7034))) % 1.40/1.55 [711]~P25(x7111)+~P34(f28(f29(x7111,x7112),x7114))+~P34(f28(f28(f30(x7111),f4(x7111)),x7113))+P34(f28(f28(f30(x7111),x7112),f28(f28(f20(x7111),x7113),x7114))) % 1.40/1.55 [712]~P25(x7121)+~P34(f28(f29(x7121,f4(x7121)),x7123))+~P34(f28(f28(f30(x7121),x7122),x7124))+P34(f28(f28(f30(x7121),x7122),f28(f28(f20(x7121),x7123),x7124))) % 1.40/1.55 [721]~P4(x7211)+~P34(f28(f28(f30(x7211),f4(x7211)),x7213))+~P34(f28(f28(f30(x7211),x7212),x7214))+P34(f28(f28(f30(x7211),x7212),f28(f28(f20(x7211),x7213),x7214))) % 1.40/1.55 [749]~P22(x7492)+~P34(f28(f29(f94(x7491,x7492),x7494),x7493))+P34(f28(f29(f94(x7491,x7492),x7493),x7494))+P34(f28(f28(f30(f94(x7491,x7492)),x7494),x7493)) % 1.40/1.55 [986]~P8(x9862,x9864)+~P8(x9861,x9863)+~P34(f28(f29(a2,f15(x9862,x9864)),f15(x9861,x9863)))+P34(f28(f29(f94(x9861,a3),f37(x9862,x9861,f80(x9863,x9861,x9864,x9862),x9864)),x9863)) % 1.40/1.55 [863]E(x8631,x8632)+E(x8633,x8632)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8633),x8631)),f28(f28(a11,x8634),x8632)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8633),x8631)),x8634)) % 1.40/1.55 [864]E(x8641,x8642)+E(x8643,x8642)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8643),x8641)),f28(f28(a13,x8644),x8642)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8643),x8641)),x8644)) % 1.40/1.55 [865]E(x8651,x8652)+E(x8653,x8651)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8653),x8651)),f28(f28(a13,x8654),x8652)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8653),x8651)),x8654)) % 1.40/1.55 [866]E(x8661,x8662)+E(x8661,x8663)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8661),x8663)),f28(f28(a11,x8664),x8662)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8661),x8663)),x8664)) % 1.40/1.55 [996]~P1(x9963)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9961),x9962)),f28(x9963,x9964)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9961),x9962)),f28(x9964,f64(x9963,x9964,x9961,x9962))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x9964),a9)) % 1.40/1.55 [937]~P8(x9373,x9374)+~P9(x9371,x9373,x9375,x9372)+P34(f28(f29(a2,f15(x9371,x9372)),f15(x9373,x9374)))+~P34(f28(f29(f94(x9373,a3),f37(x9371,x9373,x9375,x9372)),x9374)) % 1.40/1.55 [780]~P20(x7801)+~P34(f28(f29(x7801,x7803),x7805))+~P34(f28(f29(x7801,x7802),x7804))+P34(f28(f29(x7801,f28(f28(f20(x7801),x7802),x7803)),f28(f28(f20(x7801),x7804),x7805))) % 1.40/1.55 [786]~P5(x7861)+~P34(f28(f29(x7861,x7863),x7865))+~P34(f28(f28(f30(x7861),x7862),x7864))+P34(f28(f28(f30(x7861),f28(f28(f20(x7861),x7862),x7863)),f28(f28(f20(x7861),x7864),x7865))) % 1.40/1.55 [787]~P5(x7871)+~P34(f28(f29(x7871,x7872),x7874))+~P34(f28(f28(f30(x7871),x7873),x7875))+P34(f28(f28(f30(x7871),f28(f28(f20(x7871),x7872),x7873)),f28(f28(f20(x7871),x7874),x7875))) % 1.40/1.55 [794]~P5(x7941)+~P34(f28(f28(f30(x7941),x7943),x7945))+~P34(f28(f28(f30(x7941),x7942),x7944))+P34(f28(f28(f30(x7941),f28(f28(f20(x7941),x7942),x7943)),f28(f28(f20(x7941),x7944),x7945))) % 1.40/1.55 [879]~E(x8792,f28(x8793,x8791))+E(x8791,f74(x8792,x8793,x8794,x8795))+~P9(x8795,x8794,x8793,f31(f94(x8795,a3)))+~P34(f28(f28(f35(x8794),x8792),f37(x8795,x8794,x8793,f31(f94(x8795,a3))))) % 1.40/1.55 [876]E(x8761,x8762)+~E(x8763,x8764)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8763),x8764)),f14(x8765,x8761,x8762)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8765),a8)) % 1.40/1.55 [885]E(x8851,x8852)+~E(x8853,x8854)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8853),x8854)),f28(f28(f28(a12,x8855),x8851),x8852)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8855),a8)) % 1.40/1.55 [927]~P8(x9273,x9274)+~P9(x9271,x9273,x9275,x9272)+P34(f28(f29(a2,f15(x9271,x9272)),f15(x9273,x9274)))+~P34(f28(f28(f35(f94(x9271,x9273)),x9275),f18(x9271,x9273,x9272,f28(f16(f94(x9273,a3),x9271),x9274)))) % 1.40/1.55 [962]E(x9621,x9622)+~E(f28(f23(x9623,x9624,x9625,x9626),x9621),f28(f23(x9623,x9624,x9625,x9626),x9622))+~P34(f28(f28(f35(x9624),x9622),f37(x9623,x9624,x9626,x9625)))+~P34(f28(f28(f35(x9624),x9621),f37(x9623,x9624,x9626,x9625))) % 1.40/1.55 [798]~P9(x7981,x7982,x7984,x7983)+~E(f28(x7984,x7986),x7985)+E(f28(f23(x7981,x7982,x7983,x7984),x7985),x7986)+~P34(f28(f28(f35(x7981),x7986),x7983)) % 1.40/1.55 [1002]~P11(x10027,x10026,x10021,x10028,x10022,x10024)+~P8(x10026,x10025)+E(f28(f28(x10021,f28(x10022,x10023)),f28(x10024,x10025)),f28(x10024,x10025))+~P34(f28(f28(f35(x10026),x10023),x10025)) % 1.40/1.55 [1003]~P8(x10032,x10034)+~P12(x10037,x10032,x10035,x10038,x10036,x10031)+E(f28(x10031,f36(x10032,x10033,x10034)),f28(f28(x10035,f28(x10036,x10033)),f28(x10031,x10034)))+P34(f28(f28(f35(x10032),x10033),x10034)) % 1.40/1.55 [1004]~P11(x10046,x10045,x10041,x10047,x10048,x10042)+~P8(x10045,x10044)+E(f28(f28(x10041,f28(x10042,x10043)),f28(x10042,x10044)),f28(x10042,x10044))+~P34(f28(f29(f94(x10045,a3),x10043),x10044)) % 1.40/1.55 [895]E(f28(a97,x8951),a106)+P34(f28(f28(f30(a2),f28(a97,x8951)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x8951)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x8951)),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [896]E(f28(a97,x8961),a106)+~P34(f28(f28(f30(a2),f28(a97,x8961)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x8961)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x8961)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98)) % 1.40/1.55 [924]~E(f28(a97,x9241),a106)+~P34(f28(f28(f30(a2),f28(a97,x9241)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x9241)),a106))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9241)),a103),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a98)) % 1.40/1.55 [934]~E(f28(a97,x9341),a106)+P34(f28(f28(f30(a2),f28(a97,x9341)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x9341)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9341)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [957]E(f28(a97,x9571),a106)+P34(f28(f28(f30(a2),f28(a97,x9571)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x9571)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x9571)),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [972]~E(f28(a97,x9721),a106)+P34(f28(f28(f30(a2),f28(a97,x9721)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x9721)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9721)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [975]P34(f28(f28(f30(a2),f28(a97,x9751)),f28(f28(f20(a2),a106),f5(a2))))+P34(f28(f28(f30(a2),f28(a97,x9751)),a106))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x9751)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9751)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [993]P34(f28(f28(f30(a2),f28(a97,x9931)),f28(f28(f20(a2),a106),f5(a2))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a13,f28(a101,x9931)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(a11,f28(a101,x9931)),a105)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a103),a105)),f28(f28(f28(a12,f28(a101,x9931)),a103),a105)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),a100),a102)),a99)) % 1.40/1.55 [660]~P25(x6602)+E(x6601,f4(x6602))+~E(f28(f28(f20(x6602),x6603),x6601),f4(x6602))+~P34(f28(f29(x6602,f4(x6602)),x6603))+~P34(f28(f29(x6602,f4(x6602)),x6601)) % 1.40/1.55 [661]~P25(x6612)+E(x6611,f4(x6612))+~E(f28(f28(f20(x6612),x6611),x6613),f4(x6612))+~P34(f28(f29(x6612,f4(x6612)),x6613))+~P34(f28(f29(x6612,f4(x6612)),x6611)) % 1.40/1.55 [679]~P23(x6793)+E(x6791,x6792)+~E(f32(x6793,x6794,x6791),f32(x6793,x6795,x6792))+~P34(f28(f28(f30(x6793),x6795),x6792))+~P34(f28(f28(f30(x6793),x6794),x6791)) % 1.40/1.55 [680]~P23(x6803)+E(x6801,x6802)+~E(f32(x6803,x6801,x6804),f32(x6803,x6802,x6805))+~P34(f28(f28(f30(x6803),x6802),x6805))+~P34(f28(f28(f30(x6803),x6801),x6804)) % 1.40/1.55 [914]E(x9141,x9142)+~E(x9145,x9141)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9143),x9145)),f14(x9144,x9141,x9142)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9143),x9142)),x9144))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9144),a8)) % 1.40/1.55 [930]E(x9301,x9302)+~E(x9305,x9301)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9305),x9303)),f28(f28(f28(a12,x9304),x9302),x9301)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9302),x9303)),x9304))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9304),a8)) % 1.40/1.55 [743]E(x7431,x7432)+~P9(x7434,x7435,x7433,x7436)+~E(f28(x7433,x7431),f28(x7433,x7432))+~P34(f28(f28(f35(x7434),x7432),x7436))+~P34(f28(f28(f35(x7434),x7431),x7436)) % 1.40/1.55 [650]~P25(x6501)+~E(x6503,f4(x6501))+~E(x6502,f4(x6501))+E(f28(f28(f20(x6501),x6502),x6503),f4(x6501))+~P34(f28(f29(x6501,f4(x6501)),x6503))+~P34(f28(f29(x6501,f4(x6501)),x6502)) % 1.40/1.55 [903]~E(x9033,x9031)+E(x9031,x9032)+E(x9033,x9034)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9034),x9033)),f14(x9035,x9031,x9032)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9034),x9032)),x9035))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9035),a8)) % 1.40/1.55 [915]E(x9151,x9152)+E(x9151,x9153)+E(x9154,x9151)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9154),x9153)),f14(x9155,x9151,x9152)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9154),x9153)),x9155))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9155),a8)) % 1.40/1.55 [918]~E(x9183,x9181)+E(x9181,x9182)+E(x9183,x9184)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9183),x9184)),f28(f28(f28(a12,x9185),x9182),x9181)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9182),x9184)),x9185))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9185),a8)) % 1.40/1.55 [931]E(x9311,x9312)+E(x9311,x9313)+E(x9314,x9311)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9313),x9314)),f28(f28(f28(a12,x9315),x9312),x9311)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9313),x9314)),x9315))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9315),a8)) % 1.40/1.55 [1011]E(x10111,x10112)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10111),x10112)),f28(a1,x10114)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10112),x10111)),f28(a1,x10113)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10112),x10111)),f28(x10113,f68(x10113,x10114,x10112,x10111))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10111),x10112)),f28(x10114,f68(x10113,x10114,x10112,x10111))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10113),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10114),a9)) % 1.40/1.55 [1012]E(x10121,x10122)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10121),x10122)),f28(a1,x10124)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10122),x10121)),f28(a1,x10123)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10122),x10121)),f28(x10123,f68(x10124,x10123,x10121,x10122))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10121),x10122)),f28(x10124,f68(x10124,x10123,x10121,x10122))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10123),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10124),a9)) % 1.40/1.55 [1016]E(x10161,x10162)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10161),x10162)),f28(a1,x10164)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10162),x10161)),f28(a1,x10163)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10162),x10161)),f28(x10163,f68(x10163,x10164,x10162,x10161))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10161),x10162)),f28(x10164,f68(x10163,x10164,x10162,x10161))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10163),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10164),a9)) % 1.40/1.55 [1017]E(x10171,x10172)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10171),x10172)),f28(a1,x10174)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10172),x10171)),f28(a1,x10173)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10172),x10171)),f28(x10173,f68(x10174,x10173,x10171,x10172))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10171),x10172)),f28(x10174,f68(x10174,x10173,x10171,x10172))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10173),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10174),a9)) % 1.40/1.55 [851]~E(x8513,x8512)+~E(x8514,x8511)+E(x8511,x8512)+E(x8511,x8513)+E(x8514,x8513)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8514),x8513)),f14(x8515,x8511,x8512)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8515),a8)) % 1.40/1.55 [855]~E(x8553,x8552)+~E(x8554,x8551)+E(x8551,x8552)+E(x8551,x8553)+E(x8554,x8553)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x8553),x8554)),f28(f28(f28(a12,x8555),x8552),x8551)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x8555),a8)) % 1.40/1.55 [904]E(x9044,x9043)+E(x9041,x9042)+E(x9043,x9041)+E(x9044,x9041)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9044),x9043)),f14(x9045,x9041,x9042)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9044),x9043)),x9045))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9045),a8)) % 1.40/1.55 [905]~E(x9053,x9051)+E(x9051,x9052)+E(x9053,x9052)+E(x9054,x9053)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9054),x9053)),f14(x9055,x9052,x9051)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9054),x9053)),x9055))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9055),a8)) % 1.40/1.55 [906]~E(x9064,x9061)+E(x9061,x9062)+E(x9061,x9063)+E(x9064,x9062)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9064),x9062)),f14(x9065,x9061,x9063)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9063),x9062)),x9065))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9065),a8)) % 1.40/1.55 [907]~E(x9074,x9072)+~E(x9073,x9071)+E(x9071,x9072)+E(x9073,x9074)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9073),x9074)),f14(x9075,x9071,x9072)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9073),x9072)),x9075))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9075),a8)) % 1.40/1.55 [917]E(x9173,x9171)+E(x9171,x9172)+E(x9173,x9172)+~E(x9175,x9173)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9175),x9171)),f14(x9174,x9173,x9172)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9172),x9171)),x9174))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9174),a8)) % 1.40/1.55 [919]E(x9194,x9193)+E(x9191,x9192)+E(x9193,x9191)+E(x9194,x9191)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9194),x9193)),f28(f28(f28(a12,x9195),x9192),x9191)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9194),x9193)),x9195))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9195),a8)) % 1.40/1.55 [920]~E(x9203,x9201)+E(x9201,x9202)+E(x9203,x9202)+E(x9203,x9204)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9203),x9204)),f28(f28(f28(a12,x9205),x9201),x9202)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9203),x9204)),x9205))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9205),a8)) % 1.40/1.55 [921]~E(x9214,x9211)+E(x9211,x9212)+E(x9211,x9213)+E(x9214,x9213)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9213),x9214)),f28(f28(f28(a12,x9215),x9212),x9211)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9213),x9212)),x9215))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9215),a8)) % 1.40/1.55 [922]~E(x9224,x9222)+~E(x9223,x9221)+E(x9221,x9222)+E(x9223,x9224)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9224),x9223)),f28(f28(f28(a12,x9225),x9222),x9221)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9222),x9223)),x9225))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9225),a8)) % 1.40/1.55 [932]E(x9323,x9321)+E(x9321,x9322)+E(x9323,x9322)+~E(x9325,x9323)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9321),x9325)),f28(f28(f28(a12,x9324),x9322),x9323)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9321),x9322)),x9324))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9324),a8)) % 