%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SCT161+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n021.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 14:11:52 EDT 2024 % Result : Theorem 1.60s 1.58s % Output : CNFRefutation 1.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SCT161+1 : TPTP v8.2.0. Released v5.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n021.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Sat Jun 22 10:32:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.49/0.56 start to proof:theBenchmark % 1.42/1.52 %------------------------------------------- % 1.42/1.52 % File :CSE---1.7 % 1.42/1.52 % Problem :theBenchmark % 1.42/1.52 % Transform :cnf % 1.42/1.52 % Format :tptp:raw % 1.42/1.52 % Command :java -jar mcs_scs.jar %d %s % 1.42/1.52 % 1.42/1.52 % Result :Theorem 0.510000s % 1.42/1.52 % Output :CNFRefutation 0.510000s % 1.42/1.52 %------------------------------------------- % 1.42/1.53 %------------------------------------------------------------------------------ % 1.42/1.53 % File : SCT161+1 : TPTP v8.2.0. Released v5.2.0. % 1.42/1.53 % Domain : Social Choice Theory % 1.42/1.53 % Problem : Arrow's Impossibility Theorem 433512, 500 axioms selected % 1.42/1.53 % Version : Especial. % 1.42/1.53 % English : % 1.42/1.53 % 1.42/1.53 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.42/1.53 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 1.42/1.53 % Source : [Bla11] % 1.42/1.53 % Names : arrow_433512.500.p [Bla11] % 1.42/1.53 % 1.42/1.53 % Status : ContradictoryAxioms % 1.42/1.53 % Rating : 0.61 v8.2.0, 0.58 v8.1.0, 0.61 v7.5.0, 0.53 v7.4.0, 0.63 v7.3.0, 0.66 v7.2.0, 0.62 v7.1.0, 0.57 v6.4.0, 0.62 v6.3.0, 0.58 v6.2.0, 0.68 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.74 v5.4.0, 0.75 v5.3.0, 0.78 v5.2.0 % 1.42/1.53 % Syntax : Number of formulae : 535 ( 126 unt; 0 def) % 1.42/1.53 % Number of atoms : 1413 ( 336 equ) % 1.42/1.53 % Maximal formula atoms : 12 ( 2 avg) % 1.42/1.53 % Number of connectives : 1032 ( 154 ~; 26 |; 63 &) % 1.42/1.53 % ( 142 <=>; 647 =>; 0 <=; 0 <~>) % 1.42/1.53 % Maximal formula depth : 16 ( 6 avg) % 1.42/1.53 % Maximal term depth : 14 ( 2 avg) % 1.42/1.53 % Number of predicates : 33 ( 32 usr; 0 prp; 1-6 aty) % 1.42/1.53 % Number of functors : 66 ( 66 usr; 17 con; 0-5 aty) % 1.42/1.53 % Number of variables : 1584 (1564 !; 20 ?) % 1.42/1.53 % SPC : FOF_CAX_RFO_SEQ % 1.42/1.53 % 1.42/1.53 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 1.42/1.53 % 2011-03-01 11:27:36 % 1.42/1.53 % : Renamed from SWW163+1 % 1.42/1.53 %------------------------------------------------------------------------------ % 1.42/1.53 %----Relevant facts (492) % 1.42/1.53 fof(fact_ext,axiom, % 1.42/1.53 ! [V_g_2,V_f_2] : % 1.42/1.53 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 1.42/1.53 => V_f_2 = V_g_2 ) ). % 1.42/1.53 % 1.42/1.53 fof(fact_injh,axiom, % 1.42/1.53 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))) ). % 1.42/1.53 % 1.42/1.53 fof(fact_top1I,axiom, % 1.42/1.53 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_PiProf,axiom, % 1.42/1.53 ! [V_n_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_n_2))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_top__apply,axiom, % 1.42/1.53 ! [V_x_2,T_b,T_a] : % 1.42/1.53 ( class_Orderings_Otop(T_a) % 1.42/1.53 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 1.42/1.53 % 1.42/1.53 fof(fact__096Lab_A_058_ALin_096,axiom, % 1.42/1.53 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)) ). % 1.42/1.53 % 1.42/1.53 fof(fact__096Lba_A_058_ALin_096,axiom, % 1.42/1.53 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_surjh,axiom, % 1.42/1.53 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)))) ). % 1.42/1.53 % 1.42/1.53 fof(fact__C0_C,axiom, % 1.42/1.53 ! [V_n_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),V_n_2))),v_Lab____)),v_Lba____))),c_Arrow__Order__Mirabelle_OLin)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_less__not__refl,axiom, % 1.42/1.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_nat__neq__iff,axiom, % 1.42/1.53 ! [V_n_2,V_m_2] : % 1.42/1.53 ( V_m_2 != V_n_2 % 1.42/1.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.42/1.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 1.42/1.53 % 1.42/1.53 fof(fact_linorder__neqE__nat,axiom, % 1.42/1.53 ! [V_y,V_x] : % 1.42/1.53 ( V_x != V_y % 1.42/1.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.42/1.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 1.42/1.53 % 1.42/1.53 fof(fact_less__irrefl__nat,axiom, % 1.42/1.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_less__not__refl2,axiom, % 1.42/1.53 ! [V_m,V_n] : % 1.42/1.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.42/1.53 => V_m != V_n ) ). % 1.42/1.53 % 1.42/1.53 fof(fact_u,axiom, % 1.42/1.53 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ). % 1.42/1.53 % 1.42/1.53 fof(fact_assms_I3_J,axiom, % 1.42/1.53 c_Arrow__Order__Mirabelle_OIIA(v_F) ). % 1.42/1.53 % 1.42/1.53 fof(fact__096F_A_I_Fi_O_ALba_J_A_058_ALin_096,axiom, % 1.42/1.53 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,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_Lba____))),c_Arrow__Order__Mirabelle_OLin)) ). % 1.42/1.53 % 1.42/1.53 fof(fact_less__zeroE,axiom, % 1.42/1.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.42/1.53 % 1.42/1.53 fof(fact_eq__mem,axiom, % 1.42/1.53 ! [V_y_2,V_x_2,T_a] : % 1.42/1.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 1.42/1.53 <=> V_x_2 = V_y_2 ) ). % 1.42/1.54 % 1.42/1.54 fof(fact_pred__equals__eq,axiom, % 1.42/1.54 ! [V_S_2,V_R_2,T_a] : % 1.42/1.54 ( 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) % 1.42/1.54 <=> V_R_2 = V_S_2 ) ). % 1.42/1.54 % 1.42/1.54 fof(fact_const__Lin__Prof,axiom, % 1.42/1.54 ! [V_L_2] : % 1.42/1.54 ( 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)) % 1.42/1.54 => 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))),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)) ) ). % 1.42/1.54 % 1.42/1.54 fof(fact_gr0I,axiom, % 1.42/1.54 ! [V_n] : % 1.49/1.54 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_gr__implies__not0,axiom, % 1.49/1.54 ! [V_n,V_m] : % 1.49/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.54 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_less__nat__zero__code,axiom, % 1.49/1.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.49/1.54 % 1.49/1.54 fof(fact_neq0__conv,axiom, % 1.49/1.54 ! [V_n_2] : % 1.49/1.54 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.49/1.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_not__less0,axiom, % 1.49/1.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 1.49/1.54 % 1.49/1.54 fof(fact_linorder__cases,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Olinorder(T_a) % 1.49/1.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => ( V_x != V_y % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__asym,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Opreorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_xt1_I10_J,axiom, % 1.49/1.54 ! [V_z,V_x,V_y,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__trans,axiom, % 1.49/1.54 ! [V_z,V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Opreorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_xt1_I2_J,axiom, % 1.49/1.54 ! [V_c,V_a,V_b,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.49/1.54 => ( V_b = V_c % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_ord__less__eq__trans,axiom, % 1.49/1.54 ! [V_c,V_b,V_a,T_a] : % 1.49/1.54 ( class_Orderings_Oord(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.49/1.54 => ( V_b = V_c % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_xt1_I1_J,axiom, % 1.49/1.54 ! [V_c,V_b,V_a,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( V_a = V_b % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_ord__eq__less__trans,axiom, % 1.49/1.54 ! [V_c,V_b,V_a,T_a] : % 1.49/1.54 ( class_Orderings_Oord(T_a) % 1.49/1.54 => ( V_a = V_b % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_xt1_I9_J,axiom, % 1.49/1.54 ! [V_a,V_b,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 1.49/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__asym_H,axiom, % 1.49/1.54 ! [V_b,V_a,T_a] : % 1.49/1.54 ( class_Orderings_Opreorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.49/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__imp__not__eq2,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => V_y != V_x ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__imp__not__eq,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => V_x != V_y ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__imp__not__less,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Opreorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__not__sym,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Opreorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_less__imp__neq,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Oorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => V_x != V_y ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_linorder__neqE,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Olinorder(T_a) % 1.49/1.54 => ( V_x != V_y % 1.49/1.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_linorder__antisym__conv3,axiom, % 1.49/1.54 ! [V_x_2,V_y_2,T_a] : % 1.49/1.54 ( class_Orderings_Olinorder(T_a) % 1.49/1.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.49/1.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.54 <=> V_x_2 = V_y_2 ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_linorder__less__linear,axiom, % 1.49/1.54 ! [V_y,V_x,T_a] : % 1.49/1.54 ( class_Orderings_Olinorder(T_a) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.54 | V_x = V_y % 1.49/1.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_not__less__iff__gr__or__eq,axiom, % 1.49/1.54 ! [V_y_2,V_x_2,T_a] : % 1.49/1.54 ( class_Orderings_Olinorder(T_a) % 1.49/1.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 1.49/1.54 | V_x_2 = V_y_2 ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_linorder__neq__iff,axiom, % 1.49/1.54 ! [V_y_2,V_x_2,T_a] : % 1.49/1.54 ( class_Orderings_Olinorder(T_a) % 1.49/1.54 => ( V_x_2 != V_y_2 % 1.49/1.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_order__less__irrefl,axiom, % 1.49/1.54 ! [V_x,T_a] : % 1.49/1.54 ( class_Orderings_Opreorder(T_a) % 1.49/1.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_nat__less__cases,axiom, % 1.49/1.54 ! [V_P_2,V_n_2,V_m_2] : % 1.49/1.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.49/1.54 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 1.49/1.54 => ( ( V_m_2 = V_n_2 % 1.49/1.54 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 1.49/1.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 1.49/1.54 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 1.49/1.54 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_less__not__refl3,axiom, % 1.49/1.54 ! [V_t,V_s] : % 1.49/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 1.49/1.54 => V_s != V_t ) ). % 1.49/1.54 % 1.49/1.54 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, % 1.49/1.54 ~ ! [B_h] : % 1.49/1.54 ( 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))) % 1.49/1.54 => 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)))) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_image__eqI,axiom, % 1.49/1.54 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_ba_2] : % 1.49/1.54 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.49/1.54 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.49/1.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_UNIV__I,axiom, % 1.49/1.54 ! [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)))) ). % 1.49/1.54 % 1.49/1.54 fof(fact_pigeonhole,axiom, % 1.49/1.54 ! [V_A_2,V_f_2,T_b,T_a] : % 1.49/1.54 ( 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))) % 1.49/1.54 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_range__ex1__eq,axiom, % 1.49/1.54 ! [V_ba_2,V_f_2,T_b,T_a] : % 1.49/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.54 => ( 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))))) % 1.49/1.54 <=> ? [B_x] : % 1.49/1.54 ( V_ba_2 = hAPP(V_f_2,B_x) % 1.49/1.54 & ! [B_y] : % 1.49/1.54 ( V_ba_2 = hAPP(V_f_2,B_y) % 1.49/1.54 => B_y = B_x ) ) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_inj__image__mem__iff,axiom, % 1.49/1.54 ! [V_A_2,V_aa_2,V_f_2,T_b,T_a] : % 1.49/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.54 => ( 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))) % 1.49/1.54 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_ex__nat__less__eq,axiom, % 1.49/1.54 ! [V_P_2,V_n_2] : % 1.49/1.54 ( ? [B_m] : % 1.49/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 1.49/1.54 & hBOOL(hAPP(V_P_2,B_m)) ) % 1.49/1.54 <=> ? [B_x] : % 1.49/1.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 1.49/1.54 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_all__nat__less__eq,axiom, % 1.49/1.54 ! [V_P_2,V_n_2] : % 1.49/1.54 ( ! [B_m] : % 1.49/1.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 1.49/1.54 => hBOOL(hAPP(V_P_2,B_m)) ) % 1.49/1.54 <=> ! [B_x] : % 1.49/1.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 1.49/1.54 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_card__image,axiom, % 1.49/1.54 ! [V_A_2,V_f_2,T_b,T_a] : % 1.49/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.54 => 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) ) ). % 1.49/1.54 % 1.49/1.54 fof(fact_inj__image__eq__iff,axiom, % 1.49/1.54 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.54 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.54 => ( 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) % 1.49/1.54 <=> V_A_2 = V_B_2 ) ) ). % 1.49/1.54 % 1.49/1.55 fof(fact_rangeI,axiom, % 1.49/1.55 ! [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))))) ). % 1.49/1.55 % 1.49/1.55 fof(fact_equalityCE,axiom, % 1.49/1.55 ! [V_c_2,T_a,V_B_2,V_A_2] : % 1.49/1.55 ( V_A_2 = V_B_2 % 1.49/1.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 1.49/1.55 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) % 1.49/1.55 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 1.49/1.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_assms_I1_J,axiom, % 1.49/1.55 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)))) ). % 1.49/1.55 % 1.49/1.55 fof(fact_psubsetD,axiom, % 1.49/1.55 ! [V_c_2,V_B_2,V_A_2,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 1.49/1.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__on__strict__subset,axiom, % 1.49/1.55 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.55 => 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))) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_eq__mem__trans,axiom, % 1.49/1.55 ! [V_A_2,T_a,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 = V_ba_2 % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2)) % 1.49/1.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_eqelem__imp__iff,axiom, % 1.49/1.55 ! [V_A_2,T_a,V_y_2,V_x_2] : % 1.49/1.55 ( V_x_2 = V_y_2 % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_eqset__imp__iff,axiom, % 1.49/1.55 ! [V_x_2,T_a,V_B_2,V_A_2] : % 1.49/1.55 ( V_A_2 = V_B_2 % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_mem__def,axiom, % 1.49/1.55 ! [V_A_2,V_x_2,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__on__def,axiom, % 1.49/1.55 ! [V_A_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.55 <=> ! [B_x] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.49/1.55 => ! [B_xa] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 1.49/1.55 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 1.49/1.55 => B_x = B_xa ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_image__ident,axiom, % 1.49/1.55 ! [V_Y_2,T_a] : c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2 ). % 1.49/1.55 % 1.49/1.55 fof(fact_image__image,axiom, % 1.49/1.55 ! [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) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__on__id2,axiom, % 1.49/1.55 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 1.49/1.55 % 1.49/1.55 fof(fact_rev__image__eqI,axiom, % 1.49/1.55 ! [T_b,V_f_2,V_ba_2,V_A_2,V_x_2,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.49/1.55 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_imageI,axiom, % 1.49/1.55 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 => 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))) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_image__iff,axiom, % 1.49/1.55 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) % 1.49/1.55 <=> ? [B_x] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 1.49/1.55 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__onD,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.55 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.49/1.55 => V_x_2 = V_y_2 ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__on__iff,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.49/1.55 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.49/1.55 <=> V_x_2 = V_y_2 ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__on__contraD,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.55 => ( V_x_2 != V_y_2 % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 1.49/1.55 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__eq,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.55 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.49/1.55 <=> V_x_2 = V_y_2 ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_injD,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.55 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 1.49/1.55 => V_x_2 = V_y_2 ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_range__composition,axiom, % 1.49/1.55 ! [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)))) ). % 1.49/1.55 % 1.49/1.55 fof(fact_inj__fun,axiom, % 1.49/1.55 ! [T_c,V_f_2,T_b,T_a] : % 1.49/1.55 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.55 => 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))) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_range__eqI,axiom, % 1.49/1.55 ! [T_b,T_a,V_x_2,V_f_2,V_ba_2] : % 1.49/1.55 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 1.49/1.55 => 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))))) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_mktop__Lin,axiom, % 1.49/1.55 ! [V_x_2,V_L_2] : % 1.49/1.55 ( 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)) % 1.49/1.55 => 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_Omktop(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_mkbot__Lin,axiom, % 1.49/1.55 ! [V_x_2,V_L_2] : % 1.49/1.55 ( 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)) % 1.49/1.55 => 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_Omkbot(V_L_2,V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_below__Lin,axiom, % 1.49/1.55 ! [V_L_2,V_y_2,V_x_2] : % 1.49/1.55 ( V_x_2 != V_y_2 % 1.49/1.55 => ( 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)) % 1.49/1.55 => 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)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_above__Lin,axiom, % 1.49/1.55 ! [V_L_2,V_y_2,V_x_2] : % 1.49/1.55 ( V_x_2 != V_y_2 % 1.49/1.55 => ( 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)) % 1.49/1.55 => 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_Oabove(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_atLeastLessThan__eq__iff,axiom, % 1.49/1.55 ! [V_d_2,V_c_2,V_ba_2,V_aa_2,T_a] : % 1.49/1.55 ( class_Orderings_Olinorder(T_a) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 1.49/1.55 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2) % 1.49/1.55 <=> ( V_aa_2 = V_c_2 % 1.49/1.55 & V_ba_2 = V_d_2 ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 1.49/1.55 ! [V_d_2,V_c_2,V_ba_2,V_aa_2,T_a] : % 1.49/1.55 ( class_Orderings_Olinorder(T_a) % 1.49/1.55 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 1.49/1.55 => V_aa_2 = V_c_2 ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 1.49/1.55 ! [V_d_2,V_c_2,V_ba_2,V_aa_2,T_a] : % 1.49/1.55 ( class_Orderings_Olinorder(T_a) % 1.49/1.55 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 1.49/1.55 => V_ba_2 = V_d_2 ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_iso__tuple__UNIV__I,axiom, % 1.49/1.55 ! [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)))) ). % 1.49/1.55 % 1.49/1.55 fof(fact__C1_C,axiom, % 1.49/1.55 ~ 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_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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)))) ). % 1.49/1.55 % 1.49/1.55 fof(fact__096a_A_126_061_Ab_096,axiom, % 1.49/1.55 v_a____ != v_b____ ). % 1.49/1.55 % 1.49/1.55 fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom, % 1.49/1.55 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____)) ). % 1.49/1.55 % 1.49/1.55 fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom, % 1.49/1.55 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_a____),v_b____)),v_Lab____)) ). % 1.49/1.55 % 1.49/1.55 fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom, % 1.49/1.55 ~ 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_a____),v_b____)),v_Lba____)) ). % 1.49/1.55 % 1.49/1.55 fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom, % 1.49/1.55 ~ 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____)) ). % 1.49/1.55 % 1.49/1.55 fof(fact_pred__equals__eq2,axiom, % 1.49/1.55 ! [V_S_2,V_R_2,T_b,T_a] : % 1.49/1.55 ( 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) % 1.49/1.55 <=> V_R_2 = V_S_2 ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_in__mkbot,axiom, % 1.49/1.55 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.49/1.55 ( 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_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omkbot(V_L_2,V_z_2))) % 1.49/1.55 <=> ( V_y_2 != V_z_2 % 1.49/1.55 & ( V_x_2 = V_z_2 % 1.49/1.55 => V_x_2 != V_y_2 ) % 1.49/1.55 & ( V_x_2 != V_z_2 % 1.49/1.55 => 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_x_2),V_y_2)),V_L_2)) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_in__mktop,axiom, % 1.49/1.55 ! [V_z_2,V_L_2,V_y_2,V_x_2] : % 1.49/1.55 ( 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_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Omktop(V_L_2,V_z_2))) % 1.49/1.55 <=> ( V_x_2 != V_z_2 % 1.49/1.55 & ( V_y_2 = V_z_2 % 1.49/1.55 => V_x_2 != V_y_2 ) % 1.49/1.55 & ( V_y_2 != V_z_2 % 1.49/1.55 => 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_x_2),V_y_2)),V_L_2)) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_psubset__trans,axiom, % 1.49/1.55 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.49/1.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_in__above,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( 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_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Oabove(V_L_2,V_aa_2,V_ba_2))) % 1.49/1.55 <=> ( V_x_2 != V_y_2 % 1.49/1.55 & ( V_x_2 = V_ba_2 % 1.49/1.55 => 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_aa_2),V_y_2)),V_L_2)) ) % 1.49/1.55 & ( V_x_2 != V_ba_2 % 1.49/1.55 => ( ( V_y_2 = V_ba_2 % 1.49/1.55 => ( V_x_2 = V_aa_2 % 1.49/1.55 | 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_x_2),V_aa_2)),V_L_2)) ) ) % 1.49/1.55 & ( V_y_2 != V_ba_2 % 1.49/1.55 => 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_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_in__below,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( 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_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2))) % 1.49/1.55 <=> ( V_x_2 != V_y_2 % 1.49/1.55 & ( V_y_2 = V_aa_2 % 1.49/1.55 => 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_x_2),V_ba_2)),V_L_2)) ) % 1.49/1.55 & ( V_y_2 != V_aa_2 % 1.49/1.55 => ( ( V_x_2 = V_aa_2 % 1.49/1.55 => ( V_y_2 = V_ba_2 % 1.49/1.55 | 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_ba_2),V_y_2)),V_L_2)) ) ) % 1.49/1.55 & ( V_x_2 != V_aa_2 % 1.49/1.55 => 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_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_notin__Lin__iff,axiom, % 1.49/1.55 ! [V_y_2,V_x_2,V_L_2] : % 1.49/1.55 ( 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)) % 1.49/1.55 => ( V_x_2 != V_y_2 % 1.49/1.55 => ( ~ 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_x_2),V_y_2)),V_L_2)) % 1.49/1.55 <=> 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_y_2),V_x_2)),V_L_2)) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_Lin__irrefl,axiom, % 1.49/1.55 ! [V_ba_2,V_aa_2,V_L_2] : % 1.49/1.55 ( 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)) % 1.49/1.55 => ( 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_aa_2),V_ba_2)),V_L_2)) % 1.49/1.55 => ~ 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_ba_2),V_aa_2)),V_L_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 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, % 1.49/1.55 ~ ! [B_Lab] : % 1.49/1.55 ( 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_a____),v_b____)),B_Lab)) % 1.49/1.55 => ~ 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)) ) ). % 1.49/1.55 % 1.49/1.55 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, % 1.49/1.55 ~ ! [B_Lba] : % 1.49/1.55 ( 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____)),B_Lba)) % 1.49/1.55 => ~ 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)) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact__C2_C,axiom, % 1.49/1.55 ! [V_P_H_2,V_P_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( V_a_H_2 != V_b_H_2 % 1.49/1.55 => ( V_aa_2 != V_b_H_2 % 1.49/1.55 => ( V_ba_2 != V_a_H_2 % 1.49/1.55 => ( 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_2),c_Arrow__Order__Mirabelle_OProf)) % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( ! [B_i] : % 1.49/1.55 ( 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_aa_2),V_ba_2)),hAPP(V_P_2,B_i))) % 1.49/1.55 <=> 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_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) ) % 1.49/1.55 => ( 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_aa_2),V_ba_2)),hAPP(v_F,V_P_2))) % 1.49/1.55 <=> 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_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096,axiom, % 1.49/1.55 ! [V_P_H_2,V_P_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( V_a_H_2 != V_b_H_2 % 1.49/1.55 => ( V_aa_2 != V_b_H_2 % 1.49/1.55 => ( V_ba_2 != V_a_H_2 % 1.49/1.55 => ( 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_2),c_Arrow__Order__Mirabelle_OProf)) % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( ! [B_i] : % 1.49/1.55 ( 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_aa_2),V_ba_2)),hAPP(V_P_2,B_i))) % 1.49/1.55 <=> 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_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) ) % 1.49/1.55 => ( 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_aa_2),V_ba_2)),hAPP(v_F,V_P_2))) % 1.49/1.55 => 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_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact__C4_C,axiom, % 1.49/1.55 ! [V_P_H_2,V_P_2,V_c_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( V_ba_2 != V_c_2 % 1.49/1.55 => ( V_aa_2 != V_c_2 % 1.49/1.55 => ( 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_2),c_Arrow__Order__Mirabelle_OProf)) % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( ! [B_i] : % 1.49/1.55 ( 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_aa_2),V_ba_2)),hAPP(V_P_2,B_i))) % 1.49/1.55 <=> 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_ba_2),V_c_2)),hAPP(V_P_H_2,B_i))) ) % 1.49/1.55 => ( 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_aa_2),V_ba_2)),hAPP(v_F,V_P_2))) % 1.49/1.55 <=> 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_ba_2),V_c_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_pairwise__neutrality,axiom, % 1.49/1.55 ! [V_P_H_2,V_P_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( V_a_H_2 != V_b_H_2 % 1.49/1.55 => ( 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_2),c_Arrow__Order__Mirabelle_OProf)) % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( ! [B_i] : % 1.49/1.55 ( 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_aa_2),V_ba_2)),hAPP(V_P_2,B_i))) % 1.49/1.55 <=> 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_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) ) % 1.49/1.55 => ( 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_aa_2),V_ba_2)),hAPP(v_F,V_P_2))) % 1.49/1.55 <=> 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_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact__C3_C,axiom, % 1.49/1.55 ! [V_P_H_2,V_P_2,V_ba_2,V_aa_2] : % 1.49/1.55 ( V_aa_2 != V_ba_2 % 1.49/1.55 => ( 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_2),c_Arrow__Order__Mirabelle_OProf)) % 1.49/1.55 => ( 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)) % 1.49/1.55 => ( ! [B_i] : % 1.49/1.55 ( 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_aa_2),V_ba_2)),hAPP(V_P_2,B_i))) % 1.49/1.55 <=> 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_ba_2),V_aa_2)),hAPP(V_P_H_2,B_i))) ) % 1.49/1.55 => ( 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_aa_2),V_ba_2)),hAPP(v_F,V_P_2))) % 1.49/1.55 <=> 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_ba_2),V_aa_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_PiE,axiom, % 1.49/1.55 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) % 1.49/1.