1.40/1.55 [953]E(x9531,x9532)+E(x9533,x9532)+E(x9534,x9533)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9534),x9533)),f14(x9535,x9532,x9531)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9534),x9533)),x9535))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9531),x9533)),x9535))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9535),a8)) % 1.40/1.55 [954]E(x9541,x9542)+E(x9543,x9541)+E(x9543,x9544)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9543),x9544)),f14(x9545,x9541,x9542)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9543),x9544)),x9545))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9543),x9542)),x9545))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9545),a8)) % 1.40/1.55 [955]~E(x9554,x9551)+E(x9551,x9552)+E(x9553,x9554)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9553),x9554)),f14(x9555,x9552,x9551)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9553),x9554)),x9555))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9553),x9551)),x9555))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9555),a8)) % 1.40/1.55 [956]~E(x9563,x9561)+E(x9561,x9562)+E(x9563,x9564)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9563),x9564)),f14(x9565,x9561,x9562)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9562),x9564)),x9565))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9563),x9562)),x9565))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9565),a8)) % 1.40/1.55 [958]E(x9581,x9582)+E(x9583,x9581)+E(x9584,x9583)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9584),x9583)),f28(f28(f28(a12,x9585),x9582),x9581)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9584),x9583)),x9585))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9582),x9583)),x9585))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9585),a8)) % 1.40/1.55 [959]E(x9591,x9592)+E(x9593,x9592)+E(x9593,x9594)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9593),x9594)),f28(f28(f28(a12,x9595),x9591),x9592)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9593),x9594)),x9595))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9593),x9591)),x9595))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9595),a8)) % 1.40/1.55 [960]~E(x9603,x9601)+E(x9601,x9602)+E(x9603,x9604)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9603),x9604)),f28(f28(f28(a12,x9605),x9601),x9602)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9603),x9604)),x9605))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9601),x9604)),x9605))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9605),a8)) % 1.40/1.55 [961]~E(x9613,x9611)+E(x9611,x9612)+E(x9613,x9614)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9614),x9613)),f28(f28(f28(a12,x9615),x9612),x9611)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9612),x9613)),x9615))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9614),x9612)),x9615))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9615),a8)) % 1.40/1.55 [983]E(x9831,x9832)+E(x9833,x9834)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9833),x9834)),f14(x9835,x9832,x9831)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9833),x9834)),x9835))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9831),x9834)),x9835))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9833),x9831)),x9835))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9835),a8)) % 1.40/1.55 [985]E(x9851,x9852)+E(x9853,x9854)+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9853),x9854)),f28(f28(f28(a12,x9855),x9851),x9852)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9853),x9854)),x9855))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9851),x9854)),x9855))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x9853),x9851)),x9855))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x9855),a8)) % 1.40/1.55 [1025]~P2(x10253)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10251),x10252)),f28(x10253,x10255)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10251),x10252)),f28(x10253,x10254)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10251),x10252)),f28(x10255,f56(x10253,x10254,x10255,x10251,x10252))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10251),x10252)),f28(x10254,f56(x10253,x10254,x10255,x10251,x10252))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10254),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10255),a9)) % 1.40/1.55 [1026]~P2(x10263)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10261),x10262)),f28(x10263,x10265)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10261),x10262)),f28(x10263,x10264)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10261),x10262)),f28(x10265,f56(x10263,x10265,x10264,x10261,x10262))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10261),x10262)),f28(x10264,f56(x10263,x10265,x10264,x10261,x10262))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10264),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10265),a9)) % 1.40/1.55 [1029]~P2(x10293)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10291),x10292)),f28(x10293,x10295)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10291),x10292)),f28(x10293,x10294)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10291),x10292)),f28(x10295,f56(x10293,x10294,x10295,x10291,x10292))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10291),x10292)),f28(x10294,f56(x10293,x10294,x10295,x10291,x10292))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10294),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10295),a9)) % 1.40/1.55 [1030]~P2(x10303)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10301),x10302)),f28(x10303,x10305)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10301),x10302)),f28(x10303,x10304)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10301),x10302)),f28(x10305,f56(x10303,x10305,x10304,x10301,x10302))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10301),x10302)),f28(x10304,f56(x10303,x10305,x10304,x10301,x10302))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10304),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10305),a9)) % 1.40/1.55 [998]~P8(x9983,x9984)+~P8(x9981,x9982)+~P9(x9983,x9981,x9985,x9984)+~P9(x9981,x9983,x9986,x9982)+E(f15(x9981,x9982),f15(x9983,x9984))+~P34(f28(f29(f94(x9983,a3),f37(x9981,x9983,x9986,x9982)),x9984))+~P34(f28(f29(f94(x9981,a3),f37(x9983,x9981,x9985,x9984)),x9982)) % 1.40/1.55 [992]~P8(x9923,x9924)+~P8(x9921,x9922)+~P9(x9923,x9921,x9925,x9924)+~P9(x9921,x9923,x9926,x9922)+E(f15(x9921,x9922),f15(x9923,x9924))+~P34(f28(f28(f35(f94(x9923,x9921)),x9925),f18(x9923,x9921,x9924,f28(f16(f94(x9921,a3),x9923),x9922))))+~P34(f28(f28(f35(f94(x9921,x9923)),x9926),f18(x9921,x9923,x9922,f28(f16(f94(x9923,a3),x9921),x9924)))) % 1.40/1.55 [1033]E(x10331,x10332)+E(x10333,x10334)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10333),x10334)),f28(a1,x10336)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10331),x10332)),f28(a1,x10335)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10331),x10332)),f28(x10335,f81(x10335,x10336,x10332,x10331,x10334,x10333))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10333),x10334)),f28(x10336,f81(x10335,x10336,x10332,x10331,x10334,x10333))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10335),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10336),a9)) % 1.40/1.55 [1034]E(x10341,x10342)+E(x10343,x10344)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10343),x10344)),f28(a1,x10346)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10341),x10342)),f28(a1,x10345)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10341),x10342)),f28(x10345,f81(x10346,x10345,x10344,x10343,x10342,x10341))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10343),x10344)),f28(x10346,f81(x10346,x10345,x10344,x10343,x10342,x10341))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10345),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10346),a9)) % 1.40/1.55 [1039]E(x10391,x10392)+E(x10393,x10394)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10393),x10394)),f28(a1,x10396)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10391),x10392)),f28(a1,x10395)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10391),x10392)),f28(x10395,f81(x10395,x10396,x10392,x10391,x10394,x10393))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10393),x10394)),f28(x10396,f81(x10395,x10396,x10392,x10391,x10394,x10393))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10395),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10396),a9)) % 1.40/1.55 [1040]E(x10401,x10402)+E(x10403,x10404)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10403),x10404)),f28(a1,x10406)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10401),x10402)),f28(a1,x10405)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10401),x10402)),f28(x10405,f81(x10406,x10405,x10404,x10403,x10402,x10401))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10403),x10404)),f28(x10406,f81(x10406,x10405,x10404,x10403,x10402,x10401))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10405),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10406),a9)) % 1.40/1.55 [1023]E(x10233,x10231)+E(x10231,x10232)+E(x10233,x10232)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10233),x10231)),f28(a1,x10235)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10232),x10233)),f28(a1,x10234)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10232),x10233)),f28(x10234,f85(x10235,x10234,x10231,x10233,x10232))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10233),x10231)),f28(x10235,f85(x10235,x10234,x10231,x10233,x10232))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10234),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10235),a9)) % 1.40/1.55 [1024]E(x10243,x10241)+E(x10241,x10242)+E(x10243,x10242)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10243),x10241)),f28(a1,x10245)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10241),x10242)),f28(a1,x10244)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10241),x10242)),f28(x10244,f85(x10244,x10245,x10242,x10241,x10243))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10243),x10241)),f28(x10245,f85(x10244,x10245,x10242,x10241,x10243))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10244),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10245),a9)) % 1.40/1.55 [1027]E(x10273,x10271)+E(x10271,x10272)+E(x10273,x10272)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10273),x10271)),f28(a1,x10275)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10272),x10273)),f28(a1,x10274)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10272),x10273)),f28(x10274,f85(x10275,x10274,x10271,x10273,x10272))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10273),x10271)),f28(x10275,f85(x10275,x10274,x10271,x10273,x10272))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10274),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10275),a9)) % 1.40/1.55 [1028]E(x10283,x10281)+E(x10281,x10282)+E(x10283,x10282)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10283),x10281)),f28(a1,x10285)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10281),x10282)),f28(a1,x10284)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10281),x10282)),f28(x10284,f85(x10284,x10285,x10282,x10281,x10283))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10283),x10281)),f28(x10285,f85(x10284,x10285,x10282,x10281,x10283))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10284),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10285),a9)) % 1.40/1.55 [1035]E(x10354,x10353)+E(x10351,x10352)+E(x10353,x10352)+E(x10354,x10351)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10354),x10353)),f28(a1,x10356)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10352),x10351)),f28(a1,x10355)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10352),x10351)),f28(x10355,f86(x10355,x10356,x10351,x10352,x10353,x10354))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10354),x10353)),f28(x10356,f86(x10355,x10356,x10351,x10352,x10353,x10354))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10355),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10356),a9)) % 1.40/1.55 [1036]E(x10364,x10363)+E(x10361,x10362)+E(x10363,x10361)+E(x10364,x10362)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10364),x10363)),f28(a1,x10366)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10361),x10362)),f28(a1,x10365)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10361),x10362)),f28(x10365,f87(x10365,x10366,x10362,x10361,x10363,x10364))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10364),x10363)),f28(x10366,f87(x10365,x10366,x10362,x10361,x10363,x10364))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10365),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10366),a9)) % 1.40/1.55 [1037]E(x10374,x10373)+E(x10371,x10372)+E(x10373,x10371)+E(x10374,x10372)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10374),x10373)),f28(a1,x10376)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10371),x10372)),f28(a1,x10375)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10371),x10372)),f28(x10375,f87(x10376,x10375,x10373,x10374,x10372,x10371))))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10374),x10373)),f28(x10376,f87(x10376,x10375,x10373,x10374,x10372,x10371))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10375),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10376),a9)) % 1.40/1.55 [1041]E(x10414,x10413)+E(x10411,x10412)+E(x10413,x10412)+E(x10414,x10411)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10414),x10413)),f28(a1,x10416)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10412),x10411)),f28(a1,x10415)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10412),x10411)),f28(x10415,f86(x10415,x10416,x10411,x10412,x10413,x10414))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10414),x10413)),f28(x10416,f86(x10415,x10416,x10411,x10412,x10413,x10414))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10415),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10416),a9)) % 1.40/1.55 [1042]E(x10424,x10423)+E(x10421,x10422)+E(x10423,x10421)+E(x10424,x10422)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10424),x10423)),f28(a1,x10426)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10421),x10422)),f28(a1,x10425)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10421),x10422)),f28(x10425,f87(x10425,x10426,x10422,x10421,x10423,x10424))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10424),x10423)),f28(x10426,f87(x10425,x10426,x10422,x10421,x10423,x10424))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10425),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10426),a9)) % 1.40/1.55 [1043]E(x10434,x10433)+E(x10431,x10432)+E(x10433,x10431)+E(x10434,x10432)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10434),x10433)),f28(a1,x10436)))+P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10431),x10432)),f28(a1,x10435)))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10431),x10432)),f28(x10435,f87(x10436,x10435,x10433,x10434,x10432,x10431))))+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10434),x10433)),f28(x10436,f87(x10436,x10435,x10433,x10434,x10432,x10431))))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10435),a9))+~P34(f28(f28(f35(f94(a90,f94(f96(a91,a91),a3))),x10436),a9)) % 1.40/1.55 %EqnAxiom % 1.40/1.55 [1]E(x11,x11) % 1.40/1.55 [2]E(x22,x21)+~E(x21,x22) % 1.40/1.55 