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) % 1.49/1.55 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 1.49/1.55 % 1.49/1.55 fof(fact_Prof__def,axiom, % 1.49/1.55 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)) ). % 1.49/1.55 % 1.49/1.55 fof(fact_funcset__id,axiom, % 1.49/1.55 ! [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)))) ). % 1.49/1.55 % 1.49/1.56 fof(fact_Pi__UNIV,axiom, % 1.49/1.56 ! [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)) ). % 1.49/1.56 % 1.49/1.56 fof(fact_Pi__mem,axiom, % 1.49/1.56 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_funcset__mem,axiom, % 1.49/1.56 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( 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)))) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_dictatorI,axiom, % 1.49/1.56 ! [V_i_2,V_Fa_2] : % 1.49/1.56 ( 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)))) % 1.49/1.56 => ( ! [B_x] : % 1.49/1.56 ( 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)) % 1.49/1.56 => ! [B_a,B_b] : % 1.49/1.56 ( B_a != B_b % 1.49/1.56 => ( 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))) % 1.49/1.56 => 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))) ) ) ) % 1.49/1.56 => c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 1.49/1.56 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 1.49/1.56 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OatLeastLessThan__iff,axiom, % 1.49/1.56 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 1.49/1.56 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 1.49/1.56 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 1.49/1.56 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OatLeastAtMost__iff,axiom, % 1.49/1.56 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 1.49/1.56 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OgreaterThan__iff,axiom, % 1.49/1.56 ! [V_k_2,V_less_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 1.49/1.56 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OlessThan__iff,axiom, % 1.49/1.56 ! [V_k_2,V_less_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 1.49/1.56 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_dictator__def,axiom, % 1.49/1.56 ! [V_i_2,V_Fa_2] : % 1.49/1.56 ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) % 1.49/1.56 <=> ! [B_x] : % 1.49/1.56 ( 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)) % 1.49/1.56 => hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OatMost__iff,axiom, % 1.49/1.56 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 1.49/1.56 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord_OatLeast__iff,axiom, % 1.49/1.56 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 1.49/1.56 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_IIA__def,axiom, % 1.49/1.56 ! [V_Fa_2] : % 1.49/1.56 ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2) % 1.49/1.56 <=> ! [B_x] : % 1.49/1.56 ( 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)) % 1.49/1.56 => ! [B_xa] : % 1.49/1.56 ( 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)) % 1.49/1.56 => ! [B_a,B_b] : % 1.49/1.56 ( ! [B_i] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> 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))) ) % 1.49/1.56 => ( 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))) % 1.49/1.56 <=> 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))) ) ) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_unanimity__def,axiom, % 1.49/1.56 ! [V_Fa_2] : % 1.49/1.56 ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2) % 1.49/1.56 <=> ! [B_x] : % 1.49/1.56 ( 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)) % 1.49/1.56 => ! [B_a,B_b] : % 1.49/1.56 ( ! [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))) % 1.49/1.56 => 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))) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_Pi__I,axiom, % 1.49/1.56 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] : % 1.49/1.56 ( ! [B_x] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) ) % 1.49/1.56 => 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))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_in__rel__def,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 1.49/1.56 ( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2) % 1.49/1.56 <=> 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)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_f__the__inv__into__f,axiom, % 1.49/1.56 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.49/1.56 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_the__inv__into__f__eq,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_the__inv__into__f__f,axiom, % 1.49/1.56 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_the__inv__f__f,axiom, % 1.49/1.56 ! [V_x_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => hAPP(c_Fun_Othe__inv__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 ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_the__inv__into__onto,axiom, % 1.49/1.56 ! [V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = V_A_2 ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_inj__on__the__inv__into,axiom, % 1.49/1.56 ! [V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__bij,axiom, % 1.49/1.56 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( 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)))) % 1.49/1.56 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( 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)))) % 1.49/1.56 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.49/1.56 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_same__fstI,axiom, % 1.49/1.56 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 1.49/1.56 ( hBOOL(hAPP(V_P_2,V_x_2)) % 1.49/1.56 => ( 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))) % 1.49/1.56 => 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_P_2,V_R_2))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_the__inv__into__into,axiom, % 1.49/1.56 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_in__measure,axiom, % 1.49/1.56 ! [V_f_2,V_y_2,V_x_2,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> 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))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_funcsetI,axiom, % 1.49/1.56 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] : % 1.49/1.56 ( ! [B_x] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),V_B_2)) ) % 1.49/1.56 => 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)))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_complete__Lin,axiom, % 1.49/1.56 ! [V_ba_2,V_aa_2] : % 1.49/1.56 ( V_aa_2 != V_ba_2 % 1.49/1.56 => ? [B_x] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_x),c_Arrow__Order__Mirabelle_OLin)) % 1.49/1.56 & 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)),B_x)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__refl,axiom, % 1.49/1.56 ! [V_x,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_equalityI,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) % 1.49/1.56 => V_A_2 = V_B_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__atLeastLessThan,axiom, % 1.49/1.56 ! [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)) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subsetD,axiom, % 1.49/1.56 ! [V_c_2,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__imageI,axiom, % 1.49/1.56 ! [V_ha_2,T_b,V_Fa_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_Fa_2) % 1.49/1.56 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__surj,axiom, % 1.49/1.56 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( 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))) % 1.49/1.56 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_equalityE,axiom, % 1.49/1.56 ! [T_a,V_B_2,V_A_2] : % 1.49/1.56 ( V_A_2 = V_B_2 % 1.49/1.56 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__trans,axiom, % 1.49/1.56 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__subset,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.49/1.56 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_equalityD2,axiom, % 1.49/1.56 ! [T_a,V_B_2,V_A_2] : % 1.49/1.56 ( V_A_2 = V_B_2 % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_equalityD1,axiom, % 1.49/1.56 ! [T_a,V_B_2,V_A_2] : % 1.49/1.56 ( V_A_2 = V_B_2 % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_rev__finite__subset,axiom, % 1.49/1.56 ! [V_A_2,V_B_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_set__eq__subset,axiom, % 1.49/1.56 ! [T_a,V_B_2,V_A_2] : % 1.49/1.56 ( V_A_2 = V_B_2 % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__code,axiom, % 1.49/1.56 ! [V_A_2,T_a] : % 1.49/1.56 ( class_Finite__Set_Ofinite(T_a) % 1.49/1.56 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__refl,axiom, % 1.49/1.56 ! [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)) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite,axiom, % 1.49/1.56 ! [V_A_2,T_a] : % 1.49/1.56 ( class_Finite__Set_Ofinite(T_a) % 1.49/1.56 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__le__cases,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__funE,axiom, % 1.49/1.56 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.49/1.56 ( class_Orderings_Oord(T_b) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I6_J,axiom, % 1.49/1.56 ! [V_z,V_x,V_y,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I5_J,axiom, % 1.49/1.56 ! [V_x,V_y,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 => V_x = V_y ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__trans,axiom, % 1.49/1.56 ! [V_z,V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__antisym,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.49/1.56 => V_x = V_y ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I4_J,axiom, % 1.49/1.56 ! [V_c,V_a,V_b,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.49/1.56 => ( V_b = V_c % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord__le__eq__trans,axiom, % 1.49/1.56 ! [V_c,V_b,V_a,T_a] : % 1.49/1.56 ( class_Orderings_Oord(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.49/1.56 => ( V_b = V_c % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I3_J,axiom, % 1.49/1.56 ! [V_c,V_b,V_a,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( V_a = V_b % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_ord__eq__le__trans,axiom, % 1.49/1.56 ! [V_c,V_b,V_a,T_a] : % 1.49/1.56 ( class_Orderings_Oord(T_a) % 1.49/1.56 => ( V_a = V_b % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_predicate1D,axiom, % 1.49/1.56 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_P_2),V_Q_2)) % 1.49/1.56 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 1.49/1.56 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__antisym__conv,axiom, % 1.49/1.56 ! [V_x_2,V_y_2,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 <=> V_x_2 = V_y_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__funD,axiom, % 1.49/1.56 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 1.49/1.56 ( class_Orderings_Oord(T_b) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__eq__refl,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => ( V_x = V_y % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_rev__predicate1D,axiom, % 1.49/1.56 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 1.49/1.56 ( hBOOL(hAPP(V_P_2,V_x_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_P_2),V_Q_2)) % 1.49/1.56 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__eq__iff,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( V_x_2 = V_y_2 % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__linear,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__fun__def,axiom, % 1.49/1.56 ! [V_g_2,V_f_2,T_a,T_b] : % 1.49/1.56 ( class_Orderings_Oord(T_b) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.49/1.56 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_atLeastLessThan__subset__iff,axiom, % 1.49/1.56 ! [V_d_2,V_c_2,V_ba_2,V_aa_2,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2))) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_aa_2)) % 1.49/1.56 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_aa_2)) % 1.49/1.56 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_d_2)) ) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__Prod__UNIV,axiom, % 1.49/1.56 ! [T_b,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 1.49/1.56 => 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))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__Plus__UNIV__iff,axiom, % 1.49/1.56 ! [T_b,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__option__UNIV,axiom, % 1.49/1.56 ! [T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool))) % 1.49/1.56 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_Pi__anti__mono,axiom, % 1.49/1.56 ! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2)) % 1.49/1.56 => 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))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__surj__inj,axiom, % 1.49/1.56 ! [V_f_2,V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( 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))) % 1.49/1.56 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_endo__inj__surj,axiom, % 1.49/1.56 ! [V_f_2,V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( 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)) % 1.49/1.56 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 1.49/1.56 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I8_J,axiom, % 1.49/1.56 ! [V_z,V_x,V_y,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__le__less__trans,axiom, % 1.49/1.56 ! [V_z,V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I7_J,axiom, % 1.49/1.56 ! [V_z,V_x,V_y,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__less__le__trans,axiom, % 1.49/1.56 ! [V_z,V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I11_J,axiom, % 1.49/1.56 ! [V_a,V_b,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.49/1.56 => ( V_a != V_b % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__le__neq__trans,axiom, % 1.49/1.56 ! [V_b,V_a,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.49/1.56 => ( V_a != V_b % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__le__imp__less__or__eq,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.56 | V_x = V_y ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__antisym__conv2,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.56 <=> V_x_2 = V_y_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__less__imp__le,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_leD,axiom, % 1.49/1.56 ! [V_x,V_y,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.49/1.56 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_xt1_I12_J,axiom, % 1.49/1.56 ! [V_b,V_a,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( V_a != V_b % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__neq__le__trans,axiom, % 1.49/1.56 ! [V_b,V_a,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( V_a != V_b % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__antisym__conv1,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 <=> V_x_2 = V_y_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_not__leE,axiom, % 1.49/1.56 ! [V_x,V_y,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_leI,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__le__less,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.56 | V_x_2 = V_y_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_less__le__not__le,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Opreorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_order__less__le,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Oorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 & V_x_2 != V_y_2 ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__le__less__linear,axiom, % 1.49/1.56 ! [V_y,V_x,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 1.49/1.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__not__le,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 1.49/1.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_linorder__not__less,axiom, % 1.49/1.56 ! [V_y_2,V_x_2,T_a] : % 1.49/1.56 ( class_Orderings_Olinorder(T_a) % 1.49/1.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 1.49/1.56 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_in__mono,axiom, % 1.49/1.56 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_set__rev__mp,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,V_x_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_set__mp,axiom, % 1.49/1.56 ! [V_x_2,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_top__greatest,axiom, % 1.49/1.56 ! [V_x,T_a] : % 1.49/1.56 ( class_Orderings_Otop(T_a) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__UNIV,axiom, % 1.49/1.56 ! [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)))) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__image__iff,axiom, % 1.49/1.56 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> ? [B_AA] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2)) % 1.49/1.56 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_image__mono,axiom, % 1.49/1.56 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => 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))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__fun__UNIVD2,axiom, % 1.49/1.56 ! [T_b,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__inj__on,axiom, % 1.49/1.56 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__nat__set__iff__bounded,axiom, % 1.49/1.56 ! [V_N_2] : % 1.49/1.56 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.49/1.56 <=> ? [B_m] : % 1.49/1.56 ! [B_x] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__UNIV,axiom, % 1.49/1.56 ! [T_a] : % 1.49/1.56 ( class_Finite__Set_Ofinite(T_a) % 1.49/1.56 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_less__fun__def,axiom, % 1.49/1.56 ! [V_g_2,V_f_2,T_a,T_b] : % 1.49/1.56 ( class_Orderings_Oord(T_b) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2)) % 1.49/1.56 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__psubset__trans,axiom, % 1.49/1.56 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_psubset__subset__trans,axiom, % 1.49/1.56 ! [V_C_2,V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2)) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_psubset__imp__subset,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_subset__iff__psubset__eq,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.56 | V_A_2 = V_B_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_psubset__eq,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,T_a] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 & V_A_2 != V_B_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_pred__subset__eq,axiom, % 1.49/1.56 ! [V_S_2,V_R_2,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__bij__eq,axiom, % 1.49/1.56 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( 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)) % 1.49/1.56 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 1.49/1.56 => ( 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)) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.49/1.56 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__psubset,axiom, % 1.49/1.56 ! [V_A_2,V_B_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.56 => ( 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))) % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__indi,axiom, % 1.49/1.56 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__infinite,axiom, % 1.49/1.56 ! [V_A_2,T_a] : % 1.49/1.56 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__imageD,axiom, % 1.49/1.56 ! [V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) % 1.49/1.56 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 1.49/1.56 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 1.49/1.56 ! [V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => ( 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))) % 1.49/1.56 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__range__imageI,axiom, % 1.49/1.56 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 1.49/1.56 ( 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)))) % 1.49/1.56 => 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)))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_inj__image__subset__iff,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => ( 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))) % 1.49/1.56 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__ge__0__finite,axiom, % 1.49/1.56 ! [V_A_2,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__UNIV__inj__surj,axiom, % 1.49/1.56 ! [V_f_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => 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)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__UNIV__surj__inj,axiom, % 1.49/1.56 ! [V_f_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => ( 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)) % 1.49/1.56 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_inj__on__iff__eq__card,axiom, % 1.49/1.56 ! [V_f_2,T_b,V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 <=> 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) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_eq__card__imp__inj__on,axiom, % 1.49/1.56 ! [V_f_2,T_b,V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( 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) % 1.49/1.56 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_psubset__card__mono,axiom, % 1.49/1.56 ! [V_A_2,V_B_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.49/1.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.56 => 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))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_funcset__image,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( 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)))) % 1.49/1.56 => 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)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__UNIV__card__ge__0,axiom, % 1.49/1.56 ! [T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 1.49/1.56 => 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))))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_in__lex__prod,axiom, % 1.49/1.56 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> ( 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)) % 1.49/1.56 | ( V_aa_2 = V_a_H_2 % 1.49/1.56 & 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)) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_mlex__less,axiom, % 1.49/1.56 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.49/1.56 ( 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))) % 1.49/1.56 => 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))) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_in__finite__psubset,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,T_a] : % 1.49/1.56 ( 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))) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 1.49/1.56 & c_Finite__Set_Ofinite(T_a,V_B_2) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__inj,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( 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)))) % 1.49/1.56 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.49/1.56 => 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))) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_inj__on__iff__card__le,axiom, % 1.49/1.56 ! [V_B_2,T_b,V_A_2,T_a] : % 1.49/1.56 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.49/1.56 => ( ? [B_f] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 1.49/1.56 & 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)) ) % 1.49/1.56 <=> 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))) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_card__inj__on__le,axiom, % 1.49/1.56 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 1.49/1.56 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 1.49/1.56 => ( 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)) % 1.49/1.56 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.49/1.56 => 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))) ) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le0,axiom, % 1.49/1.56 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__antisym,axiom, % 1.49/1.56 ! [V_n,V_m] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 1.49/1.56 => V_m = V_n ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__trans,axiom, % 1.49/1.56 ! [V_k,V_j,V_i] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.49/1.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_eq__imp__le,axiom, % 1.49/1.56 ! [V_n,V_m] : % 1.49/1.56 ( V_m = V_n % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_nat__le__linear,axiom, % 1.49/1.56 ! [V_n,V_m] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.49/1.56 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__refl,axiom, % 1.49/1.56 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ). % 1.49/1.56 % 1.49/1.56 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 1.49/1.56 ! [V_N_2] : % 1.49/1.56 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2) % 1.49/1.56 <=> ? [B_m] : % 1.49/1.56 ! [B_x] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x),B_m)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_infinite__UNIV__nat,axiom, % 1.49/1.56 ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__0__eq,axiom, % 1.49/1.56 ! [V_n_2] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 1.49/1.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 1.49/1.56 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 1.49/1.56 % 1.49/1.56 fof(fact_termination__basic__simps_I5_J,axiom, % 1.49/1.56 ! [V_y,V_x] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_nat__less__le,axiom, % 1.49/1.56 ! [V_n_2,V_m_2] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.49/1.56 & V_m_2 != V_n_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__eq__less__or__eq,axiom, % 1.49/1.56 ! [V_n_2,V_m_2] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.49/1.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.49/1.56 | V_m_2 = V_n_2 ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_less__imp__le__nat,axiom, % 1.49/1.56 ! [V_n,V_m] : % 1.49/1.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_le__neq__implies__less,axiom, % 1.49/1.56 ! [V_n,V_m] : % 1.49/1.56 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.49/1.56 => ( V_m != V_n % 1.49/1.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_less__or__eq__imp__le,axiom, % 1.49/1.56 ! [V_n,V_m] : % 1.49/1.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.56 | V_m = V_n ) % 1.49/1.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_mlex__leq,axiom, % 1.49/1.56 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 1.49/1.56 ( 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))) % 1.49/1.56 => ( 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)) % 1.49/1.56 => 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))) ) ) ). % 1.49/1.56 % 1.49/1.56 fof(fact_pred__subset__eq2,axiom, % 1.49/1.56 ! [V_S_2,V_R_2,T_b,T_a] : % 1.49/1.57 ( 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))) % 1.49/1.57 <=> 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)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_card__mono,axiom, % 1.49/1.57 ! [V_A_2,V_B_2,T_a] : % 1.49/1.57 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.49/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.57 => 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))) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_card__seteq,axiom, % 1.49/1.57 ! [V_A_2,V_B_2,T_a] : % 1.49/1.57 ( c_Finite__Set_Ofinite(T_a,V_B_2) % 1.49/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) % 1.49/1.57 => ( 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))) % 1.49/1.57 => V_A_2 = V_B_2 ) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_card__image__le,axiom, % 1.49/1.57 ! [V_f_2,T_b,V_A_2,T_a] : % 1.49/1.57 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.49/1.57 => 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))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Pi__mono,axiom, % 1.49/1.57 ! [V_C_2,V_B_2,T_b,V_A_2,T_a] : % 1.49/1.57 ( ! [B_x] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.49/1.57 => 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))) ) % 1.49/1.57 => 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))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 1.49/1.57 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.49/1.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.49/1.57 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.49/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) % 1.49/1.57 => 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) ) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_finite__fun__UNIVD1,axiom, % 1.49/1.57 ! [T_b,T_a] : % 1.49/1.57 ( 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))) % 1.49/1.57 => ( 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)) % 1.49/1.57 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_bool_Osize_I2_J,axiom, % 1.49/1.57 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.49/1.57 % 1.49/1.57 fof(fact_lessI,axiom, % 1.49/1.57 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__mono,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_zero__less__Suc,axiom, % 1.49/1.57 ! [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))) ). % 1.49/1.57 % 1.49/1.57 fof(fact_rev__predicate2D,axiom, % 1.49/1.57 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 1.49/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2)) % 1.49/1.57 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__leD,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.49/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_le__SucE,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) % 1.49/1.57 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.49/1.57 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_predicate2D,axiom, % 1.49/1.57 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2)) % 1.49/1.57 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 1.49/1.57 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_le__SucI,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.49/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__le__mono,axiom, % 1.49/1.57 ! [V_m_2,V_n_2] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) % 1.49/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_le__Suc__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 1.49/1.57 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.49/1.57 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_not__less__eq__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.49/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__n__not__le__n,axiom, % 1.49/1.57 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__neq__Zero,axiom, % 1.49/1.57 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Zero__neq__Suc,axiom, % 1.49/1.57 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.49/1.57 % 1.49/1.57 fof(fact_nat_Osimps_I3_J,axiom, % 1.49/1.57 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__not__Zero,axiom, % 1.49/1.57 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.49/1.57 % 1.49/1.57 fof(fact_nat_Osimps_I2_J,axiom, % 1.49/1.57 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Zero__not__Suc,axiom, % 1.49/1.57 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 1.49/1.57 % 1.49/1.57 fof(fact_not__less__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.49/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__Suc__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 1.49/1.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.49/1.57 | V_m_2 = V_n_2 ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__less__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) % 1.49/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_not__less__less__Suc__eq,axiom, % 1.49/1.57 ! [V_m_2,V_n_2] : % 1.49/1.57 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 1.49/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.49/1.57 <=> V_n_2 = V_m_2 ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__antisym,axiom, % 1.49/1.57 ! [V_m,V_n] : % 1.49/1.57 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 1.49/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 1.49/1.57 => V_m = V_n ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__SucI,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__lessI,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.57 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__trans__Suc,axiom, % 1.49/1.57 ! [V_k,V_j,V_i] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.49/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__SucE,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 1.49/1.57 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.57 => V_m = V_n ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__lessD,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__less__SucD,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_image__Suc__atLeastLessThan,axiom, % 1.49/1.57 ! [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)) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__inject,axiom, % 1.49/1.57 ! [V_y,V_x] : % 1.49/1.57 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 1.49/1.57 => V_x = V_y ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_nat_Oinject,axiom, % 1.49/1.57 ! [V_nat_H_2,V_nat_2] : % 1.49/1.57 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 1.49/1.57 <=> V_nat_2 = V_nat_H_2 ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__n__not__n,axiom, % 1.49/1.57 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 1.49/1.57 % 1.49/1.57 fof(fact_n__not__Suc__n,axiom, % 1.49/1.57 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 1.49/1.57 % 1.49/1.57 fof(fact_folding__image__simple__idem_Oidem,axiom, % 1.49/1.57 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.49/1.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.49/1.57 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_inj__Suc,axiom, % 1.49/1.57 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 1.49/1.57 % 1.49/1.57 fof(fact_gr0__conv__Suc,axiom, % 1.49/1.57 ! [V_n_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 1.49/1.57 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__Suc0,axiom, % 1.49/1.57 ! [V_n_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 1.49/1.57 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__Suc__eq__0__disj,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 1.49/1.57 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.49/1.57 | ? [B_j] : % 1.49/1.57 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 1.49/1.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__le__lessD,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_le__less__Suc__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.49/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 1.49/1.57 <=> V_n_2 = V_m_2 ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__leI,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 1.49/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_le__imp__less__Suc,axiom, % 1.49/1.57 ! [V_n,V_m] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.49/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_Suc__le__eq,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 1.49/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__Suc__eq__le,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 1.49/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__eq__Suc__le,axiom, % 1.49/1.57 ! [V_m_2,V_n_2] : % 1.49/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 1.49/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__eq__Suc__le__raw,axiom, % 1.49/1.57 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)) ). % 1.49/1.57 % 1.49/1.57 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 1.49/1.57 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 1.49/1.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2) % 1.49/1.57 => ( c_Finite__Set_Ofinite(T_b,V_A_2) % 1.49/1.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 1.49/1.57 => 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) ) ) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_bool_Osize_I1_J,axiom, % 1.49/1.57 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.49/1.57 % 1.49/1.57 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 1.49/1.57 ! [V_n_2,V_m_2] : % 1.49/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 1.49/1.57 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 1.49/1.57 % 1.49/1.57 fof(fact_max__extp__max__ext__eq,axiom, % 1.49/1.57 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 1.60/1.57 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a,c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a,c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2) % 1.60/1.57 <=> 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_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__case__0,axiom, % 1.60/1.57 ! [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 ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__case__Suc,axiom, % 1.60/1.57 ! [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) ). % 1.60/1.57 % 1.60/1.57 fof(fact_greaterThan__0,axiom, % 1.60/1.57 c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_finite__Plus__iff,axiom, % 1.60/1.57 ! [V_B_2,V_A_2,T_b,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.60/1.57 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_finite__Plus,axiom, % 1.60/1.57 ! [V_B_2,T_b,V_A_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.60/1.57 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_greaterThan__eq__iff,axiom, % 1.60/1.57 ! [V_y_2,V_x_2,T_a] : % 1.60/1.57 ( class_Orderings_Olinorder(T_a) % 1.60/1.57 => ( c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2) = c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2) % 1.60/1.57 <=> V_x_2 = V_y_2 ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_greaterThan__iff,axiom, % 1.60/1.57 ! [V_k_2,V_i_2,T_a] : % 1.60/1.57 ( class_Orderings_Oord(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_k_2))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_greaterThan__subset__iff,axiom, % 1.60/1.57 ! [V_y_2,V_x_2,T_a] : % 1.60/1.57 ( class_Orderings_Olinorder(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2)),c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2))) % 1.60/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_finite__PlusD_I2_J,axiom, % 1.60/1.57 ! [V_B_2,V_A_2,T_b,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.60/1.57 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_finite__PlusD_I1_J,axiom, % 1.60/1.57 ! [V_B_2,V_A_2,T_b,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) % 1.60/1.57 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_UNIV__Plus__UNIV,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_card__Plus__conv__if,axiom, % 1.60/1.57 ! [V_B_2,T_b,V_A_2,T_a] : % 1.60/1.57 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.60/1.57 => 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)) ) % 1.60/1.57 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 & c_Finite__Set_Ofinite(T_b,V_B_2) ) % 1.60/1.57 => 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) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_card__gt__0__iff,axiom, % 1.60/1.57 ! [V_A_2,T_a] : % 1.60/1.57 ( 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))) % 1.60/1.57 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 & c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_emptyE,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_finite_OemptyI,axiom, % 1.60/1.57 ! [T_a] : c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_empty__subsetI,axiom, % 1.60/1.57 ! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_inj__on__empty,axiom, % 1.60/1.57 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_Plus__eq__empty__conv,axiom, % 1.60/1.57 ! [V_B_2,V_A_2,T_b,T_a] : % 1.60/1.57 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) % 1.60/1.57 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_termination__basic__simps_I4_J,axiom, % 1.60/1.57 ! [V_y,V_z,V_x] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_termination__basic__simps_I3_J,axiom, % 1.60/1.57 ! [V_z,V_y,V_x] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_less__by__empty,axiom, % 1.60/1.57 ! [V_B_2,T_a,V_A_2] : % 1.60/1.57 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 1.60/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_A_2),V_B_2)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__leE,axiom, % 1.60/1.57 ! [V_n,V_k,V_m] : % 1.60/1.57 ( 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)) % 1.60/1.57 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 1.60/1.57 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__leD1,axiom, % 1.60/1.57 ! [V_n,V_k,V_m] : % 1.60/1.57 ( 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)) % 1.60/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__leD2,axiom, % 1.60/1.57 ! [V_n,V_k,V_m] : % 1.60/1.57 ( 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)) % 1.60/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__mono,axiom, % 1.60/1.57 ! [V_l,V_k,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) % 1.60/1.57 => 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))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__mono1,axiom, % 1.60/1.57 ! [V_k,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_trans__le__add2,axiom, % 1.60/1.57 ! [V_m,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_trans__le__add1,axiom, % 1.60/1.57 ! [V_m,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__left__cancel__le,axiom, % 1.60/1.57 ! [V_n_2,V_m_2,V_k_2] : % 1.60/1.57 ( 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_n_2))) % 1.60/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_le__iff__add,axiom, % 1.60/1.57 ! [V_n_2,V_m_2] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.60/1.57 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_le__add1,axiom, % 1.60/1.57 ! [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))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_le__add2,axiom, % 1.60/1.57 ! [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))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_subset__empty,axiom, % 1.60/1.57 ! [V_A_2,T_a] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 1.60/1.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_UNIV__not__empty,axiom, % 1.60/1.57 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_subset__card__intvl__is__intvl,axiom, % 1.60/1.57 ! [V_k_2,V_A_2] : % 1.60/1.57 ( 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))))) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__Suc__shift,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__Suc,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__Suc__right,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot__empty__eq,axiom, % 1.60/1.57 ! [V_x_2,T_a] : % 1.60/1.57 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot__least,axiom, % 1.60/1.57 ! [V_x,T_a] : % 1.60/1.57 ( class_Orderings_Obot(T_a) % 1.60/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_Pi__eq__empty,axiom, % 1.60/1.57 ! [V_B_2,V_A_2,T_b,T_a] : % 1.60/1.57 ( c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) % 1.60/1.57 <=> ? [B_x] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.60/1.57 & hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot__fun__def,axiom, % 1.60/1.57 ! [V_x_2,T_b,T_a] : % 1.60/1.57 ( class_Orderings_Obot(T_a) % 1.60/1.57 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot__apply,axiom, % 1.60/1.57 ! [V_x_2,T_b,T_a] : % 1.60/1.57 ( class_Orderings_Obot(T_a) % 1.60/1.57 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__commute,axiom, % 1.60/1.57 ! [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) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__left__commute,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__assoc,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__left__cancel,axiom, % 1.60/1.57 ! [V_n_2,V_m_2,V_k_2] : % 1.60/1.57 ( 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_n_2) % 1.60/1.57 <=> V_m_2 = V_n_2 ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__right__cancel,axiom, % 1.60/1.57 ! [V_n_2,V_k_2,V_m_2] : % 1.60/1.57 ( 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_n_2),V_k_2) % 1.60/1.57 <=> V_m_2 = V_n_2 ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_not__psubset__empty,axiom, % 1.60/1.57 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_finite_Oequations_I1_J,axiom, % 1.60/1.57 ! [T_a] : c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_all__not__in__conv,axiom, % 1.60/1.57 ! [V_A_2,T_a] : % 1.60/1.57 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.60/1.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_ex__in__conv,axiom, % 1.60/1.57 ! [V_A_2,T_a] : % 1.60/1.57 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 1.60/1.57 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_empty__iff,axiom, % 1.60/1.57 ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_equals0D,axiom, % 1.60/1.57 ! [V_aa_2,T_a,V_A_2] : % 1.60/1.57 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__lessD1,axiom, % 1.60/1.57 ! [V_k,V_j,V_i] : % 1.60/1.57 ( 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)) % 1.60/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_less__add__eq__less,axiom, % 1.60/1.57 ! [V_n,V_m,V_l,V_k] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.60/1.57 => ( 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) % 1.60/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__mono,axiom, % 1.60/1.57 ! [V_l,V_k,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 1.60/1.57 => 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))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__mono1,axiom, % 1.60/1.57 ! [V_k,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_trans__less__add2,axiom, % 1.60/1.57 ! [V_m,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_trans__less__add1,axiom, % 1.60/1.57 ! [V_m,V_j,V_i] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__add__left__cancel__less,axiom, % 1.60/1.57 ! [V_n_2,V_m_2,V_k_2] : % 1.60/1.57 ( 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_n_2))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_not__add__less2,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_not__add__less1,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_termination__basic__simps_I1_J,axiom, % 1.60/1.57 ! [V_z,V_y,V_x] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_termination__basic__simps_I2_J,axiom, % 1.60/1.57 ! [V_y,V_z,V_x] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 1.60/1.57 => 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))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_plus__nat_Oadd__0,axiom, % 1.60/1.57 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 1.60/1.57 % 1.60/1.57 fof(fact_Nat_Oadd__0__right,axiom, % 1.60/1.57 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__is__0,axiom, % 1.60/1.57 ! [V_n_2,V_m_2] : % 1.60/1.57 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.60/1.57 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.60/1.57 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__eq__self__zero,axiom, % 1.60/1.57 ! [V_n,V_m] : % 1.60/1.57 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 1.60/1.57 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_image__is__empty,axiom, % 1.60/1.57 ! [V_A_2,V_f_2,T_a,T_b] : % 1.60/1.57 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_image__empty,axiom, % 1.60/1.57 ! [V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_empty__is__image,axiom, % 1.60/1.57 ! [V_A_2,V_f_2,T_b,T_a] : % 1.60/1.57 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) % 1.60/1.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_one__is__add,axiom, % 1.60/1.57 ! [V_n_2,V_m_2] : % 1.60/1.57 ( 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_n_2) % 1.60/1.57 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.60/1.57 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.60/1.57 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.60/1.57 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__is__1,axiom, % 1.60/1.57 ! [V_n_2,V_m_2] : % 1.60/1.57 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.60/1.57 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 1.60/1.57 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 1.60/1.57 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.60/1.57 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__gr__0,axiom, % 1.60/1.57 ! [V_n_2,V_m_2] : % 1.60/1.57 ( 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_n_2))) % 1.60/1.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 1.60/1.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_less__add__Suc1,axiom, % 1.60/1.57 ! [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)))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_less__add__Suc2,axiom, % 1.60/1.57 ! [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)))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_less__iff__Suc__add,axiom, % 1.60/1.57 ! [V_n_2,V_m_2] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.60/1.57 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_atLeastLessThan__empty,axiom, % 1.60/1.57 ! [V_aa_2,V_ba_2,T_a] : % 1.60/1.57 ( class_Orderings_Oorder(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_aa_2)) % 1.60/1.57 => c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_card_Oempty,axiom, % 1.60/1.57 ! [T_a] : c_Finite__Set_Ocard(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.60/1.57 % 1.60/1.57 fof(fact_atLeastLessThan__empty__iff,axiom, % 1.60/1.57 ! [V_ba_2,V_aa_2,T_a] : % 1.60/1.57 ( class_Orderings_Oorder(T_a) % 1.60/1.57 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_atLeastLessThan__empty__iff2,axiom, % 1.60/1.57 ! [V_ba_2,V_aa_2,T_a] : % 1.60/1.57 ( class_Orderings_Oorder(T_a) % 1.60/1.57 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) % 1.60/1.