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.40/1.55 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 1.40/1.55 [5]~E(x51,x52)+E(f21(x51),f21(x52)) % 1.40/1.55 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63)) % 1.40/1.55 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72)) % 1.40/1.55 [8]~E(x81,x82)+E(f27(x81,x83),f27(x82,x83)) % 1.40/1.55 [9]~E(x91,x92)+E(f27(x93,x91),f27(x93,x92)) % 1.40/1.55 [10]~E(x101,x102)+E(f7(x101,x103,x104),f7(x102,x103,x104)) % 1.40/1.55 [11]~E(x111,x112)+E(f7(x113,x111,x114),f7(x113,x112,x114)) % 1.40/1.55 [12]~E(x121,x122)+E(f7(x123,x124,x121),f7(x123,x124,x122)) % 1.40/1.55 [13]~E(x131,x132)+E(f94(x131,x133),f94(x132,x133)) % 1.40/1.55 [14]~E(x141,x142)+E(f94(x143,x141),f94(x143,x142)) % 1.40/1.55 [15]~E(x151,x152)+E(f5(x151),f5(x152)) % 1.40/1.55 [16]~E(x161,x162)+E(f17(x161,x163,x164,x165,x166),f17(x162,x163,x164,x165,x166)) % 1.40/1.55 [17]~E(x171,x172)+E(f17(x173,x171,x174,x175,x176),f17(x173,x172,x174,x175,x176)) % 1.40/1.55 [18]~E(x181,x182)+E(f17(x183,x184,x181,x185,x186),f17(x183,x184,x182,x185,x186)) % 1.40/1.55 [19]~E(x191,x192)+E(f17(x193,x194,x195,x191,x196),f17(x193,x194,x195,x192,x196)) % 1.40/1.55 [20]~E(x201,x202)+E(f17(x203,x204,x205,x206,x201),f17(x203,x204,x205,x206,x202)) % 1.40/1.55 [21]~E(x211,x212)+E(f30(x211),f30(x212)) % 1.40/1.55 [22]~E(x221,x222)+E(f20(x221),f20(x222)) % 1.40/1.55 [23]~E(x231,x232)+E(f6(x231),f6(x232)) % 1.40/1.55 [24]~E(x241,x242)+E(f96(x241,x243),f96(x242,x243)) % 1.40/1.55 [25]~E(x251,x252)+E(f96(x253,x251),f96(x253,x252)) % 1.40/1.55 [26]~E(x261,x262)+E(f35(x261),f35(x262)) % 1.40/1.55 [27]~E(x271,x272)+E(f29(x271,x273),f29(x272,x273)) % 1.40/1.55 [28]~E(x281,x282)+E(f29(x283,x281),f29(x283,x282)) % 1.40/1.55 [29]~E(x291,x292)+E(f81(x291,x293,x294,x295,x296,x297),f81(x292,x293,x294,x295,x296,x297)) % 1.40/1.55 [30]~E(x301,x302)+E(f81(x303,x301,x304,x305,x306,x307),f81(x303,x302,x304,x305,x306,x307)) % 1.40/1.55 [31]~E(x311,x312)+E(f81(x313,x314,x311,x315,x316,x317),f81(x313,x314,x312,x315,x316,x317)) % 1.40/1.55 [32]~E(x321,x322)+E(f81(x323,x324,x325,x321,x326,x327),f81(x323,x324,x325,x322,x326,x327)) % 1.40/1.55 [33]~E(x331,x332)+E(f81(x333,x334,x335,x336,x331,x337),f81(x333,x334,x335,x336,x332,x337)) % 1.40/1.55 [34]~E(x341,x342)+E(f81(x343,x344,x345,x346,x347,x341),f81(x343,x344,x345,x346,x347,x342)) % 1.40/1.55 [35]~E(x351,x352)+E(f33(x351,x353),f33(x352,x353)) % 1.40/1.55 [36]~E(x361,x362)+E(f33(x363,x361),f33(x363,x362)) % 1.40/1.55 [37]~E(x371,x372)+E(f60(x371),f60(x372)) % 1.40/1.55 [38]~E(x381,x382)+E(f37(x381,x383,x384,x385),f37(x382,x383,x384,x385)) % 1.40/1.55 [39]~E(x391,x392)+E(f37(x393,x391,x394,x395),f37(x393,x392,x394,x395)) % 1.40/1.55 [40]~E(x401,x402)+E(f37(x403,x404,x401,x405),f37(x403,x404,x402,x405)) % 1.40/1.55 [41]~E(x411,x412)+E(f37(x413,x414,x415,x411),f37(x413,x414,x415,x412)) % 1.40/1.55 [42]~E(x421,x422)+E(f15(x421,x423),f15(x422,x423)) % 1.40/1.55 [43]~E(x431,x432)+E(f15(x433,x431),f15(x433,x432)) % 1.40/1.55 [44]~E(x441,x442)+E(f31(x441),f31(x442)) % 1.40/1.55 [45]~E(x451,x452)+E(f68(x451,x453,x454,x455),f68(x452,x453,x454,x455)) % 1.40/1.55 [46]~E(x461,x462)+E(f68(x463,x461,x464,x465),f68(x463,x462,x464,x465)) % 1.40/1.55 [47]~E(x471,x472)+E(f68(x473,x474,x471,x475),f68(x473,x474,x472,x475)) % 1.40/1.55 [48]~E(x481,x482)+E(f68(x483,x484,x485,x481),f68(x483,x484,x485,x482)) % 1.40/1.55 [49]~E(x491,x492)+E(f14(x491,x493,x494),f14(x492,x493,x494)) % 1.40/1.55 [50]~E(x501,x502)+E(f14(x503,x501,x504),f14(x503,x502,x504)) % 1.40/1.55 [51]~E(x511,x512)+E(f14(x513,x514,x511),f14(x513,x514,x512)) % 1.40/1.55 [52]~E(x521,x522)+E(f62(x521),f62(x522)) % 1.40/1.55 [53]~E(x531,x532)+E(f10(x531,x533,x534,x535),f10(x532,x533,x534,x535)) % 1.40/1.55 [54]~E(x541,x542)+E(f10(x543,x541,x544,x545),f10(x543,x542,x544,x545)) % 1.40/1.55 [55]~E(x551,x552)+E(f10(x553,x554,x551,x555),f10(x553,x554,x552,x555)) % 1.40/1.55 [56]~E(x561,x562)+E(f10(x563,x564,x565,x561),f10(x563,x564,x565,x562)) % 1.40/1.55 [57]~E(x571,x572)+E(f42(x571),f42(x572)) % 1.40/1.55 [58]~E(x581,x582)+E(f36(x581,x583,x584),f36(x582,x583,x584)) % 1.40/1.55 [59]~E(x591,x592)+E(f36(x593,x591,x594),f36(x593,x592,x594)) % 1.40/1.55 [60]~E(x601,x602)+E(f36(x603,x604,x601),f36(x603,x604,x602)) % 1.40/1.55 [61]~E(x611,x612)+E(f95(x611,x613),f95(x612,x613)) % 1.40/1.55 [62]~E(x621,x622)+E(f95(x623,x621),f95(x623,x622)) % 1.40/1.55 [63]~E(x631,x632)+E(f19(x631,x633,x634,x635,x636,x637),f19(x632,x633,x634,x635,x636,x637)) % 1.40/1.55 [64]~E(x641,x642)+E(f19(x643,x641,x644,x645,x646,x647),f19(x643,x642,x644,x645,x646,x647)) % 1.40/1.55 [65]~E(x651,x652)+E(f19(x653,x654,x651,x655,x656,x657),f19(x653,x654,x652,x655,x656,x657)) % 1.40/1.55 [66]~E(x661,x662)+E(f19(x663,x664,x665,x661,x666,x667),f19(x663,x664,x665,x662,x666,x667)) % 1.40/1.55 [67]~E(x671,x672)+E(f19(x673,x674,x675,x676,x671,x677),f19(x673,x674,x675,x676,x672,x677)) % 1.40/1.55 [68]~E(x681,x682)+E(f19(x683,x684,x685,x686,x687,x681),f19(x683,x684,x685,x686,x687,x682)) % 1.40/1.55 [69]~E(x691,x692)+E(f63(x691),f63(x692)) % 1.40/1.55 [70]~E(x701,x702)+E(f16(x701,x703),f16(x702,x703)) % 1.40/1.55 [71]~E(x711,x712)+E(f16(x713,x711),f16(x713,x712)) % 1.40/1.55 [72]~E(x721,x722)+E(f24(x721),f24(x722)) % 1.40/1.55 [73]~E(x731,x732)+E(f23(x731,x733,x734,x735),f23(x732,x733,x734,x735)) % 1.40/1.55 [74]~E(x741,x742)+E(f23(x743,x741,x744,x745),f23(x743,x742,x744,x745)) % 1.40/1.55 [75]~E(x751,x752)+E(f23(x753,x754,x751,x755),f23(x753,x754,x752,x755)) % 1.40/1.55 [76]~E(x761,x762)+E(f23(x763,x764,x765,x761),f23(x763,x764,x765,x762)) % 1.40/1.55 [77]~E(x771,x772)+E(f85(x771,x773,x774,x775,x776),f85(x772,x773,x774,x775,x776)) % 1.40/1.55 [78]~E(x781,x782)+E(f85(x783,x781,x784,x785,x786),f85(x783,x782,x784,x785,x786)) % 1.40/1.55 [79]~E(x791,x792)+E(f85(x793,x794,x791,x795,x796),f85(x793,x794,x792,x795,x796)) % 1.40/1.55 [80]~E(x801,x802)+E(f85(x803,x804,x805,x801,x806),f85(x803,x804,x805,x802,x806)) % 1.40/1.55 [81]~E(x811,x812)+E(f85(x813,x814,x815,x816,x811),f85(x813,x814,x815,x816,x812)) % 1.40/1.55 [82]~E(x821,x822)+E(f86(x821,x823,x824,x825,x826,x827),f86(x822,x823,x824,x825,x826,x827)) % 1.40/1.55 [83]~E(x831,x832)+E(f86(x833,x831,x834,x835,x836,x837),f86(x833,x832,x834,x835,x836,x837)) % 1.40/1.55 [84]~E(x841,x842)+E(f86(x843,x844,x841,x845,x846,x847),f86(x843,x844,x842,x845,x846,x847)) % 1.40/1.55 [85]~E(x851,x852)+E(f86(x853,x854,x855,x851,x856,x857),f86(x853,x854,x855,x852,x856,x857)) % 1.40/1.55 [86]~E(x861,x862)+E(f86(x863,x864,x865,x866,x861,x867),f86(x863,x864,x865,x866,x862,x867)) % 1.40/1.55 [87]~E(x871,x872)+E(f86(x873,x874,x875,x876,x877,x871),f86(x873,x874,x875,x876,x877,x872)) % 1.40/1.55 [88]~E(x881,x882)+E(f51(x881,x883,x884,x885),f51(x882,x883,x884,x885)) % 1.40/1.55 [89]~E(x891,x892)+E(f51(x893,x891,x894,x895),f51(x893,x892,x894,x895)) % 1.40/1.55 [90]~E(x901,x902)+E(f51(x903,x904,x901,x905),f51(x903,x904,x902,x905)) % 1.40/1.55 [91]~E(x911,x912)+E(f51(x913,x914,x915,x911),f51(x913,x914,x915,x912)) % 1.40/1.55 [92]~E(x921,x922)+E(f38(x921,x923,x924,x925),f38(x922,x923,x924,x925)) % 1.40/1.55 [93]~E(x931,x932)+E(f38(x933,x931,x934,x935),f38(x933,x932,x934,x935)) % 1.40/1.55 [94]~E(x941,x942)+E(f38(x943,x944,x941,x945),f38(x943,x944,x942,x945)) % 1.40/1.55 [95]~E(x951,x952)+E(f38(x953,x954,x955,x951),f38(x953,x954,x955,x952)) % 1.40/1.55 [96]~E(x961,x962)+E(f59(x961),f59(x962)) % 1.40/1.55 [97]~E(x971,x972)+E(f53(x971,x973),f53(x972,x973)) % 1.40/1.55 [98]~E(x981,x982)+E(f53(x983,x981),f53(x983,x982)) % 1.40/1.55 [99]~E(x991,x992)+E(f61(x991),f61(x992)) % 1.40/1.55 [100]~E(x1001,x1002)+E(f18(x1001,x1003,x1004,x1005),f18(x1002,x1003,x1004,x1005)) % 1.40/1.55 [101]~E(x1011,x1012)+E(f18(x1013,x1011,x1014,x1015),f18(x1013,x1012,x1014,x1015)) % 1.40/1.55 [102]~E(x1021,x1022)+E(f18(x1023,x1024,x1021,x1025),f18(x1023,x1024,x1022,x1025)) % 1.40/1.55 [103]~E(x1031,x1032)+E(f18(x1033,x1034,x1035,x1031),f18(x1033,x1034,x1035,x1032)) % 1.40/1.55 [104]~E(x1041,x1042)+E(f50(x1041,x1043,x1044,x1045),f50(x1042,x1043,x1044,x1045)) % 1.40/1.55 [105]~E(x1051,x1052)+E(f50(x1053,x1051,x1054,x1055),f50(x1053,x1052,x1054,x1055)) % 1.40/1.55 [106]~E(x1061,x1062)+E(f50(x1063,x1064,x1061,x1065),f50(x1063,x1064,x1062,x1065)) % 1.40/1.55 [107]~E(x1071,x1072)+E(f50(x1073,x1074,x1075,x1071),f50(x1073,x1074,x1075,x1072)) % 1.40/1.55 [108]~E(x1081,x1082)+E(f76(x1081,x1083,x1084,x1085,x1086),f76(x1082,x1083,x1084,x1085,x1086)) % 1.40/1.55 [109]~E(x1091,x1092)+E(f76(x1093,x1091,x1094,x1095,x1096),f76(x1093,x1092,x1094,x1095,x1096)) % 1.40/1.55 [110]~E(x1101,x1102)+E(f76(x1103,x1104,x1101,x1105,x1106),f76(x1103,x1104,x1102,x1105,x1106)) % 1.40/1.55 [111]~E(x1111,x1112)+E(f76(x1113,x1114,x1115,x1111,x1116),f76(x1113,x1114,x1115,x1112,x1116)) % 1.40/1.55 [112]~E(x1121,x1122)+E(f76(x1123,x1124,x1125,x1126,x1121),f76(x1123,x1124,x1125,x1126,x1122)) % 1.40/1.55 [113]~E(x1131,x1132)+E(f65(x1131),f65(x1132)) % 1.40/1.55 [114]~E(x1141,x1142)+E(f93(x1141),f93(x1142)) % 1.40/1.55 [115]~E(x1151,x1152)+E(f71(x1151,x1153),f71(x1152,x1153)) % 1.40/1.55 [116]~E(x1161,x1162)+E(f71(x1163,x1161),f71(x1163,x1162)) % 1.40/1.55 [117]~E(x1171,x1172)+E(f25(x1171),f25(x1172)) % 1.40/1.55 [118]~E(x1181,x1182)+E(f52(x1181,x1183),f52(x1182,x1183)) % 1.40/1.55 [119]~E(x1191,x1192)+E(f52(x1193,x1191),f52(x1193,x1192)) % 1.40/1.55 [120]~E(x1201,x1202)+E(f34(x1201,x1203,x1204,x1205),f34(x1202,x1203,x1204,x1205)) % 1.40/1.55 [121]~E(x1211,x1212)+E(f34(x1213,x1211,x1214,x1215),f34(x1213,x1212,x1214,x1215)) % 1.40/1.55 [122]~E(x1221,x1222)+E(f34(x1223,x1224,x1221,x1225),f34(x1223,x1224,x1222,x1225)) % 1.40/1.55 [123]~E(x1231,x1232)+E(f34(x1233,x1234,x1235,x1231),f34(x1233,x1234,x1235,x1232)) % 1.40/1.55 [124]~E(x1241,x1242)+E(f32(x1241,x1243,x1244),f32(x1242,x1243,x1244)) % 1.40/1.55 [125]~E(x1251,x1252)+E(f32(x1253,x1251,x1254),f32(x1253,x1252,x1254)) % 1.40/1.55 [126]~E(x1261,x1262)+E(f32(x1263,x1264,x1261),f32(x1263,x1264,x1262)) % 1.40/1.55 [127]~E(x1271,x1272)+E(f72(x1271,x1273,x1274,x1275),f72(x1272,x1273,x1274,x1275)) % 1.40/1.55 [128]~E(x1281,x1282)+E(f72(x1283,x1281,x1284,x1285),f72(x1283,x1282,x1284,x1285)) % 1.40/1.55 [129]~E(x1291,x1292)+E(f72(x1293,x1294,x1291,x1295),f72(x1293,x1294,x1292,x1295)) % 1.40/1.55 [130]~E(x1301,x1302)+E(f72(x1303,x1304,x1305,x1301),f72(x1303,x1304,x1305,x1302)) % 1.40/1.55 [131]~E(x1311,x1312)+E(f74(x1311,x1313,x1314,x1315),f74(x1312,x1313,x1314,x1315)) % 1.40/1.55 [132]~E(x1321,x1322)+E(f74(x1323,x1321,x1324,x1325),f74(x1323,x1322,x1324,x1325)) % 1.40/1.55 [133]~E(x1331,x1332)+E(f74(x1333,x1334,x1331,x1335),f74(x1333,x1334,x1332,x1335)) % 1.40/1.55 [134]~E(x1341,x1342)+E(f74(x1343,x1344,x1345,x1341),f74(x1343,x1344,x1345,x1342)) % 1.40/1.55 [135]~E(x1351,x1352)+E(f87(x1351,x1353,x1354,x1355,x1356,x1357),f87(x1352,x1353,x1354,x1355,x1356,x1357)) % 1.40/1.55 [136]~E(x1361,x1362)+E(f87(x1363,x1361,x1364,x1365,x1366,x1367),f87(x1363,x1362,x1364,x1365,x1366,x1367)) % 1.40/1.55 [137]~E(x1371,x1372)+E(f87(x1373,x1374,x1371,x1375,x1376,x1377),f87(x1373,x1374,x1372,x1375,x1376,x1377)) % 1.40/1.55 [138]~E(x1381,x1382)+E(f87(x1383,x1384,x1385,x1381,x1386,x1387),f87(x1383,x1384,x1385,x1382,x1386,x1387)) % 1.40/1.55 [139]~E(x1391,x1392)+E(f87(x1393,x1394,x1395,x1396,x1391,x1397),f87(x1393,x1394,x1395,x1396,x1392,x1397)) % 1.40/1.55 [140]~E(x1401,x1402)+E(f87(x1403,x1404,x1405,x1406,x1407,x1401),f87(x1403,x1404,x1405,x1406,x1407,x1402)) % 1.40/1.56 [141]~E(x1411,x1412)+E(f82(x1411,x1413),f82(x1412,x1413)) % 1.40/1.56 [142]~E(x1421,x1422)+E(f82(x1423,x1421),f82(x1423,x1422)) % 1.40/1.56 [143]~E(x1431,x1432)+E(f56(x1431,x1433,x1434,x1435,x1436),f56(x1432,x1433,x1434,x1435,x1436)) % 1.40/1.56 [144]~E(x1441,x1442)+E(f56(x1443,x1441,x1444,x1445,x1446),f56(x1443,x1442,x1444,x1445,x1446)) % 1.40/1.56 [145]~E(x1451,x1452)+E(f56(x1453,x1454,x1451,x1455,x1456),f56(x1453,x1454,x1452,x1455,x1456)) % 1.40/1.56 [146]~E(x1461,x1462)+E(f56(x1463,x1464,x1465,x1461,x1466),f56(x1463,x1464,x1465,x1462,x1466)) % 1.40/1.56 [147]~E(x1471,x1472)+E(f56(x1473,x1474,x1475,x1476,x1471),f56(x1473,x1474,x1475,x1476,x1472)) % 1.40/1.56 [148]~E(x1481,x1482)+E(f70(x1481,x1483),f70(x1482,x1483)) % 1.40/1.56 [149]~E(x1491,x1492)+E(f70(x1493,x1491),f70(x1493,x1492)) % 1.40/1.56 [150]~E(x1501,x1502)+E(f66(x1501,x1503,x1504,x1505,x1506),f66(x1502,x1503,x1504,x1505,x1506)) % 1.40/1.56 [151]~E(x1511,x1512)+E(f66(x1513,x1511,x1514,x1515,x1516),f66(x1513,x1512,x1514,x1515,x1516)) % 1.40/1.56 [152]~E(x1521,x1522)+E(f66(x1523,x1524,x1521,x1525,x1526),f66(x1523,x1524,x1522,x1525,x1526)) % 1.40/1.56 [153]~E(x1531,x1532)+E(f66(x1533,x1534,x1535,x1531,x1536),f66(x1533,x1534,x1535,x1532,x1536)) % 1.40/1.56 [154]~E(x1541,x1542)+E(f66(x1543,x1544,x1545,x1546,x1541),f66(x1543,x1544,x1545,x1546,x1542)) % 1.40/1.56 [155]~E(x1551,x1552)+E(f44(x1551,x1553,x1554),f44(x1552,x1553,x1554)) % 1.40/1.56 [156]~E(x1561,x1562)+E(f44(x1563,x1561,x1564),f44(x1563,x1562,x1564)) % 1.40/1.56 [157]~E(x1571,x1572)+E(f44(x1573,x1574,x1571),f44(x1573,x1574,x1572)) % 1.40/1.56 [158]~E(x1581,x1582)+E(f79(x1581),f79(x1582)) % 1.40/1.56 [159]~E(x1591,x1592)+E(f41(x1591,x1593),f41(x1592,x1593)) % 1.40/1.56 [160]~E(x1601,x1602)+E(f41(x1603,x1601),f41(x1603,x1602)) % 1.40/1.56 [161]~E(x1611,x1612)+E(f43(x1611,x1613,x1614,x1615),f43(x1612,x1613,x1614,x1615)) % 1.40/1.56 [162]~E(x1621,x1622)+E(f43(x1623,x1621,x1624,x1625),f43(x1623,x1622,x1624,x1625)) % 1.40/1.56 [163]~E(x1631,x1632)+E(f43(x1633,x1634,x1631,x1635),f43(x1633,x1634,x1632,x1635)) % 1.40/1.56 [164]~E(x1641,x1642)+E(f43(x1643,x1644,x1645,x1641),f43(x1643,x1644,x1645,x1642)) % 1.40/1.56 [165]~E(x1651,x1652)+E(f64(x1651,x1653,x1654,x1655),f64(x1652,x1653,x1654,x1655)) % 1.40/1.56 [166]~E(x1661,x1662)+E(f64(x1663,x1661,x1664,x1665),f64(x1663,x1662,x1664,x1665)) % 1.40/1.56 [167]~E(x1671,x1672)+E(f64(x1673,x1674,x1671,x1675),f64(x1673,x1674,x1672,x1675)) % 1.40/1.56 [168]~E(x1681,x1682)+E(f64(x1683,x1684,x1685,x1681),f64(x1683,x1684,x1685,x1682)) % 1.40/1.56 [169]~E(x1691,x1692)+E(f57(x1691),f57(x1692)) % 1.40/1.56 [170]~E(x1701,x1702)+E(f67(x1701,x1703,x1704,x1705,x1706),f67(x1702,x1703,x1704,x1705,x1706)) % 1.40/1.56 [171]~E(x1711,x1712)+E(f67(x1713,x1711,x1714,x1715,x1716),f67(x1713,x1712,x1714,x1715,x1716)) % 1.40/1.56 [172]~E(x1721,x1722)+E(f67(x1723,x1724,x1721,x1725,x1726),f67(x1723,x1724,x1722,x1725,x1726)) % 1.40/1.56 [173]~E(x1731,x1732)+E(f67(x1733,x1734,x1735,x1731,x1736),f67(x1733,x1734,x1735,x1732,x1736)) % 1.40/1.56 [174]~E(x1741,x1742)+E(f67(x1743,x1744,x1745,x1746,x1741),f67(x1743,x1744,x1745,x1746,x1742)) % 1.40/1.56 [175]~E(x1751,x1752)+E(f78(x1751,x1753),f78(x1752,x1753)) % 1.40/1.56 [176]~E(x1761,x1762)+E(f78(x1763,x1761),f78(x1763,x1762)) % 1.40/1.56 [177]~E(x1771,x1772)+E(f49(x1771,x1773,x1774,x1775),f49(x1772,x1773,x1774,x1775)) % 1.40/1.56 [178]~E(x1781,x1782)+E(f49(x1783,x1781,x1784,x1785),f49(x1783,x1782,x1784,x1785)) % 1.40/1.56 [179]~E(x1791,x1792)+E(f49(x1793,x1794,x1791,x1795),f49(x1793,x1794,x1792,x1795)) % 1.40/1.56 [180]~E(x1801,x1802)+E(f49(x1803,x1804,x1805,x1801),f49(x1803,x1804,x1805,x1802)) % 1.40/1.56 [181]~E(x1811,x1812)+E(f54(x1811,x1813),f54(x1812,x1813)) % 1.40/1.56 [182]~E(x1821,x1822)+E(f54(x1823,x1821),f54(x1823,x1822)) % 1.40/1.56 [183]~E(x1831,x1832)+E(f80(x1831,x1833,x1834,x1835),f80(x1832,x1833,x1834,x1835)) % 1.40/1.56 [184]~E(x1841,x1842)+E(f80(x1843,x1841,x1844,x1845),f80(x1843,x1842,x1844,x1845)) % 1.40/1.56 [185]~E(x1851,x1852)+E(f80(x1853,x1854,x1851,x1855),f80(x1853,x1854,x1852,x1855)) % 1.40/1.56 [186]~E(x1861,x1862)+E(f80(x1863,x1864,x1865,x1861),f80(x1863,x1864,x1865,x1862)) % 