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_inj__on__add__nat,axiom, % 1.60/1.57 ! [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) ). % 1.60/1.57 % 1.60/1.57 fof(fact_atLeastLessThan0,axiom, % 1.60/1.57 ! [V_m_2] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_Pi__empty,axiom, % 1.60/1.57 ! [V_B_2,T_b,T_a] : c_FuncSet_OPi(T_a,T_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_image__add__atLeastLessThan,axiom, % 1.60/1.57 ! [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)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_card__eq__0__iff,axiom, % 1.60/1.57 ! [V_A_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 1.60/1.57 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 | ~ c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_inj__on__iff__surj,axiom, % 1.60/1.57 ! [V_A_H_2,T_b,T_a,V_A_2] : % 1.60/1.57 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 => ( ? [B_f] : % 1.60/1.57 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 1.60/1.57 & 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_A_H_2)) ) % 1.60/1.57 <=> ? [B_g] : c_Set_Oimage(T_b,T_a,B_g,V_A_H_2) = V_A_2 ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_card__Plus,axiom, % 1.60/1.57 ! [V_B_2,T_b,V_A_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_b,V_B_2) % 1.60/1.57 => 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)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__nonpos__neg,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__neg__nonpos,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__strict__increasing2,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot__nat__def,axiom, % 1.60/1.57 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot__empty__eq2,axiom, % 1.60/1.57 ! [V_y_2,V_x_2,T_b,T_a] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) % 1.60/1.57 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_zero__reorient,axiom, % 1.60/1.57 ! [V_x_2,T_a] : % 1.60/1.57 ( class_Groups_Ozero(T_a) % 1.60/1.57 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 1.60/1.57 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oab__semigroup__add(T_a) % 1.60/1.57 => 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)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__left__cancel,axiom, % 1.60/1.57 ! [V_c_2,V_ba_2,V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.60/1.57 => ( 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_c_2) % 1.60/1.57 <=> V_ba_2 = V_c_2 ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__right__cancel,axiom, % 1.60/1.57 ! [V_c_2,V_aa_2,V_ba_2,T_a] : % 1.60/1.57 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.60/1.57 => ( 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_c_2),V_aa_2) % 1.60/1.57 <=> V_ba_2 = V_c_2 ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__left__imp__eq,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.60/1.57 => ( 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) % 1.60/1.57 => V_b = V_c ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__imp__eq,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 1.60/1.57 => ( 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) % 1.60/1.57 => V_b = V_c ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__right__imp__eq,axiom, % 1.60/1.57 ! [V_c,V_a,V_b,T_a] : % 1.60/1.57 ( class_Groups_Ocancel__semigroup__add(T_a) % 1.60/1.57 => ( 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) % 1.60/1.57 => V_b = V_c ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__imp__le__left,axiom, % 1.60/1.57 ! [V_b,V_a,V_c,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__imp__le__right,axiom, % 1.60/1.57 ! [V_b,V_c,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__mono,axiom, % 1.60/1.57 ! [V_d,V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__left__mono,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.60/1.57 => 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))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__right__mono,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.60/1.57 => 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))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__cancel__left,axiom, % 1.60/1.57 ! [V_ba_2,V_aa_2,V_c_2,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_ba_2))) % 1.60/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__cancel__right,axiom, % 1.60/1.57 ! [V_ba_2,V_c_2,V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_c_2))) % 1.60/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add_Ocomm__neutral,axiom, % 1.60/1.57 ! [V_a,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__0__right,axiom, % 1.60/1.57 ! [V_a,T_a] : % 1.60/1.57 ( class_Groups_Omonoid__add(T_a) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_double__zero__sym,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.60/1.57 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) % 1.60/1.57 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__0,axiom, % 1.60/1.57 ! [V_a,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__0__left,axiom, % 1.60/1.57 ! [V_a,T_a] : % 1.60/1.57 ( class_Groups_Omonoid__add(T_a) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__cancel__right,axiom, % 1.60/1.57 ! [V_ba_2,V_c_2,V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_c_2))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__cancel__left,axiom, % 1.60/1.57 ! [V_ba_2,V_aa_2,V_c_2,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_ba_2))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__strict__right__mono,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.60/1.57 => 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))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__strict__left__mono,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.60/1.57 => 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))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__strict__mono,axiom, % 1.60/1.57 ! [V_d,V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__imp__less__right,axiom, % 1.60/1.57 ! [V_b,V_c,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__imp__less__left,axiom, % 1.60/1.57 ! [V_b,V_a,V_c,T_a] : % 1.60/1.57 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__nonpos__nonpos,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__increasing2,axiom, % 1.60/1.57 ! [V_a,V_b,V_c,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__increasing,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__nonneg__eq__0__iff,axiom, % 1.60/1.57 ! [V_y_2,V_x_2,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 1.60/1.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.60/1.57 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 1.60/1.57 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__nonneg__nonneg,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__less__le__mono,axiom, % 1.60/1.57 ! [V_d,V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__le__less__mono,axiom, % 1.60/1.57 ! [V_d,V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__neg__neg,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__pos__pos,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__pos__nonneg,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__nonneg__pos,axiom, % 1.60/1.57 ! [V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__strict__increasing,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Groups_Oordered__comm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_pos__add__strict,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Rings_Olinordered__semidom(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 1.60/1.57 => 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))) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_even__less__0__iff,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Rings_Olinordered__idom(T_a) % 1.60/1.57 => ( 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))) % 1.60/1.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_bot2E,axiom, % 1.60/1.57 ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 1.60/1.57 % 1.60/1.57 fof(fact_linorder__neqE__linordered__idom,axiom, % 1.60/1.57 ! [V_y,V_x,T_a] : % 1.60/1.57 ( class_Rings_Olinordered__idom(T_a) % 1.60/1.57 => ( V_x != V_y % 1.60/1.57 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 1.60/1.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_double__eq__0__iff,axiom, % 1.60/1.57 ! [V_aa_2,T_a] : % 1.60/1.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 1.60/1.57 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a) % 1.60/1.57 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat_Osize_I2_J,axiom, % 1.60/1.57 ! [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))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat_Osize_I4_J,axiom, % 1.60/1.57 ! [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))) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat_Osize_I3_J,axiom, % 1.60/1.57 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat__size,axiom, % 1.60/1.57 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ). % 1.60/1.57 % 1.60/1.57 fof(fact_nat_Osize_I1_J,axiom, % 1.60/1.57 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 1.60/1.57 % 1.60/1.57 fof(fact_add__0__iff,axiom, % 1.60/1.57 ! [V_aa_2,V_ba_2,T_a] : % 1.60/1.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 1.60/1.57 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) % 1.60/1.57 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 1.60/1.57 ! [V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 1.60/1.57 ! [V_c,V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => 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) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 1.60/1.57 ! [V_d,V_c,V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => 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)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 1.60/1.57 ! [V_d,V_c,V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => 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) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => 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)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 1.60/1.57 ! [V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => 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) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 1.60/1.57 ! [V_d,V_c,V_b,V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => 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)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 1.60/1.57 ! [V_a,T_a] : % 1.60/1.57 ( class_Rings_Ocomm__semiring__1(T_a) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_folding__one__idem_Osubset__idem,axiom, % 1.60/1.57 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) % 1.60/1.57 => 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) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_max__extp_Oequations,axiom, % 1.60/1.57 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 1.60/1.57 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 1.60/1.57 <=> ( c_Finite__Set_Ofinite(T_a,V_a1_2) % 1.60/1.57 & c_Finite__Set_Ofinite(T_a,V_a2_2) % 1.60/1.57 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 & ! [B_x] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 1.60/1.57 => ? [B_xa] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 1.60/1.57 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_folding__one__idem_Oidem,axiom, % 1.60/1.57 ! [V_x_2,V_Fa_2,V_f_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2) % 1.60/1.57 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_folding__one__idem_Oin__idem,axiom, % 1.60/1.57 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_a,V_A_2) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 1.60/1.57 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_max__ext_Ointros,axiom, % 1.60/1.57 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofinite(T_a,V_X_2) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_a,V_Y_2) % 1.60/1.57 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 => ( ! [B_x] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 1.60/1.57 => ? [B_xa] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 1.60/1.57 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) % 1.60/1.57 => 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_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_folding__one__idem_Ohom__commute,axiom, % 1.60/1.57 ! [V_N_2,V_ha_2,V_Fa_2,V_f_2,T_a] : % 1.60/1.57 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2) % 1.60/1.57 => ( ! [B_x,B_y] : hAPP(V_ha_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_ha_2,B_x)),hAPP(V_ha_2,B_y)) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_a,V_N_2) % 1.60/1.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 => hAPP(V_ha_2,hAPP(V_Fa_2,V_N_2)) = hAPP(V_Fa_2,c_Set_Oimage(T_a,T_a,V_ha_2,V_N_2)) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_max__ext_Osimps,axiom, % 1.60/1.57 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 1.60/1.57 ( 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_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 1.60/1.57 <=> ( c_Finite__Set_Ofinite(T_a,V_a1_2) % 1.60/1.57 & c_Finite__Set_Ofinite(T_a,V_a2_2) % 1.60/1.57 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 1.60/1.57 & ! [B_x] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 1.60/1.57 => ? [B_xa] : % 1.60/1.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 1.60/1.57 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__op__ivl__Suc,axiom, % 1.60/1.57 ! [V_f_2,V_m_2,V_n_2,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 1.60/1.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__add__nat__ivl,axiom, % 1.60/1.57 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 1.60/1.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_p_2)) % 1.60/1.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2,V_p_2))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_p_2)) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 1.60/1.57 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,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_n_2),V_k_2))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_f_2),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_m_2,V_n_2)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 1.60/1.57 ! [V_n_2,V_m_2,V_f_2,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_f_2),c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 1.60/1.57 ! [V_k_2,V_f_2,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__head__upt__Suc,axiom, % 1.60/1.57 ! [V_f_2,V_n_2,V_m_2,T_a] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_a) % 1.60/1.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__delta_H,axiom, % 1.60/1.57 ! [V_ba_2,V_aa_2,V_S_2,T_a,T_b] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_b) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_a,V_S_2) % 1.60/1.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_S_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,T_b,T_b),c_COMBS(T_a,T_b,tc_fun(T_b,T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a,c_If(T_b)),hAPP(c_fequal,V_aa_2)),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)),V_S_2) = hAPP(V_ba_2,V_aa_2) ) % 1.60/1.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_S_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,T_b,T_b),c_COMBS(T_a,T_b,tc_fun(T_b,T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a,c_If(T_b)),hAPP(c_fequal,V_aa_2)),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 fof(fact_setsum__delta,axiom, % 1.60/1.57 ! [V_ba_2,V_aa_2,V_S_2,T_a,T_b] : % 1.60/1.57 ( class_Groups_Ocomm__monoid__add(T_b) % 1.60/1.57 => ( c_Finite__Set_Ofinite(T_a,V_S_2) % 1.60/1.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_S_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,T_b,T_b),c_COMBS(T_a,T_b,tc_fun(T_b,T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a,c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_aa_2)),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)),V_S_2) = hAPP(V_ba_2,V_aa_2) ) % 1.60/1.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_S_2)) % 1.60/1.57 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,T_b,T_b),c_COMBS(T_a,T_b,tc_fun(T_b,T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a,c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_aa_2)),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 1.60/1.57 % 1.60/1.57 %----Arity declarations (33) % 1.60/1.57 fof(arity_fun__Orderings_Opreorder,axiom, % 1.60/1.57 ! [T_2,T_1] : % 1.60/1.57 ( class_Orderings_Opreorder(T_1) % 1.60/1.57 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 1.60/1.57 % 1.60/1.57 fof(arity_fun__Finite__Set_Ofinite,axiom, % 1.60/1.57 ! [T_1,T_2] : % 1.60/1.57 ( ( class_Finite__Set_Ofinite(T_2) % 1.60/1.57 & class_Finite__Set_Ofinite(T_1) ) % 1.60/1.57 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 1.60/1.57 % 1.60/1.57 fof(arity_fun__Orderings_Oorder,axiom, % 1.60/1.57 ! [T_2,T_1] : % 1.60/1.57 ( class_Orderings_Oorder(T_1) % 1.60/1.57 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 1.60/1.57 % 1.60/1.57 fof(arity_fun__Orderings_Otop,axiom, % 1.60/1.58 ! [T_2,T_1] : % 1.60/1.58 ( class_Orderings_Otop(T_1) % 1.60/1.58 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 1.60/1.58 % 1.60/1.58 fof(arity_fun__Orderings_Oord,axiom, % 1.60/1.58 ! [T_2,T_1] : % 1.60/1.58 ( class_Orderings_Oord(T_1) % 1.60/1.58 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 1.60/1.58 % 1.60/1.58 fof(arity_fun__Orderings_Obot,axiom, % 1.60/1.58 ! [T_2,T_1] : % 1.60/1.58 ( class_Orderings_Obot(T_1) % 1.60/1.58 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 1.60/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 1.60/1.58 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 1.60/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 1.60/1.58 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 1.60/1.58 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 1.60/1.58 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 1.60/1.58 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 1.60/1.58 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 1.60/1.58 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 1.60/1.58 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 1.60/1.58 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 1.60/1.58 class_Orderings_Opreorder(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 1.60/1.58 class_Orderings_Olinorder(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 1.60/1.58 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 1.60/1.58 class_Orderings_Oorder(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 1.60/1.58 class_Orderings_Oord(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 1.60/1.58 class_Orderings_Obot(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 1.60/1.58 class_Groups_Ozero(tc_Nat_Onat) ). % 1.60/1.58 % 1.60/1.58 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 1.60/1.58 class_Orderings_Opreorder(tc_HOL_Obool) ). % 1.60/1.58 % 1.60/1.58 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 1.60/1.58 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 1.60/1.58 % 1.60/1.58 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 1.60/1.58 class_Orderings_Oorder(tc_HOL_Obool) ). % 1.60/1.58 % 1.60/1.58 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 1.60/1.58 class_Orderings_Otop(tc_HOL_Obool) ). % 1.60/1.58 % 1.60/1.58 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 1.60/1.58 class_Orderings_Oord(tc_HOL_Obool) ). % 1.60/1.58 % 1.60/1.58 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 1.60/1.58 class_Orderings_Obot(tc_HOL_Obool) ). % 1.60/1.58 % 1.60/1.58 fof(arity_sum__Finite__Set_Ofinite,axiom, % 1.60/1.58 ! [T_1,T_2] : % 1.60/1.58 ( ( class_Finite__Set_Ofinite(T_2) % 1.60/1.58 & class_Finite__Set_Ofinite(T_1) ) % 1.60/1.58 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 1.60/1.58 % 1.60/1.58 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 1.60/1.58 ! [T_1] : % 1.60/1.58 ( class_Finite__Set_Ofinite(T_1) % 1.60/1.58 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 1.60/1.58 % 1.60/1.58 fof(arity_prod__Finite__Set_Ofinite,axiom, % 1.60/1.58 ! [T_1,T_2] : % 1.60/1.58 ( ( class_Finite__Set_Ofinite(T_2) % 1.60/1.58 & class_Finite__Set_Ofinite(T_1) ) % 1.60/1.58 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 1.60/1.58 % 1.60/1.58 %----Helper facts (9) % 1.60/1.58 fof(help_c__COMBI__1,axiom, % 1.60/1.58 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 1.60/1.58 % 1.60/1.58 fof(help_c__COMBK__1,axiom, % 1.60/1.58 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 1.60/1.58 % 1.60/1.58 fof(help_c__COMBB__1,axiom, % 1.60/1.58 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ). % 1.60/1.58 % 1.60/1.58 fof(help_c__COMBC__1,axiom, % 1.60/1.58 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ). % 1.60/1.58 % 1.60/1.58 fof(help_c__COMBS__1,axiom, % 1.60/1.58 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 1.60/1.58 % 1.60/1.58 fof(help_c__fequal__1,axiom, % 1.60/1.58 ! [V_y_2,V_x_2] : % 1.60/1.58 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 1.60/1.58 | V_x_2 = V_y_2 ) ). % 1.60/1.58 % 1.60/1.58 fof(help_c__fequal__2,axiom, % 1.60/1.58 ! [V_y_2,V_x_2] : % 1.60/1.58 ( V_x_2 != V_y_2 % 1.60/1.58 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 1.60/1.58 % 1.60/1.58 fof(help_c__fFalse__1,axiom, % 1.60/1.58 ~ hBOOL(c_fFalse) ). % 1.60/1.58 % 1.60/1.58 fof(help_c__fTrue__1,axiom, % 1.60/1.58 hBOOL(c_fTrue) ). % 1.60/1.58 % 1.60/1.58 %----Conjectures (1) % 1.60/1.58 fof(conj_0,conjecture, % 1.60/1.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) % 1.60/1.58 => v_Lba____ = v_Lab____ ) ). % 1.60/1.58 % 1.60/1.58 %------------------------------------------------------------------------------ % 1.60/1.58 %------------------------------------------- % 1.60/1.58 % Proof found % 1.60/1.58 % SZS status Theorem for theBenchmark % 1.60/1.58 % SZS output start Proof % 1.60/1.58 %ClaNum:1135(EqnAxiom:353) % 1.60/1.58 %VarNum:5855(SingletonVarNum:1943) % 1.60/1.58 %MaxLitNum:10 % 1.60/1.58 %MaxfuncDepth:13 % 1.60/1.58 %SharedTerms:167 % 1.60/1.58 %goalClause: 459 481 % 1.60/1.58 %singleGoalClaCount:2 % 1.60/1.58 [354]P1(a1) % 1.60/1.58 [355]P2(a49) % 1.60/1.58 [356]P3(a113) % 1.60/1.58 [357]P4(a113) % 1.60/1.58 [358]P6(a114) % 1.60/1.58 [359]P26(a114) % 1.60/1.58 [360]P26(a49) % 1.60/1.58 [361]P27(a114) % 1.60/1.58 [362]P27(a49) % 1.60/1.58 [363]P28(a114) % 1.60/1.58 [364]P28(a49) % 1.60/1.58 [365]P7(a49) % 1.60/1.58 [366]P14(a114) % 1.60/1.58 [367]P14(a49) % 1.60/1.58 [368]P15(a114) % 1.60/1.58 [369]P25(a114) % 1.60/1.58 [370]P16(a114) % 1.60/1.58 [371]P17(a114) % 1.60/1.58 [372]P18(a114) % 1.60/1.58 [373]P19(a114) % 1.60/1.58 [374]P20(a114) % 1.60/1.58 [375]P21(a114) % 1.60/1.58 [376]P22(a114) % 1.60/1.58 [377]P24(a114) % 1.60/1.58 [378]P29(a114) % 1.60/1.58 [379]P32(a114) % 1.60/1.58 [380]P30(a114) % 1.60/1.58 [459]~E(a121,a120) % 1.60/1.58 [460]~E(a124,a122) % 1.60/1.58 [461]~P1(a19) % 1.60/1.58 [381]E(f2(a114),f20(a19)) % 1.60/1.58 [382]E(f2(a114),f20(a1)) % 1.60/1.58 [383]E(f21(a114),f2(a114)) % 1.60/1.58 [384]E(f22(f2(a114)),f2(a114)) % 1.60/1.58 [391]P8(a111,f29(f115(a111,a49))) % 1.60/1.58 [422]P9(a111,a114,a119,f29(f115(a111,a49))) % 1.60/1.58 [423]P9(a111,a114,a53,f29(f115(a111,a49))) % 1.60/1.58 [471]~P8(a114,f29(f115(a114,a49))) % 1.60/1.58 [425]E(f41(a114,a114,a23,f29(f115(a114,a49))),f42(a114,f2(a114))) % 1.60/1.58 [432]E(f30(a114,f2(a114),f14(a111,f29(f115(a111,a49)))),f41(a111,a114,a119,f29(f115(a111,a49)))) % 1.60/1.58 [433]E(f30(a114,f2(a114),f14(a111,f29(f115(a111,a49)))),f41(a111,a114,a53,f29(f115(a111,a49)))) % 1.60/1.58 [481]~P1(f50(f50(f28(a114),f50(a119,a123)),f14(a111,f29(f115(a111,a49))))) % 1.60/1.58 [437]P1(f50(f50(f51(f115(f118(a112,a112),a49)),a120),a5)) % 1.60/1.58 [438]P1(f50(f50(f51(f115(f118(a112,a112),a49)),a121),a5)) % 1.60/1.58 [439]P1(f50(f50(f51(f115(f118(a112,a112),a49)),a54),a5)) % 1.60/1.58 [440]P1(f50(f50(f51(f115(f118(a112,a112),a49)),a57),a5)) % 1.60/1.58 [443]P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a122),a124)),a120)) % 1.60/1.58 [444]P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a122),a124)),a54)) % 1.60/1.58 [445]P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a124),a122)),a121)) % 1.60/1.58 [446]P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a124),a122)),a57)) % 1.60/1.58 [485]~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a122),a124)),a121)) % 1.60/1.58 [486]~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a124),a122)),a120)) % 1.60/1.58 [447]E(f17(a111,f115(f118(a112,a112),a49),f29(f115(a111,a49)),f50(f15(f115(f115(f118(a112,a112),a49),a49),a111),a5)),a6) % 1.60/1.58 [455]P1(f50(f50(f51(f115(f118(a112,a112),a49)),f50(a113,f50(f15(f115(f118(a112,a112),a49),a111),a121))),a5)) % 1.60/1.58 [456]P1(f50(f50(f51(f115(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49))),a113),f17(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49),a6,f50(f15(f115(f115(f118(a112,a112),a49),a49),f115(a111,f115(f118(a112,a112),a49))),a5)))) % 1.60/1.58 [487]~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),a122),a124)),f50(a113,f50(f50(f4(a111,f115(f118(a112,a112),a49),f115(f118(a112,a112),a49)),f50(f50(f4(a111,f115(f118(a112,a112),a49),f115(f115(f118(a112,a112),a49),f115(f118(a112,a112),a49))),f50(f7(a49,f115(f115(f118(a112,a112),a49),f115(f115(f118(a112,a112),a49),f115(f118(a112,a112),a49))),a111,f24(f115(f118(a112,a112),a49))),f50(f50(f4(a111,a114,a49),f50(f7(a114,f115(a114,a49),a111,f28(a114)),a119)),f2(a114)))),a120)),a121)))) % 1.60/1.58 [413]P9(a114,a114,a23,x4131) % 1.60/1.58 [385]E(f26(a114,x3851),x3851) % 1.60/1.58 [463]~E(f50(a23,x4631),x4631) % 1.60/1.58 [469]~E(f50(a23,x4691),f2(a114)) % 1.60/1.58 [388]E(f50(f50(f13(a114),x3881),f2(a114)),x3881) % 1.60/1.58 [389]E(f27(a114,f50(a23,x3891)),f50(f28(a114),x3891)) % 1.60/1.58 [393]P8(x3931,f21(f115(x3931,a49))) % 1.60/1.58 [395]P1(f50(f27(a114,x3951),x3951)) % 1.60/1.58 [396]E(f30(a114,x3961,f2(a114)),f21(f115(a114,a49))) % 1.60/1.58 [404]P1(f50(f50(f28(a114),x4041),f50(a23,x4041))) % 1.60/1.58 [405]P1(f50(f50(f28(a114),f2(a114)),f50(a23,x4051))) % 1.60/1.58 [470]~E(f29(f115(x4701,a49)),f21(f115(x4701,a49))) % 1.60/1.58 [476]~P1(f50(f50(f28(a114),x4761),f2(a114))) % 1.60/1.58 [390]E(f50(f50(f13(a114),f2(a114)),x3901),x3901) % 1.60/1.58 [394]E(f14(x3941,f21(f115(x3941,a49))),f2(a114)) % 1.60/1.58 [398]P1(f50(f27(a114,f2(a114)),x3981)) % 1.60/1.58 [401]E(f50(f50(f13(a114),f22(x4011)),f50(a23,f2(a114))),f22(f50(a23,x4011))) % 1.60/1.58 [406]E(f50(f50(f13(a114),f26(a114,x4061)),f50(a23,f2(a114))),f26(a114,f50(a23,x4061))) % 1.60/1.58 [473]~P1(f50(f50(f28(a114),x4731),x4731)) % 1.60/1.58 [477]~P1(f50(f27(a114,f50(a23,x4771)),x4771)) % 1.60/1.58 [457]P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f50(f50(f4(a111,f115(f118(a112,a112),a49),f115(f118(a112,a112),a49)),f50(f50(f4(a111,f115(f118(a112,a112),a49),f115(f115(f118(a112,a112),a49),f115(f118(a112,a112),a49))),f50(f7(a49,f115(f115(f118(a112,a112),a49),f115(f115(f118(a112,a112),a49),f115(f118(a112,a112),a49))),a111,f24(f115(f118(a112,a112),a49))),f50(f50(f4(a111,a114,a49),f50(f7(a114,f115(a114,a49),a111,f28(a114)),a119)),x4571))),a120)),a121)),a6)) % 1.60/1.58 [458]P1(f50(f50(f51(f115(f118(a112,a112),a49)),f50(a113,f50(f50(f4(a111,f115(f118(a112,a112),a49),f115(f118(a112,a112),a49)),f50(f50(f4(a111,f115(f118(a112,a112),a49),f115(f115(f118(a112,a112),a49),f115(f118(a112,a112),a49))),f50(f7(a49,f115(f115(f118(a112,a112),a49),f115(f115(f118(a112,a112),a49),f115(f118(a112,a112),a49))),a111,f24(f115(f118(a112,a112),a49))),f50(f50(f4(a111,a114,a49),f50(f7(a114,f115(a114,a49),a111,f28(a114)),a119)),x4581))),a120)),a121))),a5)) % 1.60/1.58 [402]P8(a114,f30(a114,x4021,x4022)) % 1.60/1.58 [415]P9(x4151,x4151,f3(x4151),x4152) % 1.60/1.58 [387]E(f50(f3(x3871),x3872),x3872) % 1.60/1.58 [416]E(f41(x4161,x4161,f3(x4161),x4162),x4162) % 1.60/1.58 [431]E(f41(a114,a114,a23,f30(a114,x4311,x4312)),f30(a114,f50(a23,x4311),f50(a23,x4312))) % 1.60/1.58 [399]E(f50(f50(f13(a114),x3991),x3992),f50(f50(f13(a114),x3992),x3991)) % 1.60/1.58 [403]P1(f50(f29(f115(x4031,a49)),x4032)) % 1.60/1.58 [407]E(f50(f50(f13(a114),f50(a23,x4071)),x4072),f50(f50(f13(a114),x4071),f50(a23,x4072))) % 1.60/1.58 [409]P1(f50(f27(f115(x4091,a49),x4092),x4092)) % 1.60/1.58 [412]P1(f50(f50(f51(x4121),x4122),f29(f115(x4121,a49)))) % 1.60/1.58 [420]P1(f50(f27(f115(x4201,a49),x4202),f29(f115(x4201,a49)))) % 1.60/1.58 [430]E(f43(x4301,x4302,f29(f115(x4301,a49)),f29(f115(x4302,a49))),f29(f115(f117(x4301,x4302),a49))) % 1.60/1.58 [442]P9(a114,a114,f50(f50(f4(a114,a114,a114),f13(a114)),x4421),x4422) % 1.60/1.58 [479]~P1(f50(f50(f51(x4791),x4792),f21(f115(x4791,a49)))) % 1.60/1.58 [480]~P1(f50(f50(f28(f115(x4801,a49)),x4802),f21(f115(x4801,a49)))) % 1.60/1.58 [408]E(f50(f50(f13(a114),x4081),f50(a23,x4082)),f50(a23,f50(f50(f13(a114),x4081),x4082))) % 1.60/1.58 [410]E(f50(f50(f13(a114),f50(a23,x4101)),x4102),f50(a23,f50(f50(f13(a114),x4101),x4102))) % 1.60/1.58 [417]P1(f50(f27(a114,x4171),f50(f50(f13(a114),x4172),x4171))) % 1.60/1.58 [418]P1(f50(f27(a114,x4181),f50(f50(f13(a114),x4181),x4182))) % 1.60/1.58 [429]P1(f50(f27(f115(x4291,a49),f21(f115(x4291,a49))),x4292)) % 1.60/1.58 [434]P1(f50(f50(f28(a114),x4341),f50(a23,f50(f50(f13(a114),x4342),x4341)))) % 1.60/1.58 [435]P1(f50(f50(f28(a114),x4351),f50(a23,f50(f50(f13(a114),x4351),x4352)))) % 1.60/1.58 [452]P1(f50(f50(f51(f115(x4521,x4521)),f3(x4521)),f17(x4521,x4521,x4522,f50(f15(f115(x4521,a49),x4521),x4522)))) % 