1.40/1.56 [187]~E(x1871,x1872)+E(f75(x1871,x1873,x1874,x1875,x1876),f75(x1872,x1873,x1874,x1875,x1876)) % 1.40/1.56 [188]~E(x1881,x1882)+E(f75(x1883,x1881,x1884,x1885,x1886),f75(x1883,x1882,x1884,x1885,x1886)) % 1.40/1.56 [189]~E(x1891,x1892)+E(f75(x1893,x1894,x1891,x1895,x1896),f75(x1893,x1894,x1892,x1895,x1896)) % 1.40/1.56 [190]~E(x1901,x1902)+E(f75(x1903,x1904,x1905,x1901,x1906),f75(x1903,x1904,x1905,x1902,x1906)) % 1.40/1.56 [191]~E(x1911,x1912)+E(f75(x1913,x1914,x1915,x1916,x1911),f75(x1913,x1914,x1915,x1916,x1912)) % 1.40/1.56 [192]~E(x1921,x1922)+E(f73(x1921,x1923,x1924),f73(x1922,x1923,x1924)) % 1.40/1.56 [193]~E(x1931,x1932)+E(f73(x1933,x1931,x1934),f73(x1933,x1932,x1934)) % 1.40/1.56 [194]~E(x1941,x1942)+E(f73(x1943,x1944,x1941),f73(x1943,x1944,x1942)) % 1.40/1.56 [195]~E(x1951,x1952)+E(f48(x1951,x1953),f48(x1952,x1953)) % 1.40/1.56 [196]~E(x1961,x1962)+E(f48(x1963,x1961),f48(x1963,x1962)) % 1.40/1.56 [197]~E(x1971,x1972)+E(f26(x1971,x1973,x1974,x1975),f26(x1972,x1973,x1974,x1975)) % 1.40/1.56 [198]~E(x1981,x1982)+E(f26(x1983,x1981,x1984,x1985),f26(x1983,x1982,x1984,x1985)) % 1.40/1.56 [199]~E(x1991,x1992)+E(f26(x1993,x1994,x1991,x1995),f26(x1993,x1994,x1992,x1995)) % 1.40/1.56 [200]~E(x2001,x2002)+E(f26(x2003,x2004,x2005,x2001),f26(x2003,x2004,x2005,x2002)) % 1.40/1.56 [201]~E(x2011,x2012)+E(f47(x2011,x2013),f47(x2012,x2013)) % 1.40/1.56 [202]~E(x2021,x2022)+E(f47(x2023,x2021),f47(x2023,x2022)) % 1.40/1.56 [203]~E(x2031,x2032)+E(f69(x2031,x2033),f69(x2032,x2033)) % 1.40/1.56 [204]~E(x2041,x2042)+E(f69(x2043,x2041),f69(x2043,x2042)) % 1.40/1.56 [205]~E(x2051,x2052)+E(f55(x2051,x2053),f55(x2052,x2053)) % 1.40/1.56 [206]~E(x2061,x2062)+E(f55(x2063,x2061),f55(x2063,x2062)) % 1.40/1.56 [207]~E(x2071,x2072)+E(f58(x2071),f58(x2072)) % 1.40/1.56 [208]~E(x2081,x2082)+E(f83(x2081),f83(x2082)) % 1.40/1.56 [209]~P1(x2091)+P1(x2092)+~E(x2091,x2092) % 1.40/1.56 [210]~P2(x2101)+P2(x2102)+~E(x2101,x2102) % 1.40/1.56 [211]~P4(x2111)+P4(x2112)+~E(x2111,x2112) % 1.40/1.56 [212]~P5(x2121)+P5(x2122)+~E(x2121,x2122) % 1.40/1.56 [213]~P6(x2131)+P6(x2132)+~E(x2131,x2132) % 1.40/1.56 [214]~P13(x2141)+P13(x2142)+~E(x2141,x2142) % 1.40/1.56 [215]~P14(x2151)+P14(x2152)+~E(x2151,x2152) % 1.40/1.56 [216]~P15(x2161)+P15(x2162)+~E(x2161,x2162) % 1.40/1.56 [217]~P19(x2171)+P19(x2172)+~E(x2171,x2172) % 1.40/1.56 [218]~P20(x2181)+P20(x2182)+~E(x2181,x2182) % 1.40/1.56 [219]~P21(x2191)+P21(x2192)+~E(x2191,x2192) % 1.40/1.56 [220]~P34(x2201)+P34(x2202)+~E(x2201,x2202) % 1.40/1.56 [221]~P22(x2211)+P22(x2212)+~E(x2211,x2212) % 1.40/1.56 [222]P8(x2222,x2223)+~E(x2221,x2222)+~P8(x2221,x2223) % 1.40/1.56 [223]P8(x2233,x2232)+~E(x2231,x2232)+~P8(x2233,x2231) % 1.40/1.56 [224]~P23(x2241)+P23(x2242)+~E(x2241,x2242) % 1.40/1.56 [225]~P27(x2251)+P27(x2252)+~E(x2251,x2252) % 1.40/1.56 [226]~P25(x2261)+P25(x2262)+~E(x2261,x2262) % 1.40/1.56 [227]~P28(x2271)+P28(x2272)+~E(x2271,x2272) % 1.40/1.56 [228]~P7(x2281)+P7(x2282)+~E(x2281,x2282) % 1.40/1.56 [229]P3(x2292,x2293)+~E(x2291,x2292)+~P3(x2291,x2293) % 1.40/1.56 [230]P3(x2303,x2302)+~E(x2301,x2302)+~P3(x2303,x2301) % 1.40/1.56 [231]~P24(x2311)+P24(x2312)+~E(x2311,x2312) % 1.40/1.56 [232]~P31(x2321)+P31(x2322)+~E(x2321,x2322) % 1.40/1.56 [233]~P16(x2331)+P16(x2332)+~E(x2331,x2332) % 1.40/1.56 [234]~P17(x2341)+P17(x2342)+~E(x2341,x2342) % 1.40/1.56 [235]P9(x2352,x2353,x2354,x2355)+~E(x2351,x2352)+~P9(x2351,x2353,x2354,x2355) % 1.40/1.56 [236]P9(x2363,x2362,x2364,x2365)+~E(x2361,x2362)+~P9(x2363,x2361,x2364,x2365) % 1.40/1.56 [237]P9(x2373,x2374,x2372,x2375)+~E(x2371,x2372)+~P9(x2373,x2374,x2371,x2375) % 1.40/1.56 [238]P9(x2383,x2384,x2385,x2382)+~E(x2381,x2382)+~P9(x2383,x2384,x2385,x2381) % 1.40/1.56 [239]~P29(x2391)+P29(x2392)+~E(x2391,x2392) % 1.40/1.56 [240]~P33(x2401)+P33(x2402)+~E(x2401,x2402) % 1.40/1.56 [241]~P26(x2411)+P26(x2412)+~E(x2411,x2412) % 1.40/1.56 [242]P10(x2422,x2423,x2424,x2425,x2426)+~E(x2421,x2422)+~P10(x2421,x2423,x2424,x2425,x2426) % 1.40/1.56 [243]P10(x2433,x2432,x2434,x2435,x2436)+~E(x2431,x2432)+~P10(x2433,x2431,x2434,x2435,x2436) % 1.40/1.56 [244]P10(x2443,x2444,x2442,x2445,x2446)+~E(x2441,x2442)+~P10(x2443,x2444,x2441,x2445,x2446) % 1.40/1.56 [245]P10(x2453,x2454,x2455,x2452,x2456)+~E(x2451,x2452)+~P10(x2453,x2454,x2455,x2451,x2456) % 1.40/1.56 [246]P10(x2463,x2464,x2465,x2466,x2462)+~E(x2461,x2462)+~P10(x2463,x2464,x2465,x2466,x2461) % 1.40/1.56 [247]~P18(x2471)+P18(x2472)+~E(x2471,x2472) % 1.40/1.56 [248]~P30(x2481)+P30(x2482)+~E(x2481,x2482) % 1.40/1.56 [249]P11(x2492,x2493,x2494,x2495,x2496,x2497)+~E(x2491,x2492)+~P11(x2491,x2493,x2494,x2495,x2496,x2497) % 1.40/1.56 [250]P11(x2503,x2502,x2504,x2505,x2506,x2507)+~E(x2501,x2502)+~P11(x2503,x2501,x2504,x2505,x2506,x2507) % 1.40/1.56 [251]P11(x2513,x2514,x2512,x2515,x2516,x2517)+~E(x2511,x2512)+~P11(x2513,x2514,x2511,x2515,x2516,x2517) % 1.40/1.56 [252]P11(x2523,x2524,x2525,x2522,x2526,x2527)+~E(x2521,x2522)+~P11(x2523,x2524,x2525,x2521,x2526,x2527) % 1.40/1.56 [253]P11(x2533,x2534,x2535,x2536,x2532,x2537)+~E(x2531,x2532)+~P11(x2533,x2534,x2535,x2536,x2531,x2537) % 1.40/1.56 [254]P11(x2543,x2544,x2545,x2546,x2547,x2542)+~E(x2541,x2542)+~P11(x2543,x2544,x2545,x2546,x2547,x2541) % 1.40/1.56 [255]~P32(x2551)+P32(x2552)+~E(x2551,x2552) % 1.40/1.56 [256]P12(x2562,x2563,x2564,x2565,x2566,x2567)+~E(x2561,x2562)+~P12(x2561,x2563,x2564,x2565,x2566,x2567) % 1.40/1.56 [257]P12(x2573,x2572,x2574,x2575,x2576,x2577)+~E(x2571,x2572)+~P12(x2573,x2571,x2574,x2575,x2576,x2577) % 1.40/1.56 [258]P12(x2583,x2584,x2582,x2585,x2586,x2587)+~E(x2581,x2582)+~P12(x2583,x2584,x2581,x2585,x2586,x2587) % 1.40/1.56 [259]P12(x2593,x2594,x2595,x2592,x2596,x2597)+~E(x2591,x2592)+~P12(x2593,x2594,x2595,x2591,x2596,x2597) % 1.40/1.56 [260]P12(x2603,x2604,x2605,x2606,x2602,x2607)+~E(x2601,x2602)+~P12(x2603,x2604,x2605,x2606,x2601,x2607) % 1.40/1.56 [261]P12(x2613,x2614,x2615,x2616,x2617,x2612)+~E(x2611,x2612)+~P12(x2613,x2614,x2615,x2616,x2617,x2611) % 1.40/1.56 % 1.40/1.56 %------------------------------------------- % 1.40/1.56 cnf(1069,plain, % 1.40/1.56 (P34(f28(f28(f35(x10692),x10691),f28(a39,x10691)))), % 1.40/1.56 inference(equality_inference,[],[478])). % 1.40/1.56 cnf(1078,plain, % 1.40/1.56 (P34(f28(f36(x10782,x10781,x10783),x10781))), % 1.40/1.56 inference(equality_inference,[],[554])). % 1.40/1.56 cnf(1086,plain, % 1.40/1.56 (~P34(f28(f28(f30(f94(x10862,a3)),x10861),x10861))), % 1.40/1.56 inference(equality_inference,[],[669])). % 1.40/1.56 cnf(1099,plain, % 1.40/1.56 (~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x10992),x10991)),f28(f28(a13,x10993),x10991)))), % 1.40/1.56 inference(equality_inference,[],[832])). % 1.40/1.56 cnf(1100,plain, % 1.40/1.56 (~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x11001),x11002)),f28(f28(a11,x11003),x11001)))), % 1.40/1.56 inference(equality_inference,[],[833])). % 1.40/1.56 cnf(1102,plain, % 1.40/1.56 (E(f37(x11021,x11022,x11023,f37(x11022,x11021,f23(x11021,x11022,x11024,x11023),x11025)),x11025)+~P34(f28(f29(f94(x11022,a3),x11025),f37(x11021,x11022,x11023,x11024)))), % 1.40/1.56 inference(equality_inference,[],[862])). % 1.40/1.56 cnf(1103,plain, % 1.40/1.56 (E(x11031,x11032)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x11033),x11033)),f14(x11034,x11031,x11032)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x11034),a8))), % 1.40/1.56 inference(equality_inference,[],[876])). % 1.40/1.56 cnf(1105,plain, % 1.40/1.56 (E(x11051,x11052)+~P34(f28(f28(f35(f96(a91,a91)),f28(f28(f33(a91,a91),x11053),x11053)),f28(f28(f28(a12,x11054),x11051),x11052)))+~P34(f28(f28(f35(f94(f96(a91,a91),a3)),x11054),a8))), % 1.40/1.56 inference(equality_inference,[],[885])). % 1.40/1.56 cnf(1124,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x11241),x11242)),x11242))), % 1.40/1.56 inference(rename_variables,[],[389])). % 1.40/1.56 cnf(1137,plain, % 1.40/1.56 (P34(f28(f29(a2,x11371),f28(f28(f20(a2),x11372),x11371)))), % 1.40/1.56 inference(rename_variables,[],[323])). % 1.40/1.56 cnf(1140,plain, % 1.40/1.56 (P34(f28(f28(f30(a2),x11401),f28(a22,x11401)))), % 1.40/1.56 inference(rename_variables,[],[309])). % 1.40/1.56 cnf(1154,plain, % 1.40/1.56 (P34(f28(f28(f35(x11541),x11542),f28(a39,x11542)))), % 1.40/1.56 inference(rename_variables,[],[1069])). % 1.40/1.56 cnf(1161,plain, % 1.40/1.56 (~P34(f28(f29(a2,f28(a22,x11611)),x11611))), % 1.40/1.56 inference(rename_variables,[],[388])). % 1.40/1.56 cnf(1167,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),x11671),f4(a2)))), % 1.40/1.56 inference(rename_variables,[],[387])). % 1.40/1.56 cnf(1170,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x11701),x11702)),x11702))), % 1.40/1.56 inference(rename_variables,[],[389])). % 1.40/1.56 cnf(1179,plain, % 1.40/1.56 (P34(f28(f28(f30(a2),x11791),f28(a22,x11791)))), % 1.40/1.56 inference(rename_variables,[],[309])). % 1.40/1.56 cnf(1186,plain, % 1.40/1.56 (~P34(f28(f29(a2,f28(a22,x11861)),x11861))), % 1.40/1.56 inference(rename_variables,[],[388])). % 1.40/1.56 cnf(1189,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x11891),x11892)),x11892))), % 1.40/1.56 inference(rename_variables,[],[389])). % 1.40/1.56 cnf(1200,plain, % 1.40/1.56 (P34(f28(f29(a2,x12001),f28(f28(f20(a2),x12002),x12001)))), % 1.40/1.56 inference(rename_variables,[],[323])). % 1.40/1.56 cnf(1205,plain, % 1.40/1.56 (~P34(f28(f29(a2,f28(a22,x12051)),x12051))), % 1.40/1.56 inference(rename_variables,[],[388])). % 1.40/1.56 cnf(1208,plain, % 1.40/1.56 (~P34(f28(f29(a2,f28(a22,x12081)),x12081))), % 1.40/1.56 inference(rename_variables,[],[388])). % 1.40/1.56 cnf(1213,plain, % 1.40/1.56 (P34(f28(f29(a2,x12131),f28(f28(f20(a2),x12131),x12132)))), % 1.40/1.56 inference(rename_variables,[],[324])). % 1.40/1.56 cnf(1216,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x12161),x12162)),x12162))), % 1.40/1.56 inference(rename_variables,[],[389])). % 1.40/1.56 cnf(1219,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x12191),x12192)),x12192))), % 1.40/1.56 inference(rename_variables,[],[389])). % 1.40/1.56 cnf(1230,plain, % 1.40/1.56 (P34(f28(f29(a2,x12301),x12301))), % 1.40/1.56 inference(rename_variables,[],[301])). % 1.40/1.56 cnf(1237,plain, % 1.40/1.56 (P34(f28(f29(f94(x12371,a3),x12372),f36(x12371,x12373,x12372)))), % 1.40/1.56 inference(rename_variables,[],[336])). % 1.40/1.56 cnf(1247,plain, % 1.40/1.56 (P34(f28(f28(f30(a2),x12471),f28(a22,x12471)))), % 1.40/1.56 inference(rename_variables,[],[309])). % 1.40/1.56 cnf(1250,plain, % 1.40/1.56 (P34(f28(f28(f30(a2),x12501),f28(a22,x12501)))), % 1.40/1.56 inference(rename_variables,[],[309])). % 1.40/1.56 cnf(1260,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),x12601),x12601))), % 1.40/1.56 inference(rename_variables,[],[384])). % 1.40/1.56 cnf(1265,plain, % 1.40/1.56 (P34(f28(f29(f94(x12651,a3),x12652),x12652))), % 1.40/1.56 inference(rename_variables,[],[314])). % 1.40/1.56 cnf(1278,plain, % 1.40/1.56 (P34(f28(f29(f94(x12781,a3),x12782),x12782))), % 1.40/1.56 inference(rename_variables,[],[314])). % 1.40/1.56 cnf(1285,plain, % 1.40/1.56 (P34(f28(f29(f94(x12851,a3),x12852),x12852))), % 1.40/1.56 inference(rename_variables,[],[314])). % 1.40/1.56 cnf(1298,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x12981),x12982)),x12982))), % 1.40/1.56 inference(rename_variables,[],[389])). % 1.40/1.56 cnf(1303,plain, % 1.40/1.56 (~P34(f28(f28(f30(a2),f28(f28(f20(a2),x13031),x13032)),x13031))), % 1.40/1.56 inference(rename_variables,[],[390])). % 1.40/1.56 cnf(1309,plain, % 1.40/1.56 (P34(f28(f28(f35(x13091),x13092),f28(a39,x13092)))), % 1.40/1.56 inference(rename_variables,[],[1069])). % 1.40/1.56 cnf(1312,plain, % 1.40/1.56 (P34(f28(f29(f94(x13121,a3),x13122),f36(x13121,x13123,x13122)))), % 1.40/1.56 inference(rename_variables,[],[336])). % 1.40/1.56 cnf(1319,plain, % 1.40/1.56 (P34(f28(f29(f94(x13191,a3),x13192),x13192))), % 1.40/1.56 inference(rename_variables,[],[314])). % 1.40/1.56 cnf(1322,plain, % 1.40/1.56 (P34(f28(f28(f35(x13221),x13222),f28(a39,x13222)))), % 1.40/1.56 inference(rename_variables,[],[1069])). % 1.40/1.56 cnf(1323,plain, % 1.40/1.56 (P9(x13231,x13231,f6(x13231),x13232)), % 1.40/1.56 inference(rename_variables,[],[321])). % 1.40/1.56 cnf(1326,plain, % 1.40/1.56 (E(f27(a2,x13261),x13261)), % 1.40/1.56 inference(rename_variables,[],[290])). % 1.40/1.56 cnf(1329,plain, % 1.40/1.56 (P34(f28(f28(f35(x13291),x13292),f28(a39,x13292)))), % 1.40/1.56 inference(rename_variables,[],[1069])). % 1.40/1.56 cnf(1330,plain, % 1.40/1.56 (P34(f28(f28(f35(f94(x13301,x13301)),f6(x13301)),f18(x13301,x13301,x13302,f28(f16(f94(x13301,a3),x13301),x13302))))), % 1.40/1.56 inference(rename_variables,[],[361])). % 1.40/1.56 cnf(1336,plain, % 1.40/1.56 (P34(f28(f28(f35(x13361),x13362),f28(a39,x13362)))), % 1.40/1.56 inference(rename_variables,[],[1069])). % 1.40/1.56 cnf(1349,plain, % 1.40/1.56 (E(f27(a2,x13491),x13491)), % 1.40/1.56 inference(rename_variables,[],[290])). % 1.40/1.56 cnf(1351,plain, % 1.40/1.56 (E(f27(a2,x13511),x13511)), % 1.40/1.56 inference(rename_variables,[],[290])). % 1.40/1.56 cnf(1355,plain, % 1.40/1.56 (E(f27(a2,x13551),x13551)), % 1.40/1.56 inference(rename_variables,[],[290])). % 1.40/1.56 cnf(1357,plain, % 1.40/1.56 (P9(x13571,x13571,f6(x13571),x13572)), % 1.40/1.56 inference(rename_variables,[],[321])). % 1.40/1.56 cnf(1394,plain, % 1.40/1.56 (P34(f28(f29(f94(x13941,a3),x13942),f36(x13941,x13943,x13942)))), % 1.40/1.56 inference(rename_variables,[],[336])). % 1.40/1.56 cnf(1409,plain, % 1.40/1.56 (P9(a2,a2,a22,x14091)), % 1.40/1.56 inference(rename_variables,[],[319])). % 1.40/1.56 cnf(1412,plain, % 1.40/1.56 (P34(f28(f29(f94(x14121,a3),x14122),f31(f94(x14121,a3))))), % 1.40/1.56 inference(rename_variables,[],[326])). % 1.40/1.56 cnf(1417,plain, % 1.40/1.56 (P34(f28(f29(f94(x14171,a3),x14172),f36(x14171,x14173,x14172)))), % 1.40/1.56 inference(rename_variables,[],[336])). % 1.40/1.56 cnf(1418,plain, % 1.40/1.56 (P34(f28(f29(f94(x14181,a3),x14182),f31(f94(x14181,a3))))), % 1.40/1.56 inference(rename_variables,[],[326])). % 1.40/1.56 cnf(1422,plain, % 1.40/1.56 (P34(f28(f29(f94(x14221,a3),x14222),f36(x14221,x14223,x14222)))), % 1.40/1.56 inference(rename_variables,[],[336])). % 1.40/1.56 cnf(1427,plain, % 1.40/1.56 (P34(f28(f29(f94(x14271,a3),x14272),f36(x14271,x14273,x14272)))), % 1.40/1.56 inference(rename_variables,[],[336])). % 1.40/1.56 cnf(1440,plain, % 1.40/1.56 ($false), % 1.40/1.56 inference(scs_inference,[],[1078,1086,1099,1100,1069,1154,1309,1322,1329,1336,392,321,1323,1357,290,1326,1349,1351,1355,376,319,1409,382,267,268,270,272,275,276,277,280,288,354,322,307,299,349,297,300,333,336,1237,1312,1394,1417,1422,1427,301,1230,309,1140,1179,1247,1250,310,387,1167,340,314,1265,1278,1285,1319,384,1260,317,326,1412,1418,388,1161,1186,1205,1208,359,323,1137,1200,324,1213,332,331,330,361,1330,389,1124,1170,1189,1216,1219,1298,390,1303,341,342,351,344,346,460,474,477,513,530,560,627,639,668,675,752,782,826,881,2,7,397,441,453,454,463,469,475,476,503,506,535,540,564,579,584,585,598,611,628,633,635,637,638,657,659,714,737,738,750,783,790,793,795,804,829,830,836,838,844,845,848,856,874,875,878,886,900,923,948,969,971,1102,859,431,433,501,502,505,512,521,602,606,624,641,692,789,799,821,870,871,894,909,928,1103,1105,3,220,223,227,235,236,237,238,438,456,481,483,484,556,558,559,567,573,586,589,592,593,612,617,618,619,682,684,688,694,726,770,774,785,808,817,842,846]), % 1.40/1.56 ['proof']). % 1.40/1.56 % SZS output end Proof % 1.40/1.56 % Total time :0.470000s %------------------------------------------------------------------------------