1.60/1.58 [482]~P1(f50(f50(f28(a114),f50(f50(f13(a114),x4821),x4822)),x4822)) % 1.60/1.58 [483]~P1(f50(f50(f28(a114),f50(f50(f13(a114),x4831),x4832)),x4831)) % 1.60/1.58 [414]E(f25(x4141,x4142,x4143,f2(a114)),x4142) % 1.60/1.58 [424]P9(x4241,x4242,x4243,f21(f115(x4241,a49))) % 1.60/1.58 [426]E(f41(x4261,x4262,x4263,f21(f115(x4261,a49))),f21(f115(x4262,a49))) % 1.60/1.58 [428]E(f17(x4281,x4282,f21(f115(x4281,a49)),x4283),f29(f115(f115(x4281,x4282),a49))) % 1.60/1.58 [419]E(f50(f50(f13(a114),x4191),f50(f50(f13(a114),x4192),x4193)),f50(f50(f13(a114),x4192),f50(f50(f13(a114),x4191),x4193))) % 1.60/1.58 [441]E(f17(x4411,x4412,x4413,f50(f15(f115(x4412,a49),x4411),f29(f115(x4412,a49)))),f29(f115(f115(x4411,x4412),a49))) % 1.60/1.58 [448]E(f41(a114,a114,f50(f50(f4(a114,a114,a114),f13(a114)),x4481),f30(a114,x4482,x4483)),f30(a114,f50(f50(f13(a114),x4482),x4481),f50(f50(f13(a114),x4483),x4481))) % 1.60/1.58 [427]E(f50(f50(f13(a114),f50(f50(f13(a114),x4271),x4272)),x4273),f50(f50(f13(a114),x4271),f50(f50(f13(a114),x4272),x4273))) % 1.60/1.58 [421]E(f25(x4211,x4212,x4213,f50(a23,x4214)),f50(x4213,x4214)) % 1.60/1.58 [400]E(f50(f50(f15(x4001,x4002),x4003),x4004),x4003) % 1.60/1.58 [450]P1(f50(f50(f51(x4501),f50(x4502,x4503)),f41(x4504,x4501,x4502,f29(f115(x4504,a49))))) % 1.60/1.58 [484]~P1(f50(f50(f21(f115(x4841,f115(x4842,a49))),x4843),x4844)) % 1.60/1.58 [453]E(f41(x4531,x4532,f50(f7(x4533,x4532,x4531,x4534),x4535),f29(f115(x4531,a49))),f41(x4533,x4532,x4534,f41(x4531,x4533,x4535,f29(f115(x4531,a49))))) % 1.60/1.58 [454]E(f50(f16(x4541,x4542,x4543,x4544,x4545),x4546),f50(f50(x4544,x4546),f50(x4545,x4546))) % 1.60/1.58 [449]E(f50(f50(f7(x4491,x4492,x4493,x4494),x4495),x4496),f50(x4494,f50(x4495,x4496))) % 1.60/1.58 [451]E(f41(x4511,x4512,x4513,f41(x4514,x4511,x4515,x4516)),f41(x4514,x4512,f50(f7(x4511,x4512,x4514,x4513),x4515),x4516)) % 1.60/1.58 [436]E(f50(f50(f50(f4(x4361,x4362,x4363),x4364),x4365),x4366),f50(f50(x4364,x4366),x4365)) % 1.60/1.58 [488]~P7(x4881)+P7(f116(x4881)) % 1.60/1.58 [557]E(x5571,f2(a114))+~P1(f50(f27(a114,x5571),f2(a114))) % 1.60/1.58 [544]E(x5441,f2(a114))+P1(f50(f50(f28(a114),f2(a114)),x5441)) % 1.60/1.58 [598]E(f50(a23,f75(x5981)),x5981)+~P1(f50(f50(f28(a114),f2(a114)),x5981)) % 1.60/1.58 [611]~P8(x6111,f29(f115(x6111,a49)))+P8(f116(x6111),f29(f115(f116(x6111),a49))) % 1.60/1.58 [622]P8(x6221,f29(f115(x6221,a49)))+~P8(f116(x6221),f29(f115(f116(x6221),a49))) % 1.60/1.58 [643]E(x6431,f2(a114))+~P1(f50(f50(f28(a114),x6431),f50(a23,f2(a114)))) % 1.60/1.58 [936]P3(x9361)+P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f68(x9361)),a6)) % 1.60/1.58 [937]P4(x9371)+P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f69(x9371)),a6)) % 1.60/1.58 [938]P4(x9381)+P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f71(x9381)),a6)) % 1.60/1.58 [958]P3(x9581)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f79(x9581)),f80(x9581))),f50(x9581,f68(x9581)))) % 1.60/1.58 [780]~P8(x7801,f29(f115(x7801,a49)))+P1(f50(f50(f28(a114),f2(a114)),f14(x7801,f29(f115(x7801,a49))))) % 1.60/1.58 [1019]~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10191),a5))+P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f50(f15(f115(f118(a112,a112),a49),a111),x10191)),a6)) % 1.60/1.58 [490]~P7(x4901)+P8(x4901,x4902) % 1.60/1.58 [492]P8(x4921,x4922)+E(f14(x4921,x4922),f2(a114)) % 1.60/1.58 [493]~P2(x4932)+P2(f115(x4931,x4932)) % 1.60/1.58 [494]~P26(x4942)+P26(f115(x4941,x4942)) % 1.60/1.58 [495]~P27(x4952)+P27(f115(x4951,x4952)) % 1.60/1.58 [496]~P28(x4962)+P28(f115(x4961,x4962)) % 1.60/1.58 [497]~P14(x4972)+P14(f115(x4971,x4972)) % 1.60/1.58 [499]E(x4991,x4992)+~E(f50(a23,x4991),f50(a23,x4992)) % 1.60/1.58 [505]E(f14(x5051,x5052),f2(a114))+~E(x5052,f21(f115(x5051,a49))) % 1.60/1.58 [506]~P21(x5061)+E(f50(f50(f13(x5061),x5062),f2(x5061)),x5062) % 1.60/1.58 [507]~P22(x5071)+E(f50(f50(f13(x5071),x5072),f2(x5071)),x5072) % 1.60/1.58 [508]~P30(x5081)+E(f50(f50(f13(x5081),x5082),f2(x5081)),x5082) % 1.60/1.58 [518]~E(x5181,x5182)+P1(f50(f50(a52,x5181),x5182)) % 1.60/1.58 [521]~E(x5211,x5212)+P1(f50(f27(a114,x5211),x5212)) % 1.60/1.58 [528]~P26(x5281)+P1(f50(f27(x5281,x5282),x5282)) % 1.60/1.58 [540]~P2(x5401)+P1(f50(f27(x5401,x5402),f29(x5401))) % 1.60/1.58 [551]E(x5511,x5512)+~P1(f50(f50(a52,x5511),x5512)) % 1.60/1.58 [553]E(x5531,x5532)+~E(f50(x5531,f58(x5532,x5531)),f50(x5532,f58(x5532,x5531))) % 1.60/1.58 [558]P5(x5581,x5582)+~E(f50(x5581,f65(x5582,x5581)),f50(f65(x5582,x5581),x5582)) % 1.60/1.58 [560]~E(x5601,x5602)+P1(f50(f50(f28(a114),x5601),f50(a23,x5602))) % 1.60/1.58 [561]~E(x5611,f2(a114))+P1(f50(f50(f28(a114),x5611),f50(a23,x5612))) % 1.60/1.58 [570]P1(f50(f27(a114,x5702),x5701))+P1(f50(f27(a114,x5701),x5702)) % 1.60/1.58 [601]E(f50(f50(f13(a114),x6011),f90(x6012,x6011)),x6012)+~P1(f50(f27(a114,x6011),x6012)) % 1.60/1.58 [640]~P1(f50(f27(a114,x6401),x6402))+P1(f50(f27(a114,x6401),f50(a23,x6402))) % 1.60/1.58 [662]~P1(f50(f27(a114,x6621),x6622))+P1(f50(f50(f28(a114),x6621),f50(a23,x6622))) % 1.60/1.58 [664]P8(x6641,x6642)+~P1(f50(f50(f28(a114),f2(a114)),f14(x6641,x6642))) % 1.60/1.58 [678]~E(x6781,f21(f115(x6782,a49)))+~P1(f50(f50(f28(a114),f2(a114)),f14(x6782,x6781))) % 1.60/1.58 [680]P1(f50(f27(a114,x6801),x6802))+~P1(f50(f50(f28(a114),x6801),f50(a23,x6802))) % 1.60/1.58 [707]~P1(f50(f27(a114,x7071),x7072))+P1(f50(f27(a114,f50(a23,x7071)),f50(a23,x7072))) % 1.60/1.58 [748]P1(f50(f27(a114,x7481),x7482))+~P1(f50(f27(a114,f50(a23,x7481)),f50(a23,x7482))) % 1.60/1.58 [895]E(x8951,x8952)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x8951),x8952)),f78(x8952,x8951))) % 1.60/1.58 [512]~P21(x5121)+E(f50(f50(f13(x5121),f2(x5121)),x5122),x5122) % 1.60/1.58 [513]~P22(x5131)+E(f50(f50(f13(x5131),f2(x5131)),x5132),x5132) % 1.60/1.58 [514]~P30(x5141)+E(f50(f50(f13(x5141),f2(x5141)),x5142),x5142) % 1.60/1.58 [517]E(x5171,f2(a114))+~E(f50(f50(f13(a114),x5172),x5171),x5172) % 1.60/1.58 [522]E(x5221,f2(a114))+~E(f50(f50(f13(a114),x5222),x5221),f2(a114)) % 1.60/1.58 [523]E(x5231,f2(a114))+~E(f50(f50(f13(a114),x5231),x5232),f2(a114)) % 1.60/1.58 [546]~P14(x5461)+P1(f50(f27(x5461,f21(x5461)),x5462)) % 1.60/1.58 [554]~E(x5541,f50(a23,x5542))+P1(f50(f50(f28(a114),f2(a114)),x5541)) % 1.60/1.58 [569]~E(x5691,x5692)+~P1(f50(f50(f28(a114),x5691),x5692)) % 1.60/1.58 [571]~E(x5711,f2(a114))+~P1(f50(f50(f28(a114),x5712),x5711)) % 1.60/1.58 [583]~P26(x5831)+~P1(f50(f50(f28(x5831),x5832),x5832)) % 1.60/1.58 [613]P8(a114,x6131)+P1(f50(f50(f51(a114),f76(x6131,x6132)),x6131)) % 1.60/1.58 [614]P8(a114,x6141)+P1(f50(f50(f51(a114),f85(x6141,x6142)),x6141)) % 1.60/1.58 [634]P1(f50(f27(a114,x6341),x6342))+~P1(f50(f50(f28(a114),x6341),x6342)) % 1.60/1.58 [635]P1(f50(f50(f28(a114),x6352),f50(a23,x6351)))+P1(f50(f50(f28(a114),x6351),x6352)) % 1.60/1.58 [637]E(x6371,f21(f115(x6372,a49)))+P1(f50(f50(f51(x6372),f92(x6371,x6372)),x6371)) % 1.60/1.58 [638]E(x6381,f21(f115(x6382,a49)))+P1(f50(f50(f51(x6382),f94(x6381,x6382)),x6381)) % 1.60/1.58 [644]P1(f50(f27(a114,x6441),x6442))+P1(f50(f27(a114,f50(a23,x6442)),x6441)) % 1.60/1.58 [677]P1(f50(f50(f28(a114),x6771),f50(a23,x6772)))+~P1(f50(f50(f28(a114),x6771),x6772)) % 1.60/1.58 [679]P8(a114,x6791)+~P1(f50(f27(a114,f85(x6791,x6792)),x6792)) % 1.60/1.58 [683]E(f50(a23,f50(f50(f13(a114),x6831),f96(x6832,x6831))),x6832)+~P1(f50(f50(f28(a114),x6831),x6832)) % 1.60/1.58 [697]~P1(f50(f50(f28(a114),x6971),x6972))+P1(f50(f27(a114,f50(a23,x6971)),x6972)) % 1.60/1.58 [705]P8(a114,x7051)+~P1(f50(f50(f28(a114),f76(x7051,x7052)),x7052)) % 1.60/1.58 [709]P1(f50(f27(a114,x7091),x7092))+~P1(f50(f27(a114,f50(a23,x7091)),x7092)) % 1.60/1.58 [725]P1(f50(f50(f28(a114),x7251),x7252))+~P1(f50(f27(a114,f50(a23,x7251)),x7252)) % 1.60/1.58 [727]~P1(f50(f50(f28(a114),x7272),f50(a23,x7271)))+~P1(f50(f50(f28(a114),x7271),x7272)) % 1.60/1.58 [728]P8(x7281,f29(f115(x7281,a49)))+~P8(f115(x7282,x7281),f29(f115(f115(x7282,x7281),a49))) % 1.60/1.58 [729]P8(x7291,f29(f115(x7291,a49)))+~P8(f117(x7292,x7291),f29(f115(f117(x7292,x7291),a49))) % 1.60/1.58 [730]P8(x7301,f29(f115(x7301,a49)))+~P8(f117(x7301,x7302),f29(f115(f117(x7301,x7302),a49))) % 1.60/1.58 [736]P1(f50(f50(f28(a114),f50(a23,x7361)),f50(a23,x7362)))+~P1(f50(f50(f28(a114),x7361),x7362)) % 1.60/1.58 [737]~P1(f50(f27(a114,x7371),x7372))+~P1(f50(f27(a114,f50(a23,x7372)),x7371)) % 1.60/1.58 [738]P1(f50(f50(f28(a114),x7381),x7382))+~P1(f50(f50(f28(a114),f50(a23,x7381)),x7382)) % 1.60/1.58 [773]~P1(f50(f50(f28(a114),f50(a23,x7731)),f50(a23,x7732)))+P1(f50(f50(f28(a114),x7731),x7732)) % 1.60/1.58 [777]E(x7771,f21(f115(x7772,a49)))+~P1(f50(f27(f115(x7772,a49),x7771),f21(f115(x7772,a49)))) % 1.60/1.58 [840]E(x8401,x8402)+P1(f50(f50(f51(f115(f118(a112,a112),a49)),f78(x8401,x8402)),a5)) % 1.60/1.58 [868]P1(f25(a49,a19,f27(a114,x8681),x8682))+~P1(f50(f27(a114,f50(a23,x8681)),x8682)) % 1.60/1.58 [902]~P1(f25(a49,a19,f27(a114,x9021),x9022))+P1(f50(f27(a114,f50(a23,x9021)),x9022)) % 1.60/1.58 [918]P3(x9181)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f79(x9181)),f80(x9181))),f50(f68(x9181),x9182))) % 1.60/1.58 [944]P5(x9441,x9442)+P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f65(x9442,x9441)),a6)) % 1.60/1.58 [953]E(f30(a114,x9531,f50(f50(f13(a114),x9531),f14(a114,x9532))),x9532)+~P1(f50(f27(f115(a114,a49),x9532),f30(a114,x9531,f50(f50(f13(a114),x9531),f14(a114,x9532))))) % 1.60/1.58 [956]P1(f50(f50(f51(f115(f118(a112,a112),a49)),f9(x9561,x9562)),a5))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9561),a5)) % 1.60/1.58 [957]P1(f50(f50(f51(f115(f118(a112,a112),a49)),f10(x9571,x9572)),a5))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9571),a5)) % 1.60/1.58 [573]~E(x5732,x5733)+P1(f50(f50(f51(x5731),x5732),f50(a52,x5733))) % 1.60/1.58 [641]E(x6411,x6412)+~P1(f50(f50(f51(x6413),x6411),f50(a52,x6412))) % 1.60/1.58 [1053]P8(x10531,x10532)+~P1(f50(f50(f51(f118(f115(x10531,a49),f115(x10531,a49))),f50(f50(f31(f115(x10531,a49),f115(x10531,a49)),x10533),x10532)),f45(x10531))) % 1.60/1.58 [524]~P2(x5242)+E(f50(f29(f115(x5241,x5242)),x5243),f29(x5242)) % 1.60/1.58 [526]~P14(x5262)+E(f50(f21(f115(x5261,x5262)),x5263),f21(x5262)) % 1.60/1.58 [545]~P30(x5451)+E(f50(f50(f13(x5451),x5452),x5453),f50(f50(f13(x5451),x5453),x5452)) % 1.60/1.58 [562]E(x5621,x5622)+~E(f50(f50(f13(a114),x5623),x5621),f50(f50(f13(a114),x5623),x5622)) % 1.60/1.58 [563]E(x5631,x5632)+~E(f50(f50(f13(a114),x5631),x5633),f50(f50(f13(a114),x5632),x5633)) % 1.60/1.58 [564]~E(x5642,f50(f50(f13(a114),x5641),x5643))+P1(f50(f27(a114,x5641),x5642)) % 1.60/1.58 [572]~P1(f50(x5723,x5722))+P1(f50(f50(f51(x5721),x5722),x5723)) % 1.60/1.58 [584]~E(x5843,x5842)+P1(f50(f27(f115(x5841,a49),x5842),x5843)) % 1.60/1.58 [590]~E(x5902,x5903)+P1(f50(f27(f115(x5901,a49),x5902),x5903)) % 1.60/1.58 [609]P1(f50(x6091,x6092))+~P1(f50(f50(f51(x6093),x6092),x6091)) % 1.60/1.58 [617]~E(x6171,f21(f115(x6172,a49)))+~P1(f50(f50(f51(x6172),x6173),x6171)) % 1.60/1.58 [916]E(x9161,x9162)+~E(f50(f50(f4(x9163,f115(x9163,a49),a49),f51(x9163)),x9161),f50(f50(f4(x9163,f115(x9163,a49),a49),f51(x9163)),x9162)) % 1.60/1.58 [659]~E(x6592,f50(a23,f50(f50(f13(a114),x6591),x6593)))+P1(f50(f50(f28(a114),x6591),x6592)) % 1.60/1.58 [732]~P1(f50(f27(a114,x7321),x7323))+P1(f50(f27(a114,x7321),f50(f50(f13(a114),x7322),x7323))) % 1.60/1.58 [734]~P1(f50(f27(a114,x7341),x7342))+P1(f50(f27(a114,x7341),f50(f50(f13(a114),x7342),x7343))) % 1.60/1.58 [757]~P1(f50(f50(f28(a114),x7571),x7573))+P1(f50(f50(f28(a114),x7571),f50(f50(f13(a114),x7572),x7573))) % 1.60/1.58 [759]~P1(f50(f50(f28(a114),x7591),x7592))+P1(f50(f50(f28(a114),x7591),f50(f50(f13(a114),x7592),x7593))) % 1.60/1.58 [774]~E(x7741,x7742)+~P1(f50(f50(f28(f115(x7743,a49)),x7741),x7742)) % 1.60/1.58 [783]~E(x7832,f21(f115(f118(x7831,x7831),a49)))+P1(f50(f27(f115(f118(x7831,x7831),a49),x7832),x7833)) % 1.60/1.58 [827]P1(f50(f27(f115(x8271,a49),x8272),x8273))+~P1(f50(f50(f28(f115(x8271,a49)),x8272),x8273)) % 1.60/1.58 [850]~P1(f50(f27(a114,x8502),x8503))+P1(f50(f27(a114,f50(f50(f13(a114),x8501),x8502)),f50(f50(f13(a114),x8501),x8503))) % 1.60/1.58 [851]~P1(f50(f27(a114,x8511),x8513))+P1(f50(f27(a114,f50(f50(f13(a114),x8511),x8512)),f50(f50(f13(a114),x8513),x8512))) % 1.60/1.58 [862]~P1(f50(f50(f28(a114),x8622),x8623))+P1(f50(f50(f28(a114),f50(f50(f13(a114),x8621),x8622)),f50(f50(f13(a114),x8621),x8623))) % 1.60/1.58 [863]~P1(f50(f50(f28(a114),x8631),x8633))+P1(f50(f50(f28(a114),f50(f50(f13(a114),x8631),x8632)),f50(f50(f13(a114),x8633),x8632))) % 1.60/1.58 [908]P1(f50(f27(a114,x9081),x9082))+~P1(f50(f27(a114,f50(f50(f13(a114),x9083),x9081)),f50(f50(f13(a114),x9083),x9082))) % 1.60/1.58 [915]P1(f50(f50(f28(a114),x9151),x9152))+~P1(f50(f50(f28(a114),f50(f50(f13(a114),x9153),x9151)),f50(f50(f13(a114),x9153),x9152))) % 1.60/1.58 [1044]~P1(f50(f27(f115(x10441,a49),x10442),x10443))+P1(f50(f27(f115(x10441,a49),f50(f50(f4(x10441,f115(x10441,a49),a49),f51(x10441)),x10442)),f50(f50(f4(x10441,f115(x10441,a49),a49),f51(x10441)),x10443))) % 1.60/1.58 [1060]~P1(f50(f50(f51(f118(f115(x10601,a49),f115(x10601,a49))),f50(f50(f31(f115(x10601,a49),f115(x10601,a49)),x10602),x10603)),f45(x10601)))+P1(f50(f50(f28(f115(x10601,a49)),x10602),x10603)) % 1.60/1.58 [1071]P1(f50(f27(f115(x10711,a49),x10712),x10713))+~P1(f50(f27(f115(x10711,a49),f50(f50(f4(x10711,f115(x10711,a49),a49),f51(x10711)),x10712)),f50(f50(f4(x10711,f115(x10711,a49),a49),f51(x10711)),x10713))) % 1.60/1.58 [856]P1(f50(f27(a114,x8561),x8562))+~P1(f50(f27(a114,f50(f50(f13(a114),x8563),x8561)),x8562)) % 1.60/1.58 [857]P1(f50(f27(a114,x8571),x8572))+~P1(f50(f27(a114,f50(f50(f13(a114),x8571),x8573)),x8572)) % 1.60/1.58 [871]P1(f50(f50(f28(a114),x8711),x8712))+~P1(f50(f50(f28(a114),f50(f50(f13(a114),x8711),x8713)),x8712)) % 1.60/1.58 [740]P8(x7401,x7402)+~P13(x7401,x7403,x7404,x7402) % 1.60/1.58 [741]P8(x7411,x7412)+~P13(x7411,x7413,x7412,x7414) % 1.60/1.58 [792]~P8(x7922,x7924)+P8(x7921,f41(x7922,x7921,x7923,x7924)) % 1.60/1.58 [878]P8(x8781,x8782)+~P8(f117(x8783,x8781),f43(x8783,x8781,x8784,x8782)) % 1.60/1.58 [879]P8(x8791,x8792)+~P8(f117(x8791,x8793),f43(x8791,x8793,x8792,x8794)) % 1.60/1.58 [907]P9(x9071,x9072,x9073,x9074)+~E(f110(x9074,x9073,x9072,x9071),f55(x9074,x9073,x9072,x9071)) % 1.60/1.58 [952]~P9(x9522,x9521,x9524,x9523)+P9(x9521,x9522,f18(x9522,x9521,x9523,x9524),f41(x9522,x9521,x9524,x9523)) % 1.60/1.58 [552]~P10(x5523,x5521,x5524)+E(f50(f50(x5521,x5522),x5522),x5522) % 1.60/1.58 [703]~E(x7034,f21(f115(x7031,a49)))+E(f41(x7031,x7032,x7033,x7034),f21(f115(x7032,a49))) % 1.60/1.58 [760]~P13(x7602,x7603,x7604,x7601)+~E(x7601,f21(f115(x7602,a49))) % 1.60/1.58 [765]~P1(f50(f50(x7653,x7654),x7652))+P1(f50(f50(f51(x7651),x7652),f32(x7651,x7653,x7654))) % 1.60/1.58 [766]~P1(f50(f50(x7663,x7664),x7662))+P1(f50(f50(f51(x7661),x7662),f33(x7661,x7663,x7664))) % 1.60/1.58 [767]~P1(f50(f50(x7673,x7672),x7674))+P1(f50(f50(f51(x7671),x7672),f38(x7671,x7673,x7674))) % 1.60/1.58 [768]~P1(f50(f50(x7683,x7682),x7684))+P1(f50(f50(f51(x7681),x7682),f35(x7681,x7683,x7684))) % 1.60/1.58 [776]~E(f41(x7762,x7763,x7764,x7761),f21(f115(x7763,a49)))+E(x7761,f21(f115(x7762,a49))) % 1.60/1.58 [806]P8(x8062,x8064)+E(f14(f117(x8061,x8062),f43(x8061,x8062,x8063,x8064)),f2(a114)) % 1.60/1.58 [807]P8(x8071,x8073)+E(f14(f117(x8071,x8072),f43(x8071,x8072,x8073,x8074)),f2(a114)) % 1.60/1.58 [814]~P1(f50(f50(f51(x8144),x8143),f32(x8144,x8141,x8142)))+P1(f50(f50(x8141,x8142),x8143)) % 1.60/1.58 [815]~P1(f50(f50(f51(x8154),x8153),f33(x8154,x8151,x8152)))+P1(f50(f50(x8151,x8152),x8153)) % 1.60/1.58 [816]~P1(f50(f50(f51(x8164),x8162),f38(x8164,x8161,x8163)))+P1(f50(f50(x8161,x8162),x8163)) % 1.60/1.58 [817]~P1(f50(f50(f51(x8174),x8172),f35(x8174,x8171,x8173)))+P1(f50(f50(x8171,x8172),x8173)) % 1.60/1.58 [890]~P9(x8902,x8901,x8903,x8904)+E(f14(x8901,f41(x8902,x8901,x8903,x8904)),f14(x8902,x8904)) % 1.60/1.58 [917]~P9(x9171,x9172,x9173,f29(f115(x9171,a49)))+E(f50(f18(x9171,x9172,f29(f115(x9171,a49)),x9173),f50(x9173,x9174)),x9174) % 1.60/1.58 [932]P9(x9324,x9323,x9321,x9322)+E(f50(x9321,f110(x9322,x9321,x9323,x9324)),f50(x9321,f55(x9322,x9321,x9323,x9324))) % 1.60/1.58 [947]P1(f50(f50(f51(f118(x9471,x9471)),f50(f50(f31(x9471,x9471),x9472),x9473)),f44(x9471,x9474)))+~P1(f50(f50(f28(a114),f50(x9474,x9472)),f50(x9474,x9473))) % 1.60/1.58 [948]~E(x9481,x9482)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9483),x9481)),f10(x9484,x9482))) % 1.60/1.58 [949]~E(x9491,x9492)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9491),x9493)),f9(x9494,x9492))) % 1.60/1.58 [954]~P9(x9542,x9541,x9544,x9543)+E(f41(x9541,x9542,f18(x9542,x9541,x9543,x9544),f41(x9542,x9541,x9544,x9543)),x9543) % 1.60/1.58 [967]~P1(f50(f50(f51(f118(x9674,x9674)),f50(f50(f31(x9674,x9674),x9672),x9673)),f44(x9674,x9671)))+P1(f50(f50(f28(a114),f50(x9671,x9672)),f50(x9671,x9673))) % 1.60/1.58 [1040]~P8(x10402,x10404)+P1(f50(f27(a114,f14(x10401,f41(x10402,x10401,x10403,x10404))),f14(x10402,x10404))) % 1.60/1.58 [1056]P8(x10561,x10562)+~P1(f50(f50(f51(f118(f115(x10561,a49),f115(x10561,a49))),f50(f50(f31(f115(x10561,a49),f115(x10561,a49)),x10563),x10562)),f46(x10561,x10564))) % 1.60/1.58 [1057]P8(x10571,x10572)+~P1(f50(f50(f51(f118(f115(x10571,a49),f115(x10571,a49))),f50(f50(f31(f115(x10571,a49),f115(x10571,a49)),x10572),x10573)),f46(x10571,x10574))) % 1.60/1.58 [1058]~E(x10581,f21(f115(x10582,a49)))+~P1(f50(f50(f51(f118(f115(x10582,a49),f115(x10582,a49))),f50(f50(f31(f115(x10582,a49),f115(x10582,a49)),x10583),x10581)),f46(x10582,x10584))) % 1.60/1.58 [1070]~P9(x10701,x10702,x10703,x10704)+~P1(f50(f50(f28(a114),f14(x10702,f41(x10701,x10702,x10703,x10704))),f14(x10701,x10704))) % 1.60/1.58 [796]E(x7961,f21(f115(x7962,a49)))+~E(f43(x7963,x7962,x7964,x7961),f21(f115(f117(x7963,x7962),a49))) % 1.60/1.58 [797]E(x7971,f21(f115(x7972,a49)))+~E(f43(x7972,x7973,x7971,x7974),f21(f115(f117(x7972,x7973),a49))) % 1.60/1.58 [909]E(f50(x9091,f93(x9091,x9092,x9093,x9094)),f21(f115(x9093,a49)))+~E(f17(x9094,x9093,x9092,x9091),f21(f115(f115(x9094,x9093),a49))) % 1.60/1.58 [959]~P21(x9591)+E(f8(a114,x9591,f50(f7(a114,x9591,a114,x9592),a23),f30(a114,x9593,x9594)),f8(a114,x9591,x9592,f30(a114,f50(a23,x9593),f50(a23,x9594)))) % 1.60/1.58 [971]~P9(x9711,x9713,x9714,f29(f115(x9711,a49)))+P9(x9711,f115(x9712,x9713),f50(f7(x9713,f115(x9712,x9713),x9711,f15(x9713,x9712)),x9714),f29(f115(x9711,a49))) % 1.60/1.58 [978]P9(x9781,x9782,x9783,x9784)+P1(f50(f50(f51(x9781),f110(x9784,x9783,x9782,x9781)),x9784)) % 1.60/1.58 [979]P9(x9791,x9792,x9793,x9794)+P1(f50(f50(f51(x9791),f55(x9794,x9793,x9792,x9791)),x9794)) % 1.60/1.58 [991]~E(f17(x9911,x9914,x9913,x9912),f21(f115(f115(x9911,x9914),a49)))+P1(f50(f50(f51(x9911),f93(x9912,x9913,x9914,x9911)),x9913)) % 1.60/1.58 [694]~P30(x6941)+E(f50(f50(f13(x6941),x6942),f50(f50(f13(x6941),x6943),x6944)),f50(f50(f13(x6941),x6943),f50(f50(f13(x6941),x6942),x6944))) % 1.60/1.58 [752]~P16(x7521)+E(f50(f50(f13(x7521),f50(f50(f13(x7521),x7522),x7523)),x7524),f50(f50(f13(x7521),x7522),f50(f50(f13(x7521),x7523),x7524))) % 1.60/1.58 [753]~P30(x7531)+E(f50(f50(f13(x7531),f50(f50(f13(x7531),x7532),x7533)),x7534),f50(f50(f13(x7531),x7532),f50(f50(f13(x7531),x7533),x7534))) % 1.60/1.58 [790]~P30(x7901)+E(f50(f50(f13(x7901),f50(f50(f13(x7901),x7902),x7903)),x7904),f50(f50(f13(x7901),f50(f50(f13(x7901),x7902),x7904)),x7903)) % 1.60/1.58 [1121]P13(x11211,f50(f50(f4(x11211,f115(f118(x11211,x11211),a49),f115(x11211,a49)),f50(f7(f115(x11211,f115(f115(f118(x11211,x11211),a49),a49)),f115(f115(f118(x11211,x11211),a49),f115(x11211,a49)),x11211,f4(x11211,f115(f118(x11211,x11211),a49),a49)),f50(f7(f115(x11211,f118(x11211,x11211)),f115(x11211,f115(f115(f118(x11211,x11211),a49),a49)),x11211,f7(f118(x11211,x11211),f115(f115(f118(x11211,x11211),a49),a49),x11211,f51(f118(x11211,x11211)))),f31(x11211,x11211)))),x11212),x11213,x11214)+~P1(f50(f50(f51(f118(f115(x11211,a49),f115(x11211,a49))),f50(f50(f31(f115(x11211,a49),f115(x11211,a49)),x11213),x11214)),f46(x11211,x11212))) % 1.60/1.58 [1127]E(x11271,x11272)+~E(f50(f50(f4(x11273,f115(f118(x11273,x11274),a49),f115(x11274,a49)),f50(f7(f115(x11274,f115(f115(f118(x11273,x11274),a49),a49)),f115(f115(f118(x11273,x11274),a49),f115(x11274,a49)),x11273,f4(x11274,f115(f118(x11273,x11274),a49),a49)),f50(f7(f115(x11274,f118(x11273,x11274)),f115(x11274,f115(f115(f118(x11273,x11274),a49),a49)),x11273,f7(f118(x11273,x11274),f115(f115(f118(x11273,x11274),a49),a49),x11274,f51(f118(x11273,x11274)))),f31(x11273,x11274)))),x11271),f50(f50(f4(x11273,f115(f118(x11273,x11274),a49),f115(x11274,a49)),f50(f7(f115(x11274,f115(f115(f118(x11273,x11274),a49),a49)),f115(f115(f118(x11273,x11274),a49),f115(x11274,a49)),x11273,f4(x11274,f115(f118(x11273,x11274),a49),a49)),f50(f7(f115(x11274,f118(x11273,x11274)),f115(x11274,f115(f115(f118(x11273,x11274),a49),a49)),x11273,f7(f118(x11273,x11274),f115(f115(f118(x11273,x11274),a49),a49),x11274,f51(f118(x11273,x11274)))),f31(x11273,x11274)))),x11272)) % 1.60/1.58 [1128]~P13(x11281,f50(f50(f4(x11281,f115(f118(x11281,x11281),a49),f115(x11281,a49)),f50(f7(f115(x11281,f115(f115(f118(x11281,x11281),a49),a49)),f115(f115(f118(x11281,x11281),a49),f115(x11281,a49)),x11281,f4(x11281,f115(f118(x11281,x11281),a49),a49)),f50(f7(f115(x11281,f118(x11281,x11281)),f115(x11281,f115(f115(f118(x11281,x11281),a49),a49)),x11281,f7(f118(x11281,x11281),f115(f115(f118(x11281,x11281),a49),a49),x11281,f51(f118(x11281,x11281)))),f31(x11281,x11281)))),x11284),x11282,x11283)+P1(f50(f50(f51(f118(f115(x11281,a49),f115(x11281,a49))),f50(f50(f31(f115(x11281,a49),f115(x11281,a49)),x11282),x11283)),f46(x11281,x11284))) % 1.60/1.58 [1134]~P1(f50(f27(f115(f118(x11341,x11342),a49),x11343),x11344))+P1(f50(f27(f115(x11341,f115(x11342,a49)),f50(f50(f4(x11341,f115(f118(x11341,x11342),a49),f115(x11342,a49)),f50(f7(f115(x11342,f115(f115(f118(x11341,x11342),a49),a49)),f115(f115(f118(x11341,x11342),a49),f115(x11342,a49)),x11341,f4(x11342,f115(f118(x11341,x11342),a49),a49)),f50(f7(f115(x11342,f118(x11341,x11342)),f115(x11342,f115(f115(f118(x11341,x11342),a49),a49)),x11341,f7(f118(x11341,x11342),f115(f115(f118(x11341,x11342),a49),a49),x11342,f51(f118(x11341,x11342)))),f31(x11341,x11342)))),x11343)),f50(f50(f4(x11341,f115(f118(x11341,x11342),a49),f115(x11342,a49)),f50(f7(f115(x11342,f115(f115(f118(x11341,x11342),a49),a49)),f115(f115(f118(x11341,x11342),a49),f115(x11342,a49)),x11341,f4(x11342,f115(f118(x11341,x11342),a49),a49)),f50(f7(f115(x11342,f118(x11341,x11342)),f115(x11342,f115(f115(f118(x11341,x11342),a49),a49)),x11341,f7(f118(x11341,x11342),f115(f115(f118(x11341,x11342),a49),a49),x11342,f51(f118(x11341,x11342)))),f31(x11341,x11342)))),x11344))) % 1.60/1.58 [1135]P1(f50(f27(f115(f118(x11351,x11352),a49),x11353),x11354))+~P1(f50(f27(f115(x11351,f115(x11352,a49)),f50(f50(f4(x11351,f115(f118(x11351,x11352),a49),f115(x11352,a49)),f50(f7(f115(x11352,f115(f115(f118(x11351,x11352),a49),a49)),f115(f115(f118(x11351,x11352),a49),f115(x11352,a49)),x11351,f4(x11352,f115(f118(x11351,x11352),a49),a49)),f50(f7(f115(x11352,f118(x11351,x11352)),f115(x11352,f115(f115(f118(x11351,x11352),a49),a49)),x11351,f7(f118(x11351,x11352),f115(f115(f118(x11351,x11352),a49),a49),x11352,f51(f118(x11351,x11352)))),f31(x11351,x11352)))),x11353)),f50(f50(f4(x11351,f115(f118(x11351,x11352),a49),f115(x11352,a49)),f50(f7(f115(x11352,f115(f115(f118(x11351,x11352),a49),a49)),f115(f115(f118(x11351,x11352),a49),f115(x11352,a49)),x11351,f4(x11352,f115(f118(x11351,x11352),a49),a49)),f50(f7(f115(x11352,f118(x11351,x11352)),f115(x11352,f115(f115(f118(x11351,x11352),a49),a49)),x11351,f7(f118(x11351,x11352),f115(f115(f118(x11351,x11352),a49),a49),x11352,f51(f118(x11351,x11352)))),f31(x11351,x11352)))),x11354))) % 1.60/1.58 [955]P1(f50(f50(f51(f118(x9551,x9551)),f50(f50(f31(x9551,x9551),x9552),x9553)),f48(x9551,x9554,x9555)))+~P1(f50(f50(f28(a114),f50(x9554,x9552)),f50(x9554,x9553))) % 1.60/1.58 [960]~P1(f50(f50(f51(x9604),x9603),f39(x9604,x9601,x9602,x9605)))+P1(f50(f50(x9601,x9602),x9603)) % 1.60/1.58 [961]~P1(f50(f50(f51(x9614),x9613),f36(x9614,x9611,x9612,x9615)))+P1(f50(f50(x9611,x9612),x9613)) % 1.60/1.58 [962]~P1(f50(f50(f51(x9624),x9622),f39(x9624,x9621,x9625,x9623)))+P1(f50(f50(x9621,x9622),x9623)) % 1.60/1.58 [963]~P1(f50(f50(f51(x9634),x9632),f36(x9634,x9631,x9635,x9633)))+P1(f50(f50(x9631,x9632),x9633)) % 1.60/1.58 [976]E(f50(x9761,f56(x9762,x9761,x9763,x9764)),x9764)+~P1(f50(f50(f51(x9765),x9764),f41(x9763,x9765,x9761,x9762))) % 1.60/1.58 [1042]E(f41(x10421,x10422,x10423,f83(x10424,x10423,x10421,x10425,x10422)),x10425)+~P1(f50(f27(f115(x10422,a49),x10425),f41(x10421,x10422,x10423,x10424))) % 1.60/1.58 [942]P1(f50(f50(f51(x9421),f50(x9422,x9423)),f41(x9424,x9421,x9422,x9425)))+~P1(f50(f50(f51(x9424),x9423),x9425)) % 1.60/1.58 [1006]P1(f50(f27(f115(x10061,a49),f41(x10062,x10061,x10063,x10064)),f41(x10062,x10061,x10063,x10065)))+~P1(f50(f27(f115(x10062,a49),x10064),x10065)) % 1.60/1.58 [1024]~P8(x10243,f41(x10242,x10243,x10245,f29(f115(x10242,a49))))+P8(x10241,f41(x10242,x10241,f50(f7(x10243,x10241,x10242,x10244),x10245),f29(f115(x10242,a49)))) % 1.60/1.58 [1027]P1(f50(f27(f115(f115(x10271,x10272),a49),f17(x10271,x10272,x10273,x10274)),f17(x10271,x10272,x10275,x10274)))+~P1(f50(f27(f115(x10271,a49),x10275),x10273)) % 1.60/1.58 [1034]~P1(f50(f50(f51(x10345),x10344),f41(x10341,x10345,x10343,x10342)))+P1(f50(f50(f51(x10341),f56(x10342,x10343,x10341,x10344)),x10342)) % 1.60/1.58 [1087]P1(f50(f50(f51(f115(x10871,x10874)),x10873),f17(x10871,x10874,x10875,x10872)))+P1(f50(f50(f51(x10871),f81(x10872,x10873,x10874,x10875,x10871)),x10875)) % 1.60/1.58 [1088]~P1(f50(f27(f115(x10885,a49),x10884),f41(x10881,x10885,x10883,x10882)))+P1(f50(f27(f115(x10881,a49),f83(x10882,x10883,x10881,x10884,x10885)),x10882)) % 1.60/1.58 [1092]P1(f50(f27(f115(f115(x10921,x10924),a49),f17(x10921,x10924,x10925,x10923)),f17(x10921,x10924,x10925,x10922)))+P1(f50(f50(f51(x10921),f89(x10922,x10923,x10924,x10925,x10921)),x10925)) % 1.60/1.58 [1119]P1(f50(f50(f51(f115(x11191,x11192)),x11193),f17(x11191,x11192,x11194,x11195)))+~P1(f50(f50(f51(x11192),f50(x11193,f81(x11195,x11193,x11192,x11194,x11191))),f50(x11195,f81(x11195,x11193,x11192,x11194,x11191)))) % 1.60/1.58 [1120]P1(f50(f27(f115(f115(x11201,x11202),a49),f17(x11201,x11202,x11203,x11204)),f17(x11201,x11202,x11203,x11205)))+~P1(f50(f27(f115(x11202,a49),f50(x11204,f89(x11205,x11204,x11202,x11203,x11201))),f50(x11205,f89(x11205,x11204,x11202,x11203,x11201)))) % 1.60/1.58 [847]~P30(x8471)+E(f50(f50(f13(x8471),f50(f50(f13(x8471),x8472),x8473)),f50(f50(f13(x8471),x8474),x8475)),f50(f50(f13(x8471),f50(f50(f13(x8471),x8472),x8474)),f50(f50(f13(x8471),x8473),x8475))) % 1.60/1.58 [939]~E(x9392,f50(x9394,x9395))+P1(f50(f50(f51(x9391),x9392),f41(x9393,x9391,x9394,f29(f115(x9393,a49))))) % 1.60/1.58 [998]P12(x9981,x9982,x9983,x9984,x9985)+~P1(f50(f50(f51(f118(x9981,x9982)),f50(f50(f31(x9981,x9982),x9984),x9985)),x9983)) % 1.60/1.58 [1001]~P12(x10011,x10012,x10015,x10013,x10014)+P1(f50(f50(f51(f118(x10011,x10012)),f50(f50(f31(x10011,x10012),x10013),x10014)),x10015)) % 1.60/1.58 [1003]~P21(x10031)+E(f8(a114,x10031,x10032,f30(a114,f50(f50(f13(a114),x10033),x10034),f50(f50(f13(a114),x10035),x10034))),f8(a114,x10031,f50(f7(a114,x10031,a114,x10032),f50(f50(f4(a114,a114,a114),f13(a114)),x10034)),f30(a114,x10033,x10035))) % 1.60/1.58 [1059]P1(f50(f27(f115(x10591,a49),f41(x10592,x10591,x10593,x10594)),x10595))+~P1(f50(f50(f51(f115(x10592,x10591)),x10593),f17(x10592,x10591,x10594,f50(f15(f115(x10591,a49),x10592),x10595)))) % 1.60/1.58 [1089]P1(f50(f50(f51(x10891),f82(x10892,x10893,x10894,x10895,x10891)),x10895))+P1(f50(f50(f51(f115(x10891,x10894)),x10893),f17(x10891,x10894,x10895,f50(f15(f115(x10894,a49),x10891),x10892)))) % 1.60/1.58 [1113]~P1(f50(f50(f51(x11132),f50(x11133,f82(x11135,x11133,x11132,x11134,x11131))),x11135))+P1(f50(f50(f51(f115(x11131,x11132)),x11133),f17(x11131,x11132,x11134,f50(f15(f115(x11132,a49),x11131),x11135)))) % 1.60/1.58 [1075]~P1(f50(f50(f51(x10754),x10753),f40(x10754,x10755,x10751,x10752,x10756)))+P1(f50(f50(x10751,x10752),x10753)) % 1.60/1.58 [1076]~P1(f50(f50(f51(x10764),x10763),f37(x10764,x10761,x10765,x10762,x10766)))+P1(f50(f50(x10761,x10762),x10763)) % 1.60/1.58 [1077]~P1(f50(f50(f51(x10774),x10772),f40(x10774,x10771,x10775,x10776,x10773)))+P1(f50(f50(x10771,x10772),x10773)) % 1.60/1.58 [1078]~P1(f50(f50(f51(x10784),x10782),f37(x10784,x10785,x10781,x10786,x10783)))+P1(f50(f50(x10781,x10782),x10783)) % 1.60/1.58 [1079]~P11(x10793,x10794,x10791,x10795,x10796,x10797)+E(f50(f50(x10791,x10792),x10792),x10792) % 1.60/1.58 [1084]P1(f50(f50(f51(f118(f118(x10841,x10842),f118(x10841,x10842))),f50(f50(f31(f118(x10841,x10842),f118(x10841,x10842)),f50(f50(f31(x10841,x10842),x10843),x10844)),f50(f50(f31(x10841,x10842),x10845),x10846))),f47(x10841,x10842,x10847,x10848)))+~P1(f50(f50(f51(f118(x10841,x10841)),f50(f50(f31(x10841,x10841),x10843),x10845)),x10847)) % 1.60/1.58 [977]P4(x9771)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x9771)),f73(x9771))),f50(x9771,f71(x9771))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x9771)),f73(x9771))),f50(x9771,f69(x9771)))) % 1.60/1.58 [1018]P4(x10181)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x10181)),f73(x10181))),f50(x10181,f71(x10181))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x10181)),f73(x10181))),f50(x10181,f69(x10181)))) % 1.60/1.58 [500]~P7(x5002)+~P7(x5001)+P7(f115(x5001,x5002)) % 1.60/1.58 [501]~P7(x5012)+~P7(x5011)+P7(f118(x5011,x5012)) % 1.60/1.58 [502]~P7(x5022)+~P7(x5021)+P7(f117(x5021,x5022)) % 1.60/1.58 [516]~P8(x5162,x5161)+~E(f14(x5162,x5161),f2(a114))+E(x5161,f21(f115(x5162,a49))) % 1.60/1.58 [612]~P8(x6122,x6121)+E(x6121,f21(f115(x6122,a49)))+P1(f50(f50(f28(a114),f2(a114)),f14(x6122,x6121))) % 1.60/1.58 [642]E(x6421,x6422)+~P1(f50(f27(a114,x6422),x6421))+~P1(f50(f27(a114,x6421),x6422)) % 1.60/1.58 [666]E(x6661,f2(a114))+E(f50(a23,f91(x6662,x6661)),x6661)+~P1(f50(f50(f28(a114),x6661),f50(a23,x6662))) % 1.60/1.58 [675]E(x6751,f50(a23,x6752))+P1(f50(f27(a114,x6751),x6752))+~P1(f50(f27(a114,x6751),f50(a23,x6752))) % 1.60/1.58 [710]E(x7101,x7102)+~P1(f50(f27(a114,x7102),x7101))+~P1(f50(f50(f28(a114),x7101),f50(a23,x7102))) % 1.60/1.58 [832]~P23(x8321)+~P1(f50(f27(x8321,x8322),f2(x8321)))+P1(f50(f27(x8321,f50(f50(f13(x8321),x8322),x8322)),f2(x8321))) % 1.60/1.58 [844]~P23(x8441)+~P1(f50(f50(f28(x8441),x8442),f2(x8441)))+P1(f50(f50(f28(x8441),f50(f50(f13(x8441),x8442),x8442)),f2(x8441))) % 1.60/1.58 [845]~P31(x8451)+~P1(f50(f50(f28(x8451),x8452),f2(x8451)))+P1(f50(f50(f28(x8451),f50(f50(f13(x8451),x8452),x8452)),f2(x8451))) % 1.60/1.58 [883]~P23(x8831)+~P1(f50(f27(x8831,f50(f50(f13(x8831),x8832),x8832)),f2(x8831)))+P1(f50(f27(x8831,x8832),f2(x8831))) % 1.60/1.58 [898]~P23(x8981)+~P1(f50(f50(f28(x8981),f50(f50(f13(x8981),x8982),x8982)),f2(x8981)))+P1(f50(f50(f28(x8981),x8982),f2(x8981))) % 1.60/1.58 [899]~P31(x8991)+~P1(f50(f50(f28(x8991),f50(f50(f13(x8991),x8992),x8992)),f2(x8991)))+P1(f50(f50(f28(x8991),x8992),f2(x8991))) % 1.60/1.58 [504]~E(x5042,f2(a114))+~E(x5041,f2(a114))+E(f50(f50(f13(a114),x5041),x5042),f2(a114)) % 1.60/1.58 [511]~P23(x5111)+~E(x5112,f2(x5111))+E(f50(f50(f13(x5111),x5112),x5112),f2(x5111)) % 1.60/1.58 [535]~E(x5352,f2(a114))+~E(x5351,f50(a23,f2(a114)))+E(f50(f50(f13(a114),x5351),x5352),f50(a23,f2(a114))) % 1.60/1.58 [536]~E(x5361,f2(a114))+~E(x5362,f50(a23,f2(a114)))+E(f50(f50(f13(a114),x5361),x5362),f50(a23,f2(a114))) % 1.60/1.58 [539]~P23(x5392)+E(x5391,f2(x5392))+~E(f50(f50(f13(x5392),x5391),x5391),f2(x5392)) % 1.60/1.58 [542]E(x5421,f2(a114))+E(x5422,f2(a114))+~E(f50(f50(f13(a114),x5422),x5421),f50(a23,f2(a114))) % 1.60/1.58 [549]E(x5491,f2(a114))+E(x5491,f50(a23,f2(a114)))+~E(f50(f50(f13(a114),x5492),x5491),f50(a23,f2(a114))) % 1.60/1.58 [550]E(x5501,f2(a114))+E(x5501,f50(a23,f2(a114)))+~E(f50(f50(f13(a114),x5501),x5502),f50(a23,f2(a114))) % 1.60/1.58 [556]E(x5561,f50(a23,f2(a114)))+E(x5562,f50(a23,f2(a114)))+~E(f50(f50(f13(a114),x5561),x5562),f50(a23,f2(a114))) % 1.60/1.58 [600]E(x6001,x6002)+P1(f50(f50(f28(a114),x6002),x6001))+P1(f50(f50(f28(a114),x6001),x6002)) % 1.60/1.58 [620]E(x6201,x6202)+~P1(f50(f27(a114,x6201),x6202))+P1(f50(f50(f28(a114),x6201),x6202)) % 1.60/1.58 [658]~P8(a114,x6582)+P1(f50(f27(a114,x6581),f86(x6582)))+~P1(f50(f50(f51(a114),x6581),x6582)) % 1.60/1.58 [660]E(x6601,f29(f115(x6602,a49)))+~P8(x6602,f29(f115(x6602,a49)))+~E(f14(x6602,x6601),f14(x6602,f29(f115(x6602,a49)))) % 1.60/1.58 [672]~P8(a114,x6722)+P1(f50(f50(f28(a114),x6721),f77(x6722)))+~P1(f50(f50(f51(a114),x6721),x6722)) % 1.60/1.58 [701]E(x7011,x7012)+~P1(f50(f50(f28(a114),x7011),f50(a23,x7012)))+P1(f50(f50(f28(a114),x7011),x7012)) % 1.60/1.58 [717]E(f50(a23,x7171),x7172)+~P1(f50(f50(f28(a114),x7171),x7172))+P1(f50(f50(f28(a114),f50(a23,x7171)),x7172)) % 1.60/1.58 [742]~P8(x7422,f29(f115(x7422,a49)))+~P8(x7421,f29(f115(x7421,a49)))+P8(f118(x7421,x7422),f29(f115(f118(x7421,x7422),a49))) % 1.60/1.58 [743]~P8(x7432,f29(f115(x7432,a49)))+~P8(x7431,f29(f115(x7431,a49)))+P8(f117(x7431,x7432),f29(f115(f117(x7431,x7432),a49))) % 1.60/1.58 [755]E(x7551,f2(a114))+~P1(f50(f50(f28(a114),x7551),f50(a23,x7552)))+P1(f50(f50(f28(a114),f91(x7552,x7551)),x7552)) % 1.60/1.58 [771]P8(x7712,f29(f115(x7712,a49)))+E(f14(x7711,f29(f115(x7711,a49))),f50(a23,f2(a114)))+~P8(f115(x7712,x7711),f29(f115(f115(x7712,x7711),a49))) % 1.60/1.58 [888]~P9(x8881,x8881,x8882,f29(f115(x8881,a49)))+~P8(x8881,f29(f115(x8881,a49)))+E(f41(x8881,x8881,x8882,f29(f115(x8881,a49))),f29(f115(x8881,a49))) % 1.60/1.58 [892]P9(x8921,x8921,x8922,f29(f115(x8921,a49)))+~P8(x8921,f29(f115(x8921,a49)))+~E(f41(x8921,x8921,x8922,f29(f115(x8921,a49))),f29(f115(x8921,a49))) % 1.60/1.58 [999]P4(x9991)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x9991)),f73(x9991))),f50(f71(x9991),x9992)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x9991)),f73(x9991))),f50(f69(x9991),x9992))) % 1.60/1.58 [1000]P4(x10001)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x10001)),f73(x10001))),f50(f69(x10001),x10002)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f72(x10001)),f73(x10001))),f50(f71(x10001),x10002))) % 1.60/1.58 [782]~P23(x7821)+~P1(f50(f27(x7821,f2(x7821)),x7822))+P1(f50(f27(x7821,f2(x7821)),f50(f50(f13(x7821),x7822),x7822))) % 1.60/1.58 [805]~P23(x8051)+~P1(f50(f50(f28(x8051),f2(x8051)),x8052))+P1(f50(f50(f28(x8051),f2(x8051)),f50(f50(f13(x8051),x8052),x8052))) % 1.60/1.58 [821]~P23(x8211)+P1(f50(f27(x8211,f2(x8211)),x8212))+~P1(f50(f27(x8211,f2(x8211)),f50(f50(f13(x8211),x8212),x8212))) % 1.60/1.58 [834]P1(f50(f50(f28(a114),f2(a114)),x8342))+P1(f50(f50(f28(a114),f2(a114)),x8341))+~P1(f50(f50(f28(a114),f2(a114)),f50(f50(f13(a114),x8342),x8341))) % 1.60/1.58 [835]~P23(x8351)+P1(f50(f50(f28(x8351),f2(x8351)),x8352))+~P1(f50(f50(f28(x8351),f2(x8351)),f50(f50(f13(x8351),x8352),x8352))) % 1.60/1.58 [1098]P5(x10981,x10982)+~E(f66(x10982,x10981),f67(x10982,x10981))+~P1(f50(f50(f51(f115(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49))),x10981),f17(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49),a6,f50(f15(f115(f115(f118(a112,a112),a49),a49),f115(a111,f115(f118(a112,a112),a49))),a5)))) % 1.60/1.58 [1101]P5(x11011,x11012)+P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),f64(x11012,x11011)),a6))+~P1(f50(f50(f51(f115(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49))),x11011),f17(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49),a6,f50(f15(f115(f115(f118(a112,a112),a49),a49),f115(a111,f115(f118(a112,a112),a49))),a5)))) % 1.60/1.58 [1102]P5(x11021,x11022)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f67(x11022,x11021)),f66(x11022,x11021))),f50(f64(x11022,x11021),x11022)))+~P1(f50(f50(f51(f115(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49))),x11021),f17(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49),a6,f50(f15(f115(f115(f118(a112,a112),a49),a49),f115(a111,f115(f118(a112,a112),a49))),a5)))) % 1.60/1.58 [1103]P5(x11031,x11032)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),f67(x11032,x11031)),f66(x11032,x11031))),f50(x11031,f64(x11032,x11031))))+~P1(f50(f50(f51(f115(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49))),x11031),f17(f115(a111,f115(f118(a112,a112),a49)),f115(f118(a112,a112),a49),a6,f50(f15(f115(f115(f118(a112,a112),a49),a49),f115(a111,f115(f118(a112,a112),a49))),a5)))) % 1.60/1.58 [503]~P6(x5033)+E(x5031,x5032)+~E(f42(x5033,x5031),f42(x5033,x5032)) % 1.60/1.58 [530]~E(x5302,x5303)+~P26(x5301)+P1(f50(f27(x5301,x5302),x5303)) % 1.60/1.58 [532]~E(x5322,x5323)+~P27(x5321)+P1(f50(f27(x5321,x5322),x5323)) % 1.60/1.58 [576]~P6(x5761)+P1(f50(f27(x5761,x5763),x5762))+P1(f50(f27(x5761,x5762),x5763)) % 1.60/1.58 [621]~P27(x6211)+E(f30(x6211,x6212,x6213),f21(f115(x6211,a49)))+~P1(f50(f27(x6211,x6213),x6212)) % 1.60/1.58 [693]~P1(f50(f27(a114,x6931),x6933))+P1(f50(f27(a114,x6931),x6932))+~P1(f50(f27(a114,x6933),x6932)) % 1.60/1.58 [779]~P6(x7791)+~P1(f50(f27(x7791,x7793),x7792))+P1(f50(f27(f115(x7791,a49),f42(x7791,x7792)),f42(x7791,x7793))) % 1.60/1.58 [822]~P6(x8221)+P1(f50(f27(x8221,x8222),x8223))+~P1(f50(f27(f115(x8221,a49),f42(x8221,x8223)),f42(x8221,x8222))) % 1.60/1.58 [975]~P8(x9751,x9753)+P9(x9751,x9751,x9752,x9753)+~P1(f50(f27(f115(x9751,a49),x9753),f41(x9751,x9751,x9752,x9753))) % 1.60/1.58 [509]~P32(x5091)+~E(x5093,f2(x5091))+E(f50(f50(f13(x5091),x5092),x5093),x5092) % 1.60/1.58 [537]~P32(x5372)+E(x5371,f2(x5372))+~E(f50(f50(f13(x5372),x5373),x5371),x5373) % 1.60/1.58 [596]~E(x5961,x5962)+~P6(x5963)+~P1(f50(f50(f28(x5963),x5961),x5962)) % 1.60/1.58 [597]~E(x5971,x5972)+~P27(x5973)+~P1(f50(f50(f28(x5973),x5971),x5972)) % 1.60/1.58 [602]~P27(x6021)+E(f30(x6021,x6022,x6023),f21(f115(x6021,a49)))+P1(f50(f50(f28(x6021),x6022),x6023)) % 1.60/1.58 [603]~P27(x6031)+E(f21(f115(x6031,a49)),f30(x6031,x6032,x6033))+P1(f50(f50(f28(x6031),x6032),x6033)) % 1.60/1.58 [608]~P6(x6081)+P1(f50(f27(x6081,x6082),x6083))+P1(f50(f50(f28(x6081),x6083),x6082)) % 1.60/1.58 [655]~P26(x6551)+P1(f50(f27(x6551,x6552),x6553))+~P1(f50(f50(f28(x6551),x6552),x6553)) % 1.60/1.58 [657]~P27(x6571)+P1(f50(f27(x6571,x6572),x6573))+~P1(f50(f50(f28(x6571),x6572),x6573)) % 1.60/1.58 [673]~P1(f50(x6731,x6733))+P1(f50(x6731,f95(x6731,x6732)))+~P1(f50(f50(f28(a114),x6733),x6732)) % 1.60/1.58 [681]~P27(x6811)+~E(f30(x6811,x6812,x6813),f21(f115(x6811,a49)))+~P1(f50(f50(f28(x6811),x6812),x6813)) % 1.60/1.58 [682]~P27(x6821)+~E(f21(f115(x6821,a49)),f30(x6821,x6822,x6823))+~P1(f50(f50(f28(x6821),x6822),x6823)) % 1.60/1.58 [686]~P6(x6861)+~P1(f50(f27(x6861,x6862),x6863))+~P1(f50(f50(f28(x6861),x6863),x6862)) % 1.60/1.58 [687]~P26(x6871)+~P1(f50(f27(x6871,x6872),x6873))+~P1(f50(f50(f28(x6871),x6873),x6872)) % 1.60/1.58 [689]P1(f50(x6891,x6892))+~P1(f50(x6891,f107(x6891,x6893)))+~P1(f50(f50(f28(a114),x6892),x6893)) % 1.60/1.58 [691]P8(x6911,x6912)+~P8(x6911,x6913)+~P1(f50(f27(f115(x6911,a49),x6912),x6913)) % 1.60/1.58 [692]~E(x6921,f50(a23,x6923))+P1(f50(f50(f28(a114),x6921),f50(a23,x6922)))+~P1(f50(f50(f28(a114),x6923),x6922)) % 1.60/1.58 [708]~P28(x7081)+P1(f50(f50(f51(x7081),x7082),f42(x7081,x7083)))+~P1(f50(f50(f28(x7081),x7083),x7082)) % 1.60/1.58 [711]~P6(x7111)+~P1(f50(f50(f28(x7111),x7113),x7112))+~P1(f50(f50(f28(x7111),x7112),x7113)) % 1.60/1.58 [715]~P26(x7151)+~P1(f50(f50(f28(x7151),x7153),x7152))+~P1(f50(f50(f28(x7151),x7152),x7153)) % 1.60/1.58 [716]~P27(x7161)+~P1(f50(f50(f28(x7161),x7163),x7162))+~P1(f50(f50(f28(x7161),x7162),x7163)) % 1.60/1.58 [726]~P28(x7261)+~P1(f50(f50(f51(x7261),x7263),f42(x7261,x7262)))+P1(f50(f50(f28(x7261),x7262),x7263)) % 1.60/1.58 [781]~P1(f50(f50(f28(a114),x7811),x7813))+~P1(f50(f50(f28(a114),x7813),x7812))+P1(f50(f50(f28(a114),f50(a23,x7811)),x7812)) % 1.60/1.58 [791]~P8(x7911,x7913)+P1(f50(f27(a114,f14(x7911,x7912)),f14(x7911,x7913)))+~P1(f50(f27(f115(x7911,a49),x7912),x7913)) % 1.60/1.58 [804]E(x8041,x8042)+~P1(f50(f27(f115(x8043,a49),x8041),x8042))+~P1(f50(f27(f115(x8043,a49),x8042),x8041)) % 1.60/1.58 [820]P1(f50(x8201,x8202))+~P1(f50(f50(f28(a114),x8202),x8203))+P1(f50(f50(f51(a114),f107(x8201,x8203)),f30(a114,f2(a114),x8203))) % 1.60/1.58 [823]~P1(f50(x8231,x8233))+~P1(f50(f50(f28(a114),x8233),x8232))+P1(f50(f50(f51(a114),f95(x8231,x8232)),f30(a114,f2(a114),x8232))) % 1.60/1.58 [824]~P1(f50(x8241,x8243))+P1(f50(x8241,f108(x8241,x8242)))+~P1(f50(f50(f51(a114),x8243),f30(a114,f2(a114),x8242))) % 1.60/1.58 [828]P1(f50(x8281,x8282))+~P1(f50(x8281,f109(x8281,x8283)))+~P1(f50(f50(f51(a114),x8282),f30(a114,f2(a114),x8283))) % 1.60/1.58 [846]P1(f50(x8461,x8462))+P1(f50(f50(f28(a114),f109(x8461,x8463)),x8463))+~P1(f50(f50(f51(a114),x8462),f30(a114,f2(a114),x8463))) % 1.60/1.58 [852]~P1(f50(x8521,x8523))+P1(f50(f50(f28(a114),f108(x8521,x8522)),x8522))+~P1(f50(f50(f51(a114),x8523),f30(a114,f2(a114),x8522))) % 1.60/1.58 [811]E(x8111,x8112)+~P1(f50(f27(f115(x8113,a49),x8111),x8112))+P1(f50(f50(f28(f115(x8113,a49)),x8111),x8112)) % 1.60/1.58 [848]~P8(x8481,x8483)+P1(f50(f50(f28(a114),f14(x8481,x8482)),f14(x8481,x8483)))+~P1(f50(f50(f28(f115(x8481,a49)),x8482),x8483)) % 1.60/1.58 [869]~P21(x8691)+~E(f50(x8692,f2(a114)),f2(x8691))+E(f8(a114,x8691,x8692,f30(a114,f50(a23,f2(a114)),x8693)),f8(a114,x8691,x8692,f30(a114,f2(a114),x8693))) % 1.60/1.58 [1030]~P8(x10301,x10303)+P1(f50(f50(f51(f118(f115(x10301,a49),f115(x10301,a49))),f50(f50(f31(f115(x10301,a49),f115(x10301,a49)),x10302),x10303)),f45(x10301)))+~P1(f50(f50(f28(f115(x10301,a49)),x10302),x10303)) % 1.60/1.58 [969]E(x9691,x9692)+P1(f50(f50(f51(f115(f118(a112,a112),a49)),f11(x9693,x9691,x9692)),a5))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9693),a5)) % 1.60/1.58 [970]E(x9701,x9702)+P1(f50(f50(f51(f115(f118(a112,a112),a49)),f12(x9703,x9701,x9702)),a5))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9703),a5)) % 1.60/1.58 [1032]~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10323),x10322)),x10321))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10322),x10323)),x10321))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10321),a5)) % 1.60/1.58 [974]~P5(x9741,x9743)+E(f50(x9741,x9742),f50(x9742,x9743))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x9742),a6)) % 1.60/1.58 [813]~P8(x8132,x8134)+~P8(x8131,x8133)+P8(f117(x8131,x8132),f43(x8131,x8132,x8133,x8134)) % 1.60/1.58 [926]P8(x9261,x9262)+~P9(x9261,x9263,x9264,x9262)+~P8(x9263,f41(x9261,x9263,x9264,x9262)) % 1.60/1.58 [839]~P8(x8392,x8394)+~P8(x8391,x8393)+E(f14(f117(x8391,x8392),f43(x8391,x8392,x8393,x8394)),f50(f50(f13(a114),f14(x8391,x8393)),f14(x8392,x8394))) % 1.60/1.58 [912]~P8(x9121,x9124)+P9(x9121,x9122,x9123,x9124)+~E(f14(x9122,f41(x9121,x9122,x9123,x9124)),f14(x9121,x9124)) % 1.60/1.58 [950]~E(x9501,x9502)+~E(x9501,x9503)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9502),x9501)),f9(x9504,x9503))) % 1.60/1.58 [951]~E(x9511,x9512)+~E(x9511,x9513)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9511),x9512)),f10(x9514,x9513))) % 1.60/1.58 [578]~P17(x5783)+E(x5781,x5782)+~E(f50(f50(f13(x5783),x5784),x5781),f50(f50(f13(x5783),x5784),x5782)) % 1.60/1.58 [579]~P18(x5793)+E(x5791,x5792)+~E(f50(f50(f13(x5793),x5794),x5791),f50(f50(f13(x5793),x5794),x5792)) % 1.60/1.58 [581]~P17(x5813)+E(x5811,x5812)+~E(f50(f50(f13(x5813),x5811),x5814),f50(f50(f13(x5813),x5812),x5814)) % 1.60/1.58 [721]P1(f50(x7211,x7212))+~P1(f50(x7213,x7212))+~P1(f50(f27(f115(x7214,a49),x7213),x7211)) % 1.60/1.58 [739]~E(f50(f50(f13(a114),x7393),x7392),f50(f50(f13(a114),x7391),x7394))+~P1(f50(f50(f28(a114),x7393),x7394))+P1(f50(f50(f28(a114),x7391),x7392)) % 1.60/1.58 [749]~E(x7494,f21(f115(x7492,a49)))+~E(x7493,f21(f115(x7491,a49)))+E(f43(x7491,x7492,x7493,x7494),f21(f115(f117(x7491,x7492),a49))) % 1.60/1.58 [802]P1(f50(f50(f51(x8021),x8022),x8023))+~P1(f50(f50(f51(x8021),x8022),x8024))+~P1(f50(f27(f115(x8021,a49),x8024),x8023)) % 1.60/1.58 [808]~P21(x8081)+E(f8(a114,x8081,x8082,f30(a114,x8083,f50(a23,x8084))),f2(x8081))+~P1(f50(f50(f28(a114),x8084),x8083)) % 1.60/1.58 [843]~P1(f50(f27(f115(x8431,a49),x8432),x8434))+~P1(f50(f27(f115(x8431,a49),x8434),x8433))+P1(f50(f27(f115(x8431,a49),x8432),x8433)) % 1.60/1.58 [968]~P21(x9681)+E(f50(f50(f13(x9681),f8(a114,x9681,x9682,f30(a114,x9683,x9684))),f50(x9682,x9684)),f8(a114,x9681,x9682,f30(a114,x9683,f50(a23,x9684))))+P1(f50(f50(f28(a114),x9684),x9683)) % 1.60/1.58 [1082]~P28(x10822)+~P1(f50(f27(x10822,f50(x10823,f84(x10824,x10823,x10821,x10822))),f50(x10824,f84(x10824,x10823,x10821,x10822))))+P1(f50(f27(f115(x10821,x10822),x10823),x10824)) % 1.60/1.58 [836]~P28(x8362)+P1(f50(f27(f115(x8361,x8362),x8363),x8364))+~P1(f50(f50(f28(f115(x8361,x8362)),x8363),x8364)) % 1.60/1.58 [849]P1(f50(f50(f51(x8491),x8492),x8493))+~P1(f50(f50(f51(x8491),x8492),x8494))+~P1(f50(f50(f28(f115(x8491,a49)),x8494),x8493)) % 1.60/1.58 [866]~P28(x8661)+~P1(f50(f27(f115(x8662,x8661),x8663),x8664))+~P1(f50(f50(f28(f115(x8662,x8661)),x8664),x8663)) % 1.60/1.58 [872]~P19(x8721)+~P1(f50(f27(x8721,x8723),x8724))+P1(f50(f27(x8721,f50(f50(f13(x8721),x8722),x8723)),f50(f50(f13(x8721),x8722),x8724))) % 1.60/1.58 [873]~P20(x8731)+~P1(f50(f27(x8731,x8733),x8734))+P1(f50(f27(x8731,f50(f50(f13(x8731),x8732),x8733)),f50(f50(f13(x8731),x8732),x8734))) % 1.60/1.58 [874]~P19(x8741)+~P1(f50(f27(x8741,x8742),x8744))+P1(f50(f27(x8741,f50(f50(f13(x8741),x8742),x8743)),f50(f50(f13(x8741),x8744),x8743))) % 1.60/1.58 [875]~P20(x8751)+~P1(f50(f27(x8751,x8752),x8754))+P1(f50(f27(x8751,f50(f50(f13(x8751),x8752),x8753)),f50(f50(f13(x8751),x8754),x8753))) % 1.60/1.58 [880]~P1(f50(f27(a114,x8802),x8804))+~P1(f50(f27(a114,x8801),x8803))+P1(f50(f27(a114,f50(f50(f13(a114),x8801),x8802)),f50(f50(f13(a114),x8803),x8804))) % 1.60/1.58 [884]~P19(x8841)+~P1(f50(f50(f28(x8841),x8843),x8844))+P1(f50(f50(f28(x8841),f50(f50(f13(x8841),x8842),x8843)),f50(f50(f13(x8841),x8842),x8844))) % 1.60/1.58 [885]~P24(x8851)+~P1(f50(f50(f28(x8851),x8853),x8854))+P1(f50(f50(f28(x8851),f50(f50(f13(x8851),x8852),x8853)),f50(f50(f13(x8851),x8852),x8854))) % 1.60/1.58 [886]~P19(x8861)+~P1(f50(f50(f28(x8861),x8862),x8864))+P1(f50(f50(f28(x8861),f50(f50(f13(x8861),x8862),x8863)),f50(f50(f13(x8861),x8864),x8863))) % 1.60/1.58 [887]~P24(x8871)+~P1(f50(f50(f28(x8871),x8872),x8874))+P1(f50(f50(f28(x8871),f50(f50(f13(x8871),x8872),x8873)),f50(f50(f13(x8871),x8874),x8873))) % 1.60/1.58 [893]~P1(f50(f50(f28(a114),x8932),x8934))+~P1(f50(f50(f28(a114),x8931),x8933))+P1(f50(f50(f28(a114),f50(f50(f13(a114),x8931),x8932)),f50(f50(f13(a114),x8933),x8934))) % 1.60/1.58 [903]~P1(f50(f27(f115(x9031,a49),x9034),x9033))+~P1(f50(f50(f28(f115(x9031,a49)),x9032),x9034))+P1(f50(f50(f28(f115(x9031,a49)),x9032),x9033)) % 1.60/1.58 [904]~P1(f50(f27(f115(x9041,a49),x9042),x9044))+~P1(f50(f50(f28(f115(x9041,a49)),x9044),x9043))+P1(f50(f50(f28(f115(x9041,a49)),x9042),x9043)) % 1.60/1.58 [922]~P19(x9221)+P1(f50(f27(x9221,x9222),x9223))+~P1(f50(f27(x9221,f50(f50(f13(x9221),x9224),x9222)),f50(f50(f13(x9221),x9224),x9223))) % 1.60/1.58 [924]~P19(x9241)+P1(f50(f27(x9241,x9242),x9243))+~P1(f50(f27(x9241,f50(f50(f13(x9241),x9242),x9244)),f50(f50(f13(x9241),x9243),x9244))) % 1.60/1.58 [925]~P1(f50(f50(f28(f115(x9251,a49)),x9252),x9254))+P1(f50(f50(f28(f115(x9251,a49)),x9252),x9253))+~P1(f50(f50(f28(f115(x9251,a49)),x9254),x9253)) % 1.60/1.58 [928]~P19(x9281)+P1(f50(f50(f28(x9281),x9282),x9283))+~P1(f50(f50(f28(x9281),f50(f50(f13(x9281),x9284),x9282)),f50(f50(f13(x9281),x9284),x9283))) % 1.60/1.58 [930]~P19(x9301)+P1(f50(f50(f28(x9301),x9302),x9303))+~P1(f50(f50(f28(x9301),f50(f50(f13(x9301),x9302),x9304)),f50(f50(f13(x9301),x9303),x9304))) % 1.60/1.58 [943]~P21(x9431)+E(f50(f50(f13(x9431),f50(x9432,x9433)),f8(a114,x9431,x9432,f30(a114,f50(a23,x9433),x9434))),f8(a114,x9431,x9432,f30(a114,x9433,x9434)))+~P1(f50(f50(f28(a114),x9433),x9434)) % 1.60/1.58 [1002]~P9(x10024,x10023,x10021,f29(f115(x10024,a49)))+E(f50(x10021,f88(x10022,x10021,x10023,x10024)),x10022)+~P1(f50(f50(f51(x10023),x10022),f41(x10024,x10023,x10021,f29(f115(x10024,a49))))) % 1.60/1.58 [984]E(x9841,x9842)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9843),x9841)),f9(x9844,x9842)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9843),x9841)),x9844)) % 1.60/1.58 [985]E(x9851,x9852)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9851),x9853)),f10(x9854,x9852)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9851),x9853)),x9854)) % 1.60/1.58 [789]E(x7891,x7892)+~E(f50(x7893,x7891),f50(x7893,x7892))+~P9(x7894,x7895,x7893,f29(f115(x7894,a49))) % 1.60/1.58 [920]P9(x9202,x9203,f97(x9204,x9203,x9202,x9201),x9201)+~E(f41(x9203,x9202,x9205,x9204),x9201)+E(x9201,f21(f115(x9202,a49))) % 1.60/1.58 [931]E(x9311,x9312)+~E(f41(x9313,x9314,x9315,x9311),f41(x9313,x9314,x9315,x9312))+~P9(x9313,x9314,x9315,f29(f115(x9313,a49))) % 1.60/1.58 [940]~P1(f50(f50(x9403,x9402),x9405))+~P1(f50(f50(x9403,x9404),x9402))+P1(f50(f50(f51(x9401),x9402),f39(x9401,x9403,x9404,x9405))) % 1.60/1.58 [941]~P1(f50(f50(x9413,x9412),x9415))+~P1(f50(f50(x9413,x9414),x9412))+P1(f50(f50(f51(x9411),x9412),f36(x9411,x9413,x9414,x9415))) % 1.60/1.58 [966]P8(x9661,x9662)+~P8(x9663,x9664)+~P1(f50(f27(f115(x9661,a49),x9662),f41(x9663,x9661,x9665,x9664))) % 1.60/1.58 [795]~P28(x7951)+P1(f50(f27(x7951,f50(x7952,x7953)),f50(x7954,x7953)))+~P1(f50(f27(f115(x7955,x7951),x7952),x7954)) % 1.60/1.58 [809]~E(f50(x8094,x8095),f21(f115(x8092,a49)))+E(f17(x8091,x8092,x8093,x8094),f21(f115(f115(x8091,x8092),a49)))+~P1(f50(f50(f51(x8091),x8095),x8093)) % 1.60/1.58 [891]P9(x8911,x8912,x8913,x8914)+~P9(x8911,x8912,x8913,x8915)+~P1(f50(f27(f115(x8911,a49),x8914),x8915)) % 1.60/1.58 [914]~P9(x9141,x9142,x9144,x9143)+E(f50(f18(x9141,x9142,x9143,x9144),f50(x9144,x9145)),x9145)+~P1(f50(f50(f51(x9141),x9145),x9143)) % 1.60/1.58 [988]~P9(x9881,x9884,x9885,f29(f115(x9881,a49)))+~P1(f50(f50(f51(x9884),f50(x9885,x9882)),f41(x9881,x9884,x9885,x9883)))+P1(f50(f50(f51(x9881),x9882),x9883)) % 1.60/1.58 [1004]~P9(x10042,x10043,x10041,x10044)+E(f50(x10041,f50(f18(x10042,x10043,x10044,x10041),x10045)),x10045)+~P1(f50(f50(f51(x10043),x10045),f41(x10042,x10043,x10041,x10044))) % 1.60/1.58 [1063]~P13(x10635,x10631,x10634,x10633)+P1(f50(f50(x10631,x10632),f101(x10633,x10634,x10631,x10635,x10632)))+~P1(f50(f50(f51(x10635),x10632),x10634)) % 1.60/1.58 [1064]~P9(x10641,x10644,x10645,f29(f115(x10641,a49)))+~P1(f50(f27(f115(x10644,a49),f41(x10641,x10644,x10645,x10642)),f41(x10641,x10644,x10645,x10643)))+P1(f50(f27(f115(x10641,a49),x10642),x10643)) % 1.60/1.58 [1083]~P13(x10831,x10834,x10833,x10832)+~P1(f50(f50(f51(x10831),x10835),x10833))+P1(f50(f50(f51(x10831),f101(x10832,x10833,x10834,x10831,x10835)),x10832)) % 1.60/1.58 [1094]~P1(f50(f50(f51(f118(f115(x10941,a49),f115(x10941,a49))),f50(f50(f31(f115(x10941,a49),f115(x10941,a49)),x10944),x10943)),f46(x10941,x10942)))+~P1(f50(f50(f51(x10941),x10945),x10944))+P1(f50(f50(f51(x10941),f104(x10942,x10943,x10944,x10941,x10945)),x10943)) % 1.60/1.58 [1039]~P9(x10392,x10391,x10393,x10395)+P1(f50(f50(f28(f115(x10391,a49)),f41(x10392,x10391,x10393,x10394)),f41(x10392,x10391,x10393,x10395)))+~P1(f50(f50(f28(f115(x10392,a49)),x10394),x10395)) % 1.60/1.58 [1068]~E(f41(x10683,x10682,x10685,x10684),x10681)+E(x10681,f21(f115(x10682,a49)))+P1(f50(f27(f115(x10683,a49),f41(x10682,x10683,f97(x10684,x10683,x10682,x10681),x10681)),x10684)) % 1.60/1.58 [1106]~P1(f50(f50(f51(f118(f115(x11061,a49),f115(x11061,a49))),f50(f50(f31(f115(x11061,a49),f115(x11061,a49)),x11065),x11064)),f46(x11061,x11063)))+~P1(f50(f50(f51(x11061),x11062),x11065))+P1(f50(f50(f51(f118(x11061,x11061)),f50(f50(f31(x11061,x11061),x11062),f104(x11063,x11064,x11065,x11061,x11062))),x11063)) % 1.60/1.58 [1005]P1(f50(f50(f51(f118(x10051,x10051)),f50(f50(f31(x10051,x10051),x10052),x10053)),f48(x10051,x10054,x10055)))+~P1(f50(f27(a114,f50(x10054,x10052)),f50(x10054,x10053)))+~P1(f50(f50(f51(f118(x10051,x10051)),f50(f50(f31(x10051,x10051),x10052),x10053)),x10055)) % 1.60/1.58 [1054]~P1(f50(f50(x10543,x10542),x10546))+~P1(f50(f50(x10544,x10545),x10542))+P1(f50(f50(f51(x10541),x10542),f40(x10541,x10543,x10544,x10545,x10546))) % 1.60/1.58 [1055]~P1(f50(f50(x10554,x10552),x10556))+~P1(f50(f50(x10553,x10555),x10552))+P1(f50(f50(f51(x10551),x10552),f37(x10551,x10553,x10554,x10555,x10556))) % 1.60/1.58 [935]~E(x9352,f50(x9354,x9356))+P1(f50(f50(f51(x9351),x9352),f41(x9353,x9351,x9354,x9355)))+~P1(f50(f50(f51(x9353),x9356),x9355)) % 1.60/1.58 [964]~E(x9642,f41(x9643,x9641,x9644,x9646))+P1(f50(f27(f115(x9641,a49),x9642),f41(x9643,x9641,x9644,x9645)))+~P1(f50(f27(f115(x9643,a49),x9646),x9645)) % 1.60/1.58 [990]~P1(f50(f50(f51(f115(x9905,x9901)),x9902),f17(x9905,x9901,x9906,x9904)))+P1(f50(f50(f51(x9901),f50(x9902,x9903)),f50(x9904,x9903)))+~P1(f50(f50(f51(x9905),x9903),x9906)) % 1.60/1.58 [865]P1(f50(f50(x8651,x8652),x8653))+~P1(f50(f50(x8654,x8652),x8653))+~P1(f50(f27(f115(x8655,f115(x8656,a49)),x8654),x8651)) % 1.60/1.58 [1017]P1(f50(f50(f51(x10171),f50(x10172,x10173)),x10174))+~P1(f50(f50(f51(x10175),x10173),x10176))+~P1(f50(f50(f51(f115(x10175,x10171)),x10172),f17(x10175,x10171,x10176,f50(f15(f115(x10171,a49),x10175),x10174)))) % 1.60/1.58 [1086]~P1(f50(x10866,x10863))+~P1(f50(f50(f51(f118(x10862,x10862)),f50(f50(f31(x10862,x10862),x10864),x10865)),f50(x10867,x10863)))+P1(f50(f50(f51(f118(f118(x10861,x10862),f118(x10861,x10862))),f50(f50(f31(f118(x10861,x10862),f118(x10861,x10862)),f50(f50(f31(x10861,x10862),x10863),x10864)),f50(f50(f31(x10861,x10862),x10863),x10865))),f34(x10861,x10862,x10866,x10867))) % 1.60/1.58 [1085]~E(x10853,x10855)+P1(f50(f50(f51(f118(f118(x10851,x10852),f118(x10851,x10852))),f50(f50(f31(f118(x10851,x10852),f118(x10851,x10852)),f50(f50(f31(x10851,x10852),x10853),x10854)),f50(f50(f31(x10851,x10852),x10855),x10856))),f47(x10851,x10852,x10857,x10858)))+~P1(f50(f50(f51(f118(x10852,x10852)),f50(f50(f31(x10852,x10852),x10854),x10856)),x10858)) % 1.60/1.58 [1093]E(x10931,x10932)+~P1(f50(f50(f51(f118(f118(x10933,x10935),f118(x10933,x10935))),f50(f50(f31(f118(x10933,x10935),f118(x10933,x10935)),f50(f50(f31(x10933,x10935),x10931),x10936)),f50(f50(f31(x10933,x10935),x10932),x10937))),f47(x10933,x10935,x10934,x10938)))+P1(f50(f50(f51(f118(x10933,x10933)),f50(f50(f31(x10933,x10933),x10931),x10932)),x10934)) % 1.60/1.58 [1097]~P1(f50(f50(f51(f118(f118(x10971,x10975),f118(x10971,x10975))),f50(f50(f31(f118(x10971,x10975),f118(x10971,x10975)),f50(f50(f31(x10971,x10975),x10972),x10976)),f50(f50(f31(x10971,x10975),x10973),x10977))),f47(x10971,x10975,x10974,x10978)))+P1(f50(f50(f51(f118(x10971,x10971)),f50(f50(f31(x10971,x10971),x10972),x10973)),x10974))+P1(f50(f50(f51(f118(x10975,x10975)),f50(f50(f31(x10975,x10975),x10976),x10977)),x10978)) % 1.60/1.58 [670]E(x6701,x6702)+~P27(x6703)+~P1(f50(f27(x6703,x6702),x6701))+~P1(f50(f27(x6703,x6701),x6702)) % 1.60/1.58 [870]~P15(x8701)+~P1(f50(f27(x8701,x8703),f2(x8701)))+~P1(f50(f27(x8701,x8702),f2(x8701)))+P1(f50(f27(x8701,f50(f50(f13(x8701),x8702),x8703)),f2(x8701))) % 1.60/1.58 [881]~P15(x8811)+~P1(f50(f27(x8811,x8813),f2(x8811)))+~P1(f50(f50(f28(x8811),x8812),f2(x8811)))+P1(f50(f50(f28(x8811),f50(f50(f13(x8811),x8812),x8813)),f2(x8811))) % 1.60/1.58 [882]~P15(x8821)+~P1(f50(f27(x8821,x8822),f2(x8821)))+~P1(f50(f50(f28(x8821),x8823),f2(x8821)))+P1(f50(f50(f28(x8821),f50(f50(f13(x8821),x8822),x8823)),f2(x8821))) % 1.60/1.58 [889]~P15(x8891)+~P1(f50(f50(f28(x8891),x8893),f2(x8891)))+~P1(f50(f50(f28(x8891),x8892),f2(x8891)))+P1(f50(f50(f28(x8891),f50(f50(f13(x8891),x8892),x8893)),f2(x8891))) % 1.60/1.58 [610]~E(x6102,x6103)+~P6(x6101)+P1(f50(f27(x6101,x6102),x6103))+P1(f50(f50(f28(x6101),x6102),x6103)) % 1.60/1.58 [628]~P31(x6283)+E(x6281,x6282)+P1(f50(f50(f28(x6283),x6282),x6281))+P1(f50(f50(f28(x6283),x6281),x6282)) % 1.60/1.58 [629]~P6(x6293)+E(x6291,x6292)+P1(f50(f50(f28(x6293),x6292),x6291))+P1(f50(f50(f28(x6293),x6291),x6292)) % 1.60/1.58 [645]~P27(x6453)+E(x6451,x6452)+~P1(f50(f27(x6453,x6452),x6451))+P1(f50(f50(f28(x6453),x6452),x6451)) % 1.60/1.58 [647]~P6(x6473)+E(x6471,x6472)+~P1(f50(f27(x6473,x6471),x6472))+P1(f50(f50(f28(x6473),x6471),x6472)) % 1.60/1.58 [653]~P27(x6533)+E(x6531,x6532)+~P1(f50(f27(x6533,x6531),x6532))+P1(f50(f50(f28(x6533),x6531),x6532)) % 1.60/1.58 [706]~P26(x7061)+~P1(f50(f27(x7061,x7063),x7062))+P1(f50(f27(x7061,x7062),x7063))+P1(f50(f50(f28(x7061),x7063),x7062)) % 1.60/1.58 [833]E(x8331,x8332)+~P8(x8333,x8331)+~P1(f50(f27(a114,f14(x8333,x8331)),f14(x8333,x8332)))+~P1(f50(f27(f115(x8333,a49),x8332),x8331)) % 1.60/1.58 [1037]~P8(x10371,x10373)+~P9(x10371,x10371,x10372,x10373)+E(f41(x10371,x10371,x10372,x10373),x10373)+~P1(f50(f27(f115(x10371,a49),f41(x10371,x10371,x10372,x10373)),x10373)) % 1.60/1.58 [853]~P15(x8531)+~P1(f50(f50(f28(x8531),f2(x8531)),x8533))+~P1(f50(f50(f28(x8531),f2(x8531)),x8532))+P1(f50(f50(f28(x8531),f2(x8531)),f50(f50(f13(x8531),x8532),x8533))) % 1.60/1.58 [901]~P8(x9011,x9013)+~P1(f50(f50(f28(a114),f14(x9011,x9012)),f14(x9011,x9013)))+~P1(f50(f27(f115(x9011,a49),x9012),x9013))+P1(f50(f50(f28(f115(x9011,a49)),x9012),x9013)) % 1.60/1.58 [994]E(x9941,x9942)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9941),x9942)),x9943))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9942),x9941)),x9943))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9943),a5)) % 1.60/1.58 [718]~P27(x7181)+~P1(f50(f27(x7181,x7184),x7183))+P1(f50(f27(x7181,x7182),x7183))+~P1(f50(f27(x7181,x7182),x7184)) % 1.60/1.58 [719]~P26(x7191)+~P1(f50(f27(x7191,x7192),x7194))+P1(f50(f27(x7191,x7192),x7193))+~P1(f50(f27(x7191,x7194),x7193)) % 1.60/1.58 [896]~E(x8963,x8961)+E(x8961,x8962)+E(x8963,x8962)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x8962),x8963)),f9(x8964,x8961))) % 1.60/1.58 [897]~E(x8973,x8971)+E(x8971,x8972)+E(x8973,x8972)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x8973),x8972)),f10(x8974,x8971))) % 1.60/1.58 [919]~P8(x9192,x9193)+~P8(x9191,x9194)+P9(x9191,x9192,f87(x9193,x9192,x9194,x9191),x9194)+~P1(f50(f27(a114,f14(x9191,x9194)),f14(x9192,x9193))) % 1.60/1.58 [744]~P27(x7441)+~P1(f50(f27(x7441,x7442),x7444))+~P1(f50(f50(f28(x7441),x7444),x7443))+P1(f50(f50(f28(x7441),x7442),x7443)) % 1.60/1.58 [745]~P27(x7451)+~P1(f50(f27(x7451,x7454),x7453))+~P1(f50(f50(f28(x7451),x7452),x7454))+P1(f50(f50(f28(x7451),x7452),x7453)) % 1.60/1.58 [746]~P26(x7461)+~P1(f50(f27(x7461,x7464),x7463))+~P1(f50(f50(f28(x7461),x7462),x7464))+P1(f50(f50(f28(x7461),x7462),x7463)) % 1.60/1.58 [747]~P26(x7471)+~P1(f50(f27(x7471,x7472),x7474))+~P1(f50(f50(f28(x7471),x7474),x7473))+P1(f50(f50(f28(x7471),x7472),x7473)) % 1.60/1.58 [763]~P27(x7631)+~P1(f50(f50(f28(x7631),x7634),x7633))+P1(f50(f50(f28(x7631),x7632),x7633))+~P1(f50(f50(f28(x7631),x7632),x7634)) % 1.60/1.58 [764]~P26(x7641)+~P1(f50(f50(f28(x7641),x7642),x7644))+P1(f50(f50(f28(x7641),x7642),x7643))+~P1(f50(f50(f28(x7641),x7644),x7643)) % 1.60/1.58 [818]~P15(x8181)+~P1(f50(f27(x8181,x8182),x8183))+~P1(f50(f27(x8181,f2(x8181)),x8184))+P1(f50(f27(x8181,x8182),f50(f50(f13(x8181),x8183),x8184))) % 1.60/1.58 [819]~P15(x8191)+~P1(f50(f27(x8191,x8192),x8194))+~P1(f50(f27(x8191,f2(x8191)),x8193))+P1(f50(f27(x8191,x8192),f50(f50(f13(x8191),x8193),x8194))) % 1.60/1.58 [830]~P15(x8301)+~P1(f50(f27(x8301,x8302),x8304))+~P1(f50(f50(f28(x8301),f2(x8301)),x8303))+P1(f50(f50(f28(x8301),x8302),f50(f50(f13(x8301),x8303),x8304))) % 1.60/1.58 [831]~P15(x8311)+~P1(f50(f27(x8311,f2(x8311)),x8313))+~P1(f50(f50(f28(x8311),x8312),x8314))+P1(f50(f50(f28(x8311),x8312),f50(f50(f13(x8311),x8313),x8314))) % 1.60/1.58 [837]~P29(x8371)+~P1(f50(f50(f28(x8371),f2(x8371)),x8373))+~P1(f50(f50(f28(x8371),x8372),x8374))+P1(f50(f50(f28(x8371),x8372),f50(f50(f13(x8371),x8373),x8374))) % 1.60/1.58 [867]~P28(x8672)+~P1(f50(f27(f115(x8671,x8672),x8674),x8673))+P1(f50(f27(f115(x8671,x8672),x8673),x8674))+P1(f50(f50(f28(f115(x8671,x8672)),x8674),x8673)) % 1.60/1.58 [1067]~P8(x10672,x10674)+~P8(x10671,x10673)+~P1(f50(f27(a114,f14(x10672,x10674)),f14(x10671,x10673)))+P1(f50(f27(f115(x10671,a49),f41(x10672,x10671,f87(x10673,x10671,x10674,x10672),x10674)),x10673)) % 1.60/1.58 [980]E(x9801,x9802)+E(x9803,x9802)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9803),x9801)),f9(x9804,x9802)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9803),x9801)),x9804)) % 1.60/1.58 [981]E(x9811,x9812)+E(x9813,x9812)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9813),x9811)),f10(x9814,x9812)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9813),x9811)),x9814)) % 1.60/1.58 [982]E(x9821,x9822)+E(x9823,x9821)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9823),x9821)),f10(x9824,x9822)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9823),x9821)),x9824)) % 1.60/1.58 [983]E(x9831,x9832)+E(x9831,x9833)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9831),x9833)),f9(x9834,x9832)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9831),x9833)),x9834)) % 1.60/1.58 [1073]~P3(x10733)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10731),x10732)),f50(x10733,x10734)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10731),x10732)),f50(x10734,f74(x10733,x10734,x10731,x10732))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10734),a6)) % 1.60/1.58 [945]~P6(x9451)+P1(f50(f27(x9451,x9452),x9453))+P1(f50(f27(x9451,x9454),x9453))+~P1(f50(f27(f115(x9451,a49),f30(x9451,x9453,x9452)),f30(x9451,x9454,x9455))) % 1.60/1.58 [946]~P6(x9461)+P1(f50(f27(x9461,x9462),x9463))+P1(f50(f27(x9461,x9462),x9464))+~P1(f50(f27(f115(x9461,a49),f30(x9461,x9463,x9462)),f30(x9461,x9465,x9464))) % 1.60/1.58 [722]~P10(x7225,x7221,x7223)+~P8(x7225,x7224)+E(f50(f50(x7221,x7222),f50(x7223,x7224)),f50(x7223,x7224))+~P1(f50(f50(f51(x7225),x7222),x7224)) % 1.60/1.58 [995]~P21(x9951)+E(f50(f50(f13(x9951),f8(a114,x9951,x9952,f30(a114,x9953,x9954))),f8(a114,x9951,x9952,f30(a114,x9954,x9955))),f8(a114,x9951,x9952,f30(a114,x9953,x9955)))+~P1(f50(f27(a114,x9954),x9955))+~P1(f50(f27(a114,x9953),x9954)) % 1.60/1.58 [1036]~P8(x10363,x10364)+~P9(x10361,x10363,x10365,x10362)+P1(f50(f27(a114,f14(x10361,x10362)),f14(x10363,x10364)))+~P1(f50(f27(f115(x10363,a49),f41(x10361,x10363,x10365,x10362)),x10364)) % 1.60/1.58 [1043]~P9(x10432,x10433,x10435,x10431)+E(f41(x10433,x10432,f99(x10434,x10433,x10432,x10431),x10434),x10431)+E(x10431,f21(f115(x10432,a49)))+~P1(f50(f27(f115(x10433,a49),f41(x10432,x10433,x10435,x10431)),x10434)) % 1.60/1.58 [1104]~P21(x11042)+~P8(x11041,x11045)+E(f8(x11041,x11042,f50(f50(f4(x11041,x11042,x11042),f16(x11041,x11042,f115(x11042,x11042),f50(f7(a49,f115(x11042,f115(x11042,x11042)),x11041,f24(x11042)),f50(a52,x11043)),x11044)),f2(x11042)),x11045),f2(x11042))+P1(f50(f50(f51(x11041),x11043),x11045)) % 1.60/1.58 [1105]~P21(x11052)+~P8(x11051,x11055)+E(f8(x11051,x11052,f50(f50(f4(x11051,x11052,x11052),f16(x11051,x11052,f115(x11052,x11052),f50(f7(a49,f115(x11052,f115(x11052,x11052)),x11051,f24(x11052)),f50(a52,x11053)),x11054)),f2(x11052)),x11055),f50(x11054,x11053))+~P1(f50(f50(f51(x11051),x11053),x11055)) % 1.60/1.58 [1111]~P21(x11112)+~P8(x11111,x11115)+E(f8(x11111,x11112,f50(f50(f4(x11111,x11112,x11112),f16(x11111,x11112,f115(x11112,x11112),f50(f7(a49,f115(x11112,f115(x11112,x11112)),x11111,f24(x11112)),f50(f50(f4(x11111,x11111,a49),a52),x11113)),x11114)),f2(x11112)),x11115),f2(x11112))+P1(f50(f50(f51(x11111),x11113),x11115)) % 1.60/1.58 [1112]~P21(x11122)+~P8(x11121,x11125)+E(f8(x11121,x11122,f50(f50(f4(x11121,x11122,x11122),f16(x11121,x11122,f115(x11122,x11122),f50(f7(a49,f115(x11122,f115(x11122,x11122)),x11121,f24(x11122)),f50(f50(f4(x11121,x11121,a49),a52),x11123)),x11124)),f2(x11122)),x11125),f50(x11124,x11123))+~P1(f50(f50(f51(x11121),x11123),x11125)) % 1.60/1.58 [900]~P20(x9001)+~P1(f50(f27(x9001,x9003),x9005))+~P1(f50(f27(x9001,x9002),x9004))+P1(f50(f27(x9001,f50(f50(f13(x9001),x9002),x9003)),f50(f50(f13(x9001),x9004),x9005))) % 1.60/1.58 [905]~P24(x9051)+~P1(f50(f27(x9051,x9053),x9055))+~P1(f50(f50(f28(x9051),x9052),x9054))+P1(f50(f50(f28(x9051),f50(f50(f13(x9051),x9052),x9053)),f50(f50(f13(x9051),x9054),x9055))) % 1.60/1.58 [906]~P24(x9061)+~P1(f50(f27(x9061,x9062),x9064))+~P1(f50(f50(f28(x9061),x9063),x9065))+P1(f50(f50(f28(x9061),f50(f50(f13(x9061),x9062),x9063)),f50(f50(f13(x9061),x9064),x9065))) % 1.60/1.58 [910]~P24(x9101)+~P1(f50(f50(f28(x9101),x9103),x9105))+~P1(f50(f50(f28(x9101),x9102),x9104))+P1(f50(f50(f28(x9101),f50(f50(f13(x9101),x9102),x9103)),f50(f50(f13(x9101),x9104),x9105))) % 1.60/1.58 [996]~E(x9962,f50(x9963,x9961))+E(x9961,f88(x9962,x9963,x9964,x9965))+~P9(x9965,x9964,x9963,f29(f115(x9965,a49)))+~P1(f50(f50(f51(x9964),x9962),f41(x9965,x9964,x9963,f29(f115(x9965,a49))))) % 1.60/1.58 [992]E(x9921,x9922)+~E(x9923,x9924)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9923),x9924)),f11(x9925,x9921,x9922)))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9925),a5)) % 1.60/1.58 [993]E(x9931,x9932)+~E(x9933,x9934)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9933),x9934)),f12(x9935,x9931,x9932)))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9935),a5)) % 1.60/1.58 [1031]~P8(x10313,x10314)+~P9(x10311,x10313,x10315,x10312)+P1(f50(f27(a114,f14(x10311,x10312)),f14(x10313,x10314)))+~P1(f50(f50(f51(f115(x10311,x10313)),x10315),f17(x10311,x10313,x10312,f50(f15(f115(x10313,a49),x10311),x10314)))) % 1.60/1.58 [913]~P9(x9131,x9132,x9134,x9133)+~E(f50(x9134,x9136),x9135)+E(f50(f18(x9131,x9132,x9133,x9134),x9135),x9136)+~P1(f50(f50(f51(x9131),x9136),x9133)) % 1.60/1.58 [1069]~P9(x10691,x10692,x10694,x10693)+~P1(f50(f50(f51(x10692),x10695),f41(x10691,x10692,x10694,x10693)))+~P1(f50(f27(f115(x10691,a49),x10693),x10696))+P1(f50(f50(f51(x10691),f50(f18(x10691,x10692,x10693,x10694),x10695)),x10696)) % 1.60/1.58 [1080]~P11(x10807,x10806,x10801,x10808,x10802,x10804)+~P8(x10806,x10805)+E(f50(f50(x10801,f50(x10802,x10803)),f50(x10804,x10805)),f50(x10804,x10805))+~P1(f50(f50(f51(x10806),x10803),x10805)) % 1.60/1.58 [1081]~P11(x10816,x10815,x10811,x10817,x10818,x10812)+~P8(x10815,x10814)+E(f50(f50(x10811,f50(x10812,x10813)),f50(x10812,x10814)),f50(x10812,x10814))+~P1(f50(f27(f115(x10815,a49),x10813),x10814)) % 1.60/1.58 [761]~P15(x7612)+E(x7611,f2(x7612))+~E(f50(f50(f13(x7612),x7613),x7611),f2(x7612))+~P1(f50(f27(x7612,f2(x7612)),x7613))+~P1(f50(f27(x7612,f2(x7612)),x7611)) % 1.60/1.58 [762]~P15(x7622)+E(x7621,f2(x7622))+~E(f50(f50(f13(x7622),x7621),x7623),f2(x7622))+~P1(f50(f27(x7622,f2(x7622)),x7623))+~P1(f50(f27(x7622,f2(x7622)),x7621)) % 1.60/1.58 [986]~P8(x9862,x9864)+~P8(x9862,x9861)+P13(x9862,x9863,x9864,x9861)+E(x9861,f21(f115(x9862,a49)))+P1(f50(f50(f51(x9862),f100(x9861,x9864,x9863,x9862)),x9864)) % 1.60/1.58 [1061]~P8(x10612,x10614)+~P8(x10612,x10611)+E(x10611,f21(f115(x10612,a49)))+P1(f50(f50(f51(f118(f115(x10612,a49),f115(x10612,a49))),f50(f50(f31(f115(x10612,a49),f115(x10612,a49)),x10614),x10611)),f46(x10612,x10613)))+P1(f50(f50(f51(x10612),f102(x10613,x10611,x10614,x10612)),x10614)) % 1.60/1.58 [1062]~P8(x10622,x10624)+~P8(x10622,x10621)+E(x10621,f21(f115(x10622,a49)))+P1(f50(f50(f51(f118(f115(x10622,a49),f115(x10622,a49))),f50(f50(f31(f115(x10622,a49),f115(x10622,a49)),x10624),x10621)),f46(x10622,x10623)))+P1(f50(f50(f51(x10622),f103(x10623,x10621,x10624,x10622)),x10624)) % 1.60/1.58 [786]~P6(x7863)+E(x7861,x7862)+~E(f30(x7863,x7864,x7861),f30(x7863,x7865,x7862))+~P1(f50(f50(f28(x7863),x7865),x7862))+~P1(f50(f50(f28(x7863),x7864),x7861)) % 1.60/1.58 [787]~P6(x7873)+E(x7871,x7872)+~E(f30(x7873,x7871,x7874),f30(x7873,x7872,x7875))+~P1(f50(f50(f28(x7873),x7872),x7875))+~P1(f50(f50(f28(x7873),x7871),x7874)) % 1.60/1.58 [798]~P8(x7982,x7985)+~P10(x7982,x7983,x7984)+E(f50(f50(x7983,f50(x7984,x7981)),f50(x7984,x7985)),f50(x7984,x7985))+E(x7981,f21(f115(x7982,a49)))+~P1(f50(f27(f115(x7982,a49),x7981),x7985)) % 1.60/1.58 [1118]~P8(x11182,x11181)+~P10(x11182,x11185,x11183)+E(f50(x11183,f41(x11182,x11182,x11184,x11181)),f50(x11184,f50(x11183,x11181)))+E(x11181,f21(f115(x11182,a49)))+~E(f50(f50(x11185,f50(x11184,f105(x11181,x11184,x11183,x11185,x11182))),f50(x11184,f106(x11181,x11184,x11183,x11185,x11182))),f50(x11184,f50(f50(x11185,f105(x11181,x11184,x11183,x11185,x11182)),f106(x11181,x11184,x11183,x11185,x11182)))) % 1.60/1.58 [1020]E(x10201,x10202)+~E(x10205,x10201)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10203),x10205)),f11(x10204,x10201,x10202)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10203),x10202)),x10204))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10204),a5)) % 1.60/1.58 [1021]E(x10211,x10212)+~E(x10215,x10211)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10215),x10213)),f12(x10214,x10212,x10211)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10212),x10213)),x10214))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10214),a5)) % 1.60/1.58 [861]E(x8611,x8612)+~P9(x8614,x8615,x8613,x8616)+~E(f50(x8613,x8611),f50(x8613,x8612))+~P1(f50(f50(f51(x8614),x8612),x8616))+~P1(f50(f50(f51(x8614),x8611),x8616)) % 1.60/1.58 [750]~P15(x7501)+~E(x7503,f2(x7501))+~E(x7502,f2(x7501))+E(f50(f50(f13(x7501),x7502),x7503),f2(x7501))+~P1(f50(f27(x7501,f2(x7501)),x7503))+~P1(f50(f27(x7501,f2(x7501)),x7502)) % 1.60/1.58 [1029]~P8(x10292,x10294)+~P8(x10292,x10291)+P13(x10292,x10293,x10294,x10291)+E(x10291,f21(f115(x10292,a49)))+~P1(f50(f50(x10293,f100(x10291,x10294,x10293,x10292)),x10295))+~P1(f50(f50(f51(x10292),x10295),x10291)) % 1.60/1.58 [1007]~E(x10073,x10071)+E(x10071,x10072)+E(x10073,x10074)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10074),x10073)),f11(x10075,x10071,x10072)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10074),x10072)),x10075))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10075),a5)) % 1.60/1.58 [1008]~E(x10083,x10081)+E(x10081,x10082)+E(x10083,x10084)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10083),x10084)),f12(x10085,x10082,x10081)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10082),x10084)),x10085))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10085),a5)) % 1.60/1.58 [1022]E(x10221,x10222)+E(x10221,x10223)+E(x10224,x10221)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10223),x10224)),f12(x10225,x10222,x10221)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10223),x10224)),x10225))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10225),a5)) % 1.60/1.58 [1023]E(x10231,x10232)+E(x10231,x10233)+E(x10234,x10231)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10234),x10233)),f11(x10235,x10231,x10232)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10234),x10233)),x10235))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10235),a5)) % 1.60/1.58 [1099]~P8(x10992,x10993)+~P8(x10992,x10991)+E(x10991,f21(f115(x10992,a49)))+P1(f50(f50(f51(f118(f115(x10992,a49),f115(x10992,a49))),f50(f50(f31(f115(x10992,a49),f115(x10992,a49)),x10993),x10991)),f46(x10992,x10994)))+~P1(f50(f50(f51(x10992),x10995),x10991))+~P1(f50(f50(f51(f118(x10992,x10992)),f50(f50(f31(x10992,x10992),f102(x10994,x10991,x10993,x10992)),x10995)),x10994)) % 1.60/1.58 [1100]~P8(x11002,x11003)+~P8(x11002,x11001)+E(x11001,f21(f115(x11002,a49)))+P1(f50(f50(f51(f118(f115(x11002,a49),f115(x11002,a49))),f50(f50(f31(f115(x11002,a49),f115(x11002,a49)),x11003),x11001)),f46(x11002,x11004)))+~P1(f50(f50(f51(x11002),x11005),x11001))+~P1(f50(f50(f51(f118(x11002,x11002)),f50(f50(f31(x11002,x11002),f103(x11004,x11001,x11003,x11002)),x11005)),x11004)) % 1.60/1.58 [1090]E(x10901,x10902)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10901),x10902)),f50(a113,x10904)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10902),x10901)),f50(a113,x10903)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10902),x10901)),f50(x10903,f59(x10903,x10904,x10902,x10901))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10901),x10902)),f50(x10904,f59(x10903,x10904,x10902,x10901))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10903),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10904),a6)) % 1.60/1.58 [1091]E(x10911,x10912)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10911),x10912)),f50(a113,x10914)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10912),x10911)),f50(a113,x10913)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10912),x10911)),f50(x10913,f59(x10914,x10913,x10911,x10912))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10911),x10912)),f50(x10914,f59(x10914,x10913,x10911,x10912))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10913),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10914),a6)) % 1.60/1.58 [1095]E(x10951,x10952)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10951),x10952)),f50(a113,x10954)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10952),x10951)),f50(a113,x10953)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10952),x10951)),f50(x10953,f59(x10953,x10954,x10952,x10951))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10951),x10952)),f50(x10954,f59(x10953,x10954,x10952,x10951))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10953),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10954),a6)) % 1.60/1.58 [1096]E(x10961,x10962)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10961),x10962)),f50(a113,x10964)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10962),x10961)),f50(a113,x10963)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10962),x10961)),f50(x10963,f59(x10964,x10963,x10961,x10962))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10961),x10962)),f50(x10964,f59(x10964,x10963,x10961,x10962))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10963),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x10964),a6)) % 1.60/1.58 [972]~E(x9723,x9722)+~E(x9724,x9721)+E(x9721,x9722)+E(x9721,x9723)+E(x9724,x9723)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9723),x9724)),f12(x9725,x9722,x9721)))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9725),a5)) % 1.60/1.58 [973]~E(x9733,x9732)+~E(x9734,x9731)+E(x9731,x9732)+E(x9731,x9733)+E(x9734,x9733)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x9734),x9733)),f11(x9735,x9731,x9732)))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x9735),a5)) % 1.60/1.58 [1009]E(x10094,x10093)+E(x10091,x10092)+E(x10093,x10091)+E(x10094,x10091)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10094),x10093)),f11(x10095,x10091,x10092)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10094),x10093)),x10095))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10095),a5)) % 1.60/1.58 [1010]E(x10104,x10103)+E(x10101,x10102)+E(x10103,x10101)+E(x10104,x10101)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10104),x10103)),f12(x10105,x10102,x10101)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10104),x10103)),x10105))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10105),a5)) % 1.60/1.58 [1011]~E(x10113,x10111)+E(x10111,x10112)+E(x10113,x10112)+E(x10114,x10113)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10114),x10113)),f11(x10115,x10112,x10111)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10114),x10113)),x10115))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10115),a5)) % 1.60/1.58 [1012]~E(x10123,x10121)+E(x10121,x10122)+E(x10123,x10122)+E(x10123,x10124)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10123),x10124)),f12(x10125,x10121,x10122)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10123),x10124)),x10125))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10125),a5)) % 1.60/1.58 [1013]~E(x10134,x10131)+E(x10131,x10132)+E(x10131,x10133)+E(x10134,x10132)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10134),x10132)),f11(x10135,x10131,x10133)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10133),x10132)),x10135))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10135),a5)) % 1.60/1.58 [1014]~E(x10144,x10141)+E(x10141,x10142)+E(x10141,x10143)+E(x10144,x10143)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10143),x10144)),f12(x10145,x10142,x10141)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10143),x10142)),x10145))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10145),a5)) % 1.60/1.58 [1015]~E(x10154,x10152)+~E(x10153,x10151)+E(x10151,x10152)+E(x10153,x10154)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10154),x10153)),f12(x10155,x10152,x10151)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10152),x10153)),x10155))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10155),a5)) % 1.60/1.58 [1016]~E(x10164,x10162)+~E(x10163,x10161)+E(x10161,x10162)+E(x10163,x10164)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10163),x10164)),f11(x10165,x10161,x10162)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10163),x10162)),x10165))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10165),a5)) % 1.60/1.58 [1025]E(x10253,x10251)+E(x10251,x10252)+E(x10253,x10252)+~E(x10255,x10253)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10255),x10251)),f11(x10254,x10253,x10252)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10252),x10251)),x10254))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10254),a5)) % 1.60/1.58 [1026]E(x10263,x10261)+E(x10261,x10262)+E(x10263,x10262)+~E(x10265,x10263)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10261),x10265)),f12(x10264,x10262,x10263)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10261),x10262)),x10264))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10264),a5)) % 1.60/1.58 [1045]E(x10451,x10452)+E(x10453,x10452)+E(x10454,x10453)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10454),x10453)),f11(x10455,x10452,x10451)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10454),x10453)),x10455))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10451),x10453)),x10455))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10455),a5)) % 1.60/1.58 [1046]E(x10461,x10462)+E(x10463,x10461)+E(x10464,x10463)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10464),x10463)),f12(x10465,x10462,x10461)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10464),x10463)),x10465))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10462),x10463)),x10465))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10465),a5)) % 1.60/1.58 [1047]E(x10471,x10472)+E(x10473,x10472)+E(x10473,x10474)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10473),x10474)),f12(x10475,x10471,x10472)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10473),x10474)),x10475))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10473),x10471)),x10475))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10475),a5)) % 1.60/1.58 [1048]E(x10481,x10482)+E(x10483,x10481)+E(x10483,x10484)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10483),x10484)),f11(x10485,x10481,x10482)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10483),x10484)),x10485))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10483),x10482)),x10485))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10485),a5)) % 1.60/1.58 [1049]~E(x10494,x10491)+E(x10491,x10492)+E(x10493,x10494)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10493),x10494)),f11(x10495,x10492,x10491)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10493),x10494)),x10495))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10493),x10491)),x10495))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10495),a5)) % 1.60/1.58 [1050]~E(x10503,x10501)+E(x10501,x10502)+E(x10503,x10504)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10503),x10504)),f12(x10505,x10501,x10502)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10503),x10504)),x10505))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10501),x10504)),x10505))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10505),a5)) % 1.60/1.58 [1051]~E(x10513,x10511)+E(x10511,x10512)+E(x10513,x10514)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10514),x10513)),f12(x10515,x10512,x10511)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10512),x10513)),x10515))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10514),x10512)),x10515))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10515),a5)) % 1.60/1.58 [1052]~E(x10523,x10521)+E(x10521,x10522)+E(x10523,x10524)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10523),x10524)),f11(x10525,x10521,x10522)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10522),x10524)),x10525))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10523),x10522)),x10525))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10525),a5)) % 1.60/1.58 [1065]E(x10651,x10652)+E(x10653,x10654)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10653),x10654)),f11(x10655,x10652,x10651)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10653),x10654)),x10655))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10651),x10654)),x10655))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10653),x10651)),x10655))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10655),a5)) % 1.60/1.58 [1066]E(x10661,x10662)+E(x10663,x10664)+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10663),x10664)),f12(x10665,x10661,x10662)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10663),x10664)),x10665))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10661),x10664)),x10665))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x10663),x10661)),x10665))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x10665),a5)) % 1.60/1.58 [1109]~P4(x11093)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11091),x11092)),f50(x11093,x11095)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11091),x11092)),f50(x11093,x11094)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11091),x11092)),f50(x11095,f70(x11093,x11094,x11095,x11091,x11092))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11091),x11092)),f50(x11094,f70(x11093,x11094,x11095,x11091,x11092))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11094),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11095),a6)) % 1.60/1.58 [1110]~P4(x11103)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11101),x11102)),f50(x11103,x11105)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11101),x11102)),f50(x11103,x11104)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11101),x11102)),f50(x11105,f70(x11103,x11105,x11104,x11101,x11102))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11101),x11102)),f50(x11104,f70(x11103,x11105,x11104,x11101,x11102))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11104),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11105),a6)) % 1.60/1.58 [1116]~P4(x11163)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11161),x11162)),f50(x11163,x11165)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11161),x11162)),f50(x11163,x11164)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11161),x11162)),f50(x11165,f70(x11163,x11164,x11165,x11161,x11162))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11161),x11162)),f50(x11164,f70(x11163,x11164,x11165,x11161,x11162))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11164),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11165),a6)) % 1.60/1.58 [1117]~P4(x11173)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11171),x11172)),f50(x11173,x11175)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11171),x11172)),f50(x11173,x11174)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11171),x11172)),f50(x11175,f70(x11173,x11175,x11174,x11171,x11172))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11171),x11172)),f50(x11174,f70(x11173,x11175,x11174,x11171,x11172))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11174),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11175),a6)) % 1.60/1.58 [1074]~P8(x10743,x10744)+~P8(x10741,x10742)+~P9(x10743,x10741,x10745,x10744)+~P9(x10741,x10743,x10746,x10742)+E(f14(x10741,x10742),f14(x10743,x10744))+~P1(f50(f27(f115(x10743,a49),f41(x10741,x10743,x10746,x10742)),x10744))+~P1(f50(f27(f115(x10741,a49),f41(x10743,x10741,x10745,x10744)),x10742)) % 1.60/1.58 [1072]~P8(x10723,x10724)+~P8(x10721,x10722)+~P9(x10723,x10721,x10725,x10724)+~P9(x10721,x10723,x10726,x10722)+E(f14(x10721,x10722),f14(x10723,x10724))+~P1(f50(f50(f51(f115(x10723,x10721)),x10725),f17(x10723,x10721,x10724,f50(f15(f115(x10721,a49),x10723),x10722))))+~P1(f50(f50(f51(f115(x10721,x10723)),x10726),f17(x10721,x10723,x10722,f50(f15(f115(x10723,a49),x10721),x10724)))) % 1.60/1.58 [1122]E(x11221,x11222)+E(x11223,x11224)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11223),x11224)),f50(a113,x11226)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11221),x11222)),f50(a113,x11225)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11221),x11222)),f50(x11225,f63(x11225,x11226,x11222,x11221,x11224,x11223))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11223),x11224)),f50(x11226,f63(x11225,x11226,x11222,x11221,x11224,x11223))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11225),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11226),a6)) % 1.60/1.58 [1123]E(x11231,x11232)+E(x11233,x11234)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11233),x11234)),f50(a113,x11236)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11231),x11232)),f50(a113,x11235)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11231),x11232)),f50(x11235,f63(x11236,x11235,x11234,x11233,x11232,x11231))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11233),x11234)),f50(x11236,f63(x11236,x11235,x11234,x11233,x11232,x11231))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11235),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11236),a6)) % 1.60/1.58 [1129]E(x11291,x11292)+E(x11293,x11294)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11293),x11294)),f50(a113,x11296)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11291),x11292)),f50(a113,x11295)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11291),x11292)),f50(x11295,f63(x11295,x11296,x11292,x11291,x11294,x11293))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11293),x11294)),f50(x11296,f63(x11295,x11296,x11292,x11291,x11294,x11293))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11295),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11296),a6)) % 1.60/1.58 [1130]E(x11301,x11302)+E(x11303,x11304)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11303),x11304)),f50(a113,x11306)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11301),x11302)),f50(a113,x11305)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11301),x11302)),f50(x11305,f63(x11306,x11305,x11304,x11303,x11302,x11301))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11303),x11304)),f50(x11306,f63(x11306,x11305,x11304,x11303,x11302,x11301))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11305),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11306),a6)) % 1.60/1.58 [1107]E(x11073,x11071)+E(x11071,x11072)+E(x11073,x11072)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11073),x11071)),f50(a113,x11075)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11072),x11073)),f50(a113,x11074)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11072),x11073)),f50(x11074,f60(x11075,x11074,x11071,x11073,x11072))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11073),x11071)),f50(x11075,f60(x11075,x11074,x11071,x11073,x11072))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11074),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11075),a6)) % 1.60/1.58 [1108]E(x11083,x11081)+E(x11081,x11082)+E(x11083,x11082)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11083),x11081)),f50(a113,x11085)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11081),x11082)),f50(a113,x11084)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11081),x11082)),f50(x11084,f60(x11084,x11085,x11082,x11081,x11083))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11083),x11081)),f50(x11085,f60(x11084,x11085,x11082,x11081,x11083))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11084),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11085),a6)) % 1.60/1.58 [1114]E(x11143,x11141)+E(x11141,x11142)+E(x11143,x11142)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11143),x11141)),f50(a113,x11145)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11142),x11143)),f50(a113,x11144)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11142),x11143)),f50(x11144,f60(x11145,x11144,x11141,x11143,x11142))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11143),x11141)),f50(x11145,f60(x11145,x11144,x11141,x11143,x11142))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11144),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11145),a6)) % 1.60/1.58 [1115]E(x11153,x11151)+E(x11151,x11152)+E(x11153,x11152)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11153),x11151)),f50(a113,x11155)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11151),x11152)),f50(a113,x11154)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11151),x11152)),f50(x11154,f60(x11154,x11155,x11152,x11151,x11153))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11153),x11151)),f50(x11155,f60(x11154,x11155,x11152,x11151,x11153))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11154),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11155),a6)) % 1.60/1.58 [1124]E(x11244,x11243)+E(x11241,x11242)+E(x11243,x11242)+E(x11244,x11241)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11244),x11243)),f50(a113,x11246)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11242),x11241)),f50(a113,x11245)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11242),x11241)),f50(x11245,f61(x11245,x11246,x11241,x11242,x11243,x11244))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11244),x11243)),f50(x11246,f61(x11245,x11246,x11241,x11242,x11243,x11244))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11245),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11246),a6)) % 1.60/1.58 [1125]E(x11254,x11253)+E(x11251,x11252)+E(x11253,x11251)+E(x11254,x11252)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11254),x11253)),f50(a113,x11256)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11251),x11252)),f50(a113,x11255)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11251),x11252)),f50(x11255,f62(x11255,x11256,x11252,x11251,x11253,x11254))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11254),x11253)),f50(x11256,f62(x11255,x11256,x11252,x11251,x11253,x11254))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11255),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11256),a6)) % 1.60/1.58 [1126]E(x11264,x11263)+E(x11261,x11262)+E(x11263,x11261)+E(x11264,x11262)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11264),x11263)),f50(a113,x11266)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11261),x11262)),f50(a113,x11265)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11261),x11262)),f50(x11265,f62(x11266,x11265,x11263,x11264,x11262,x11261))))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11264),x11263)),f50(x11266,f62(x11266,x11265,x11263,x11264,x11262,x11261))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11265),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11266),a6)) % 1.60/1.58 [1131]E(x11314,x11313)+E(x11311,x11312)+E(x11313,x11312)+E(x11314,x11311)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11314),x11313)),f50(a113,x11316)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11312),x11311)),f50(a113,x11315)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11312),x11311)),f50(x11315,f61(x11315,x11316,x11311,x11312,x11313,x11314))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11314),x11313)),f50(x11316,f61(x11315,x11316,x11311,x11312,x11313,x11314))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11315),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11316),a6)) % 1.60/1.58 [1132]E(x11324,x11323)+E(x11321,x11322)+E(x11323,x11321)+E(x11324,x11322)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11324),x11323)),f50(a113,x11326)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11321),x11322)),f50(a113,x11325)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11321),x11322)),f50(x11325,f62(x11325,x11326,x11322,x11321,x11323,x11324))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11324),x11323)),f50(x11326,f62(x11325,x11326,x11322,x11321,x11323,x11324))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11325),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11326),a6)) % 1.60/1.58 [1133]E(x11334,x11333)+E(x11331,x11332)+E(x11333,x11331)+E(x11334,x11332)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11334),x11333)),f50(a113,x11336)))+P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11331),x11332)),f50(a113,x11335)))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11331),x11332)),f50(x11335,f62(x11336,x11335,x11333,x11334,x11332,x11331))))+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11334),x11333)),f50(x11336,f62(x11336,x11335,x11333,x11334,x11332,x11331))))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11335),a6))+~P1(f50(f50(f51(f115(a111,f115(f118(a112,a112),a49))),x11336),a6)) % 1.60/1.58 %EqnAxiom % 1.60/1.58 [1]E(x11,x11) % 1.60/1.58 [2]E(x22,x21)+~E(x21,x22) % 1.60/1.58 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.60/1.58 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 1.60/1.58 [5]~E(x51,x52)+E(f20(x51),f20(x52)) % 1.60/1.58 [6]~E(x61,x62)+E(f50(x61,x63),f50(x62,x63)) % 1.60/1.58 [7]~E(x71,x72)+E(f50(x73,x71),f50(x73,x72)) % 1.60/1.58 [8]~E(x81,x82)+E(f31(x81,x83),f31(x82,x83)) % 1.60/1.58 [9]~E(x91,x92)+E(f31(x93,x91),f31(x93,x92)) % 1.60/1.58 [10]~E(x101,x102)+E(f21(x101),f21(x102)) % 1.60/1.58 [11]~E(x111,x112)+E(f51(x111),f51(x112)) % 1.60/1.58 [12]~E(x121,x122)+E(f118(x121,x123),f118(x122,x123)) % 1.60/1.58 [13]~E(x131,x132)+E(f118(x133,x131),f118(x133,x132)) % 1.60/1.58 [14]~E(x141,x142)+E(f22(x141),f22(x142)) % 1.60/1.58 [15]~E(x151,x152)+E(f62(x151,x153,x154,x155,x156,x157),f62(x152,x153,x154,x155,x156,x157)) % 1.60/1.58 [16]~E(x161,x162)+E(f62(x163,x161,x164,x165,x166,x167),f62(x163,x162,x164,x165,x166,x167)) % 1.60/1.58 [17]~E(x171,x172)+E(f62(x173,x174,x171,x175,x176,x177),f62(x173,x174,x172,x175,x176,x177)) % 1.60/1.58 [18]~E(x181,x182)+E(f62(x183,x184,x185,x181,x186,x187),f62(x183,x184,x185,x182,x186,x187)) % 1.60/1.58 [19]~E(x191,x192)+E(f62(x193,x194,x195,x196,x191,x197),f62(x193,x194,x195,x196,x192,x197)) % 1.60/1.58 [20]~E(x201,x202)+E(f62(x203,x204,x205,x206,x207,x201),f62(x203,x204,x205,x206,x207,x202)) % 1.60/1.58 [21]~E(x211,x212)+E(f26(x211,x213),f26(x212,x213)) % 1.60/1.58 [22]~E(x221,x222)+E(f26(x223,x221),f26(x223,x222)) % 1.60/1.58 [23]~E(x231,x232)+E(f115(x231,x233),f115(x232,x233)) % 1.60/1.58 [24]~E(x241,x242)+E(f115(x243,x241),f115(x243,x242)) % 1.60/1.58 [25]~E(x251,x252)+E(f27(x251,x253),f27(x252,x253)) % 1.60/1.58 [26]~E(x261,x262)+E(f27(x263,x261),f27(x263,x262)) % 1.60/1.58 [27]~E(x271,x272)+E(f41(x271,x273,x274,x275),f41(x272,x273,x274,x275)) % 1.60/1.58 [28]~E(x281,x282)+E(f41(x283,x281,x284,x285),f41(x283,x282,x284,x285)) % 1.60/1.58 [29]~E(x291,x292)+E(f41(x293,x294,x291,x295),f41(x293,x294,x292,x295)) % 1.60/1.58 [30]~E(x301,x302)+E(f41(x303,x304,x305,x301),f41(x303,x304,x305,x302)) % 1.60/1.58 [31]~E(x311,x312)+E(f3(x311),f3(x312)) % 1.60/1.58 [32]~E(x321,x322)+E(f100(x321,x323,x324,x325),f100(x322,x323,x324,x325)) % 1.60/1.58 [33]~E(x331,x332)+E(f100(x333,x331,x334,x335),f100(x333,x332,x334,x335)) % 1.60/1.58 [34]~E(x341,x342)+E(f100(x343,x344,x341,x345),f100(x343,x344,x342,x345)) % 1.60/1.58 [35]~E(x351,x352)+E(f100(x353,x354,x355,x351),f100(x353,x354,x355,x352)) % 1.60/1.58 [36]~E(x361,x362)+E(f13(x361),f13(x362)) % 1.60/1.58 [37]~E(x371,x372)+E(f28(x371),f28(x372)) % 1.60/1.58 [38]~E(x381,x382)+E(f7(x381,x383,x384,x385),f7(x382,x383,x384,x385)) % 1.60/1.58 [39]~E(x391,x392)+E(f7(x393,x391,x394,x395),f7(x393,x392,x394,x395)) % 1.60/1.58 [40]~E(x401,x402)+E(f7(x403,x404,x401,x405),f7(x403,x404,x402,x405)) % 1.60/1.58 [41]~E(x411,x412)+E(f7(x413,x414,x415,x411),f7(x413,x414,x415,x412)) % 1.60/1.58 [42]~E(x421,x422)+E(f59(x421,x423,x424,x425),f59(x422,x423,x424,x425)) % 1.60/1.58 [43]~E(x431,x432)+E(f59(x433,x431,x434,x435),f59(x433,x432,x434,x435)) % 1.60/1.58 [44]~E(x441,x442)+E(f59(x443,x444,x441,x445),f59(x443,x444,x442,x445)) % 1.60/1.58 [45]~E(x451,x452)+E(f59(x453,x454,x455,x451),f59(x453,x454,x455,x452)) % 1.60/1.58 [46]~E(x461,x462)+E(f12(x461,x463,x464),f12(x462,x463,x464)) % 1.60/1.58 [47]~E(x471,x472)+E(f12(x473,x471,x474),f12(x473,x472,x474)) % 1.60/1.58 [48]~E(x481,x482)+E(f12(x483,x484,x481),f12(x483,x484,x482)) % 1.60/1.58 [49]~E(x491,x492)+E(f29(x491),f29(x492)) % 1.60/1.58 [50]~E(x501,x502)+E(f60(x501,x503,x504,x505,x506),f60(x502,x503,x504,x505,x506)) % 1.60/1.58 [51]~E(x511,x512)+E(f60(x513,x511,x514,x515,x516),f60(x513,x512,x514,x515,x516)) % 1.60/1.58 [52]~E(x521,x522)+E(f60(x523,x524,x521,x525,x526),f60(x523,x524,x522,x525,x526)) % 1.60/1.58 [53]~E(x531,x532)+E(f60(x533,x534,x535,x531,x536),f60(x533,x534,x535,x532,x536)) % 1.60/1.58 [54]~E(x541,x542)+E(f60(x543,x544,x545,x546,x541),f60(x543,x544,x545,x546,x542)) % 1.60/1.58 [55]~E(x551,x552)+E(f15(x551,x553),f15(x552,x553)) % 1.60/1.58 [56]~E(x561,x562)+E(f15(x563,x561),f15(x563,x562)) % 1.60/1.58 [57]~E(x571,x572)+E(f8(x571,x573,x574,x575),f8(x572,x573,x574,x575)) % 1.60/1.58 [58]~E(x581,x582)+E(f8(x583,x581,x584,x585),f8(x583,x582,x584,x585)) % 1.60/1.58 [59]~E(x591,x592)+E(f8(x593,x594,x591,x595),f8(x593,x594,x592,x595)) % 1.60/1.58 [60]~E(x601,x602)+E(f8(x603,x604,x605,x601),f8(x603,x604,x605,x602)) % 1.60/1.58 [61]~E(x611,x612)+E(f4(x611,x613,x614),f4(x612,x613,x614)) % 1.60/1.58 [62]~E(x621,x622)+E(f4(x623,x621,x624),f4(x623,x622,x624)) % 1.60/1.58 [63]~E(x631,x632)+E(f4(x633,x634,x631),f4(x633,x634,x632)) % 1.60/1.58 [64]~E(x641,x642)+E(f18(x641,x643,x644,x645),f18(x642,x643,x644,x645)) % 1.60/1.58 [65]~E(x651,x652)+E(f18(x653,x651,x654,x655),f18(x653,x652,x654,x655)) % 1.60/1.58 [66]~E(x661,x662)+E(f18(x663,x664,x661,x665),f18(x663,x664,x662,x665)) % 1.60/1.58 [67]~E(x671,x672)+E(f18(x673,x674,x675,x671),f18(x673,x674,x675,x672)) % 1.60/1.58 [68]~E(x681,x682)+E(f55(x681,x683,x684,x685),f55(x682,x683,x684,x685)) % 1.60/1.58 [69]~E(x691,x692)+E(f55(x693,x691,x694,x695),f55(x693,x692,x694,x695)) % 1.60/1.58 [70]~E(x701,x702)+E(f55(x703,x704,x701,x705),f55(x703,x704,x702,x705)) % 1.60/1.58 [71]~E(x711,x712)+E(f55(x713,x714,x715,x711),f55(x713,x714,x715,x712)) % 1.60/1.58 [72]~E(x721,x722)+E(f116(x721),f116(x722)) % 1.60/1.58 [73]~E(x731,x732)+E(f17(x731,x733,x734,x735),f17(x732,x733,x734,x735)) % 1.60/1.58 [74]~E(x741,x742)+E(f17(x743,x741,x744,x745),f17(x743,x742,x744,x745)) % 1.60/1.58 [75]~E(x751,x752)+E(f17(x753,x754,x751,x755),f17(x753,x754,x752,x755)) % 1.60/1.58 [76]~E(x761,x762)+E(f17(x763,x764,x765,x761),f17(x763,x764,x765,x762)) % 1.60/1.58 [77]~E(x771,x772)+E(f24(x771),f24(x772)) % 1.60/1.58 [78]~E(x781,x782)+E(f108(x781,x783),f108(x782,x783)) % 1.60/1.58 [79]~E(x791,x792)+E(f108(x793,x791),f108(x793,x792)) % 1.60/1.58 [80]~E(x801,x802)+E(f74(x801,x803,x804,x805),f74(x802,x803,x804,x805)) % 1.60/1.58 [81]~E(x811,x812)+E(f74(x813,x811,x814,x815),f74(x813,x812,x814,x815)) % 1.60/1.58 [82]~E(x821,x822)+E(f74(x823,x824,x821,x825),f74(x823,x824,x822,x825)) % 1.60/1.58 [83]~E(x831,x832)+E(f74(x833,x834,x835,x831),f74(x833,x834,x835,x832)) % 1.60/1.58 [84]~E(x841,x842)+E(f71(x841),f71(x842)) % 1.60/1.58 [85]~E(x851,x852)+E(f65(x851,x853),f65(x852,x853)) % 1.60/1.58 [86]~E(x861,x862)+E(f65(x863,x861),f65(x863,x862)) % 1.60/1.58 [87]~E(x871,x872)+E(f16(x871,x873,x874,x875,x876),f16(x872,x873,x874,x875,x876)) % 1.60/1.58 [88]~E(x881,x882)+E(f16(x883,x881,x884,x885,x886),f16(x883,x882,x884,x885,x886)) % 1.60/1.58 [89]~E(x891,x892)+E(f16(x893,x894,x891,x895,x896),f16(x893,x894,x892,x895,x896)) % 1.60/1.58 [90]~E(x901,x902)+E(f16(x903,x904,x905,x901,x906),f16(x903,x904,x905,x902,x906)) % 1.60/1.58 [91]~E(x911,x912)+E(f16(x913,x914,x915,x916,x911),f16(x913,x914,x915,x916,x912)) % 1.60/1.58 [92]~E(x921,x922)+E(f14(x921,x923),f14(x922,x923)) % 1.60/1.58 [93]~E(x931,x932)+E(f14(x933,x931),f14(x933,x932)) % 1.60/1.58 [94]~E(x941,x942)+E(f56(x941,x943,x944,x945),f56(x942,x943,x944,x945)) % 1.60/1.58 [95]~E(x951,x952)+E(f56(x953,x951,x954,x955),f56(x953,x952,x954,x955)) % 1.60/1.58 [96]~E(x961,x962)+E(f56(x963,x964,x961,x965),f56(x963,x964,x962,x965)) % 1.60/1.58 [97]~E(x971,x972)+E(f56(x973,x974,x975,x971),f56(x973,x974,x975,x972)) % 1.60/1.58 [98]~E(x981,x982)+E(f10(x981,x983),f10(x982,x983)) % 1.60/1.58 [99]~E(x991,x992)+E(f10(x993,x991),f10(x993,x992)) % 1.60/1.58 [100]~E(x1001,x1002)+E(f82(x1001,x1003,x1004,x1005,x1006),f82(x1002,x1003,x1004,x1005,x1006)) % 1.60/1.58 [101]~E(x1011,x1012)+E(f82(x1013,x1011,x1014,x1015,x1016),f82(x1013,x1012,x1014,x1015,x1016)) % 1.60/1.58 [102]~E(x1021,x1022)+E(f82(x1023,x1024,x1021,x1025,x1026),f82(x1023,x1024,x1022,x1025,x1026)) % 1.60/1.58 [103]~E(x1031,x1032)+E(f82(x1033,x1034,x1035,x1031,x1036),f82(x1033,x1034,x1035,x1032,x1036)) % 1.60/1.58 [104]~E(x1041,x1042)+E(f82(x1043,x1044,x1045,x1046,x1041),f82(x1043,x1044,x1045,x1046,x1042)) % 1.60/1.58 [105]~E(x1051,x1052)+E(f73(x1051),f73(x1052)) % 1.60/1.58 [106]~E(x1061,x1062)+E(f30(x1061,x1063,x1064),f30(x1062,x1063,x1064)) % 1.60/1.58 [107]~E(x1071,x1072)+E(f30(x1073,x1071,x1074),f30(x1073,x1072,x1074)) % 1.60/1.58 [108]~E(x1081,x1082)+E(f30(x1083,x1084,x1081),f30(x1083,x1084,x1082)) % 1.60/1.58 [109]~E(x1091,x1092)+E(f75(x1091),f75(x1092)) % 1.60/1.58 [110]~E(x1101,x1102)+E(f47(x1101,x1103,x1104,x1105),f47(x1102,x1103,x1104,x1105)) % 1.60/1.58 [111]~E(x1111,x1112)+E(f47(x1113,x1111,x1114,x1115),f47(x1113,x1112,x1114,x1115)) % 1.60/1.58 [112]~E(x1121,x1122)+E(f47(x1123,x1124,x1121,x1125),f47(x1123,x1124,x1122,x1125)) % 1.60/1.58 [113]~E(x1131,x1132)+E(f47(x1133,x1134,x1135,x1131),f47(x1133,x1134,x1135,x1132)) % 1.60/1.58 [114]~E(x1141,x1142)+E(f43(x1141,x1143,x1144,x1145),f43(x1142,x1143,x1144,x1145)) % 1.60/1.58 [115]~E(x1151,x1152)+E(f43(x1153,x1151,x1154,x1155),f43(x1153,x1152,x1154,x1155)) % 1.60/1.58 [116]~E(x1161,x1162)+E(f43(x1163,x1164,x1161,x1165),f43(x1163,x1164,x1162,x1165)) % 1.60/1.58 [117]~E(x1171,x1172)+E(f43(x1173,x1174,x1175,x1171),f43(x1173,x1174,x1175,x1172)) % 1.60/1.58 [118]~E(x1181,x1182)+E(f42(x1181,x1183),f42(x1182,x1183)) % 1.60/1.58 [119]~E(x1191,x1192)+E(f42(x1193,x1191),f42(x1193,x1192)) % 1.60/1.58 [120]~E(x1201,x1202)+E(f63(x1201,x1203,x1204,x1205,x1206,x1207),f63(x1202,x1203,x1204,x1205,x1206,x1207)) % 1.60/1.58 [121]~E(x1211,x1212)+E(f63(x1213,x1211,x1214,x1215,x1216,x1217),f63(x1213,x1212,x1214,x1215,x1216,x1217)) % 1.60/1.58 [122]~E(x1221,x1222)+E(f63(x1223,x1224,x1221,x1225,x1226,x1227),f63(x1223,x1224,x1222,x1225,x1226,x1227)) % 1.60/1.58 [123]~E(x1231,x1232)+E(f63(x1233,x1234,x1235,x1231,x1236,x1237),f63(x1233,x1234,x1235,x1232,x1236,x1237)) % 1.60/1.58 [124]~E(x1241,x1242)+E(f63(x1243,x1244,x1245,x1246,x1241,x1247),f63(x1243,x1244,x1245,x1246,x1242,x1247)) % 1.60/1.58 [125]~E(x1251,x1252)+E(f63(x1253,x1254,x1255,x1256,x1257,x1251),f63(x1253,x1254,x1255,x1256,x1257,x1252)) % 1.60/1.58 [126]~E(x1261,x1262)+E(f109(x1261,x1263),f109(x1262,x1263)) % 1.60/1.58 [127]~E(x1271,x1272)+E(f109(x1273,x1271),f109(x1273,x1272)) % 1.60/1.58 [128]~E(x1281,x1282)+E(f11(x1281,x1283,x1284),f11(x1282,x1283,x1284)) % 1.60/1.58 [129]~E(x1291,x1292)+E(f11(x1293,x1291,x1294),f11(x1293,x1292,x1294)) % 1.60/1.58 [130]~E(x1301,x1302)+E(f11(x1303,x1304,x1301),f11(x1303,x1304,x1302)) % 1.60/1.58 [131]~E(x1311,x1312)+E(f46(x1311,x1313),f46(x1312,x1313)) % 1.60/1.58 [132]~E(x1321,x1322)+E(f46(x1323,x1321),f46(x1323,x1322)) % 1.60/1.58 [133]~E(x1331,x1332)+E(f117(x1331,x1333),f117(x1332,x1333)) % 1.60/1.58 [134]~E(x1341,x1342)+E(f117(x1343,x1341),f117(x1343,x1342)) % 1.60/1.58 [135]~E(x1351,x1352)+E(f88(x1351,x1353,x1354,x1355),f88(x1352,x1353,x1354,x1355)) % 1.60/1.58 [136]~E(x1361,x1362)+E(f88(x1363,x1361,x1364,x1365),f88(x1363,x1362,x1364,x1365)) % 1.60/1.58 [137]~E(x1371,x1372)+E(f88(x1373,x1374,x1371,x1375),f88(x1373,x1374,x1372,x1375)) % 1.60/1.58 [138]~E(x1381,x1382)+E(f88(x1383,x1384,x1385,x1381),f88(x1383,x1384,x1385,x1382)) % 1.60/1.58 [139]~E(x1391,x1392)+E(f76(x1391,x1393),f76(x1392,x1393)) % 1.60/1.58 [140]~E(x1401,x1402)+E(f76(x1403,x1401),f76(x1403,x1402)) % 1.60/1.58 [141]~E(x1411,x1412)+E(f39(x1411,x1413,x1414,x1415),f39(x1412,x1413,x1414,x1415)) % 1.60/1.58 [142]~E(x1421,x1422)+E(f39(x1423,x1421,x1424,x1425),f39(x1423,x1422,x1424,x1425)) % 1.60/1.58 [143]~E(x1431,x1432)+E(f39(x1433,x1434,x1431,x1435),f39(x1433,x1434,x1432,x1435)) % 1.60/1.58 [144]~E(x1441,x1442)+E(f39(x1443,x1444,x1445,x1441),f39(x1443,x1444,x1445,x1442)) % 1.60/1.58 [145]~E(x1451,x1452)+E(f72(x1451),f72(x1452)) % 1.60/1.58 [146]~E(x1461,x1462)+E(f32(x1461,x1463,x1464),f32(x1462,x1463,x1464)) % 1.60/1.58 [147]~E(x1471,x1472)+E(f32(x1473,x1471,x1474),f32(x1473,x1472,x1474)) % 1.60/1.58 [148]~E(x1481,x1482)+E(f32(x1483,x1484,x1481),f32(x1483,x1484,x1482)) % 1.60/1.58 [149]~E(x1491,x1492)+E(f9(x1491,x1493),f9(x1492,x1493)) % 1.60/1.58 [150]~E(x1501,x1502)+E(f9(x1503,x1501),f9(x1503,x1502)) % 1.60/1.58 [151]~E(x1511,x1512)+E(f102(x1511,x1513,x1514,x1515),f102(x1512,x1513,x1514,x1515)) % 1.60/1.58 [152]~E(x1521,x1522)+E(f102(x1523,x1521,x1524,x1525),f102(x1523,x1522,x1524,x1525)) % 1.60/1.58 [153]~E(x1531,x1532)+E(f102(x1533,x1534,x1531,x1535),f102(x1533,x1534,x1532,x1535)) % 1.60/1.58 [154]~E(x1541,x1542)+E(f102(x1543,x1544,x1545,x1541),f102(x1543,x1544,x1545,x1542)) % 1.60/1.58 [155]~E(x1551,x1552)+E(f70(x1551,x1553,x1554,x1555,x1556),f70(x1552,x1553,x1554,x1555,x1556)) % 1.60/1.58 [156]~E(x1561,x1562)+E(f70(x1563,x1561,x1564,x1565,x1566),f70(x1563,x1562,x1564,x1565,x1566)) % 1.60/1.58 [157]~E(x1571,x1572)+E(f70(x1573,x1574,x1571,x1575,x1576),f70(x1573,x1574,x1572,x1575,x1576)) % 1.60/1.58 [158]~E(x1581,x1582)+E(f70(x1583,x1584,x1585,x1581,x1586),f70(x1583,x1584,x1585,x1582,x1586)) % 1.60/1.58 [159]~E(x1591,x1592)+E(f70(x1593,x1594,x1595,x1596,x1591),f70(x1593,x1594,x1595,x1596,x1592)) % 1.60/1.58 [160]~E(x1601,x1602)+E(f89(x1601,x1603,x1604,x1605,x1606),f89(x1602,x1603,x1604,x1605,x1606)) % 1.60/1.58 [161]~E(x1611,x1612)+E(f89(x1613,x1611,x1614,x1615,x1616),f89(x1613,x1612,x1614,x1615,x1616)) % 1.60/1.58 [162]~E(x1621,x1622)+E(f89(x1623,x1624,x1621,x1625,x1626),f89(x1623,x1624,x1622,x1625,x1626)) % 1.60/1.58 [163]~E(x1631,x1632)+E(f89(x1633,x1634,x1635,x1631,x1636),f89(x1633,x1634,x1635,x1632,x1636)) % 1.60/1.58 [164]~E(x1641,x1642)+E(f89(x1643,x1644,x1645,x1646,x1641),f89(x1643,x1644,x1645,x1646,x1642)) % 1.60/1.58 [165]~E(x1651,x1652)+E(f87(x1651,x1653,x1654,x1655),f87(x1652,x1653,x1654,x1655)) % 1.60/1.58 [166]~E(x1661,x1662)+E(f87(x1663,x1661,x1664,x1665),f87(x1663,x1662,x1664,x1665)) % 1.60/1.58 [167]~E(x1671,x1672)+E(f87(x1673,x1674,x1671,x1675),f87(x1673,x1674,x1672,x1675)) % 1.60/1.58 [168]~E(x1681,x1682)+E(f87(x1683,x1684,x1685,x1681),f87(x1683,x1684,x1685,x1682)) % 1.60/1.58 [169]~E(x1691,x1692)+E(f61(x1691,x1693,x1694,x1695,x1696,x1697),f61(x1692,x1693,x1694,x1695,x1696,x1697)) % 1.60/1.58 [170]~E(x1701,x1702)+E(f61(x1703,x1701,x1704,x1705,x1706,x1707),f61(x1703,x1702,x1704,x1705,x1706,x1707)) % 1.60/1.58 [171]~E(x1711,x1712)+E(f61(x1713,x1714,x1711,x1715,x1716,x1717),f61(x1713,x1714,x1712,x1715,x1716,x1717)) % 1.60/1.58 [172]~E(x1721,x1722)+E(f61(x1723,x1724,x1725,x1721,x1726,x1727),f61(x1723,x1724,x1725,x1722,x1726,x1727)) % 1.60/1.58 [173]~E(x1731,x1732)+E(f61(x1733,x1734,x1735,x1736,x1731,x1737),f61(x1733,x1734,x1735,x1736,x1732,x1737)) % 1.60/1.58 [174]~E(x1741,x1742)+E(f61(x1743,x1744,x1745,x1746,x1747,x1741),f61(x1743,x1744,x1745,x1746,x1747,x1742)) % 1.60/1.58 [175]~E(x1751,x1752)+E(f93(x1751,x1753,x1754,x1755),f93(x1752,x1753,x1754,x1755)) % 1.60/1.58 [176]~E(x1761,x1762)+E(f93(x1763,x1761,x1764,x1765),f93(x1763,x1762,x1764,x1765)) % 1.60/1.58 [177]~E(x1771,x1772)+E(f93(x1773,x1774,x1771,x1775),f93(x1773,x1774,x1772,x1775)) % 1.60/1.58 [178]~E(x1781,x1782)+E(f93(x1783,x1784,x1785,x1781),f93(x1783,x1784,x1785,x1782)) % 1.60/1.58 [179]~E(x1791,x1792)+E(f36(x1791,x1793,x1794,x1795),f36(x1792,x1793,x1794,x1795)) % 1.60/1.58 [180]~E(x1801,x1802)+E(f36(x1803,x1801,x1804,x1805),f36(x1803,x1802,x1804,x1805)) % 1.60/1.58 [181]~E(x1811,x1812)+E(f36(x1813,x1814,x1811,x1815),f36(x1813,x1814,x1812,x1815)) % 1.60/1.58 [182]~E(x1821,x1822)+E(f36(x1823,x1824,x1825,x1821),f36(x1823,x1824,x1825,x1822)) % 1.60/1.58 [183]~E(x1831,x1832)+E(f45(x1831),f45(x1832)) % 1.60/1.58 [184]~E(x1841,x1842)+E(f66(x1841,x1843),f66(x1842,x1843)) % 1.60/1.58 [185]~E(x1851,x1852)+E(f66(x1853,x1851),f66(x1853,x1852)) % 1.60/1.58 [186]~E(x1861,x1862)+E(f58(x1861,x1863),f58(x1862,x1863)) % 1.60/1.58 [187]~E(x1871,x1872)+E(f58(x1873,x1871),f58(x1873,x1872)) % 1.60/1.58 [188]~E(x1881,x1882)+E(f67(x1881,x1883),f67(x1882,x1883)) % 1.60/1.58 [189]~E(x1891,x1892)+E(f67(x1893,x1891),f67(x1893,x1892)) % 1.60/1.58 [190]~E(x1901,x1902)+E(f64(x1901,x1903),f64(x1902,x1903)) % 1.60/1.58 [191]~E(x1911,x1912)+E(f64(x1913,x1911),f64(x1913,x1912)) % 1.60/1.58 [192]~E(x1921,x1922)+E(f68(x1921),f68(x1922)) % 1.60/1.58 [193]~E(x1931,x1932)+E(f83(x1931,x1933,x1934,x1935,x1936),f83(x1932,x1933,x1934,x1935,x1936)) % 1.60/1.58 [194]~E(x1941,x1942)+E(f83(x1943,x1941,x1944,x1945,x1946),f83(x1943,x1942,x1944,x1945,x1946)) % 1.60/1.58 [195]~E(x1951,x1952)+E(f83(x1953,x1954,x1951,x1955,x1956),f83(x1953,x1954,x1952,x1955,x1956)) % 1.60/1.58 [196]~E(x1961,x1962)+E(f83(x1963,x1964,x1965,x1961,x1966),f83(x1963,x1964,x1965,x1962,x1966)) % 1.60/1.58 [197]~E(x1971,x1972)+E(f83(x1973,x1974,x1975,x1976,x1971),f83(x1973,x1974,x1975,x1976,x1972)) % 1.60/1.58 [198]~E(x1981,x1982)+E(f77(x1981),f77(x1982)) % 1.60/1.58 [199]~E(x1991,x1992)+E(f110(x1991,x1993,x1994,x1995),f110(x1992,x1993,x1994,x1995)) % 1.60/1.58 [200]~E(x2001,x2002)+E(f110(x2003,x2001,x2004,x2005),f110(x2003,x2002,x2004,x2005)) % 1.60/1.58 [201]~E(x2011,x2012)+E(f110(x2013,x2014,x2011,x2015),f110(x2013,x2014,x2012,x2015)) % 1.60/1.58 [202]~E(x2021,x2022)+E(f110(x2023,x2024,x2025,x2021),f110(x2023,x2024,x2025,x2022)) % 1.60/1.58 [203]~E(x2031,x2032)+E(f105(x2031,x2033,x2034,x2035,x2036),f105(x2032,x2033,x2034,x2035,x2036)) % 1.60/1.58 [204]~E(x2041,x2042)+E(f105(x2043,x2041,x2044,x2045,x2046),f105(x2043,x2042,x2044,x2045,x2046)) % 1.60/1.58 [205]~E(x2051,x2052)+E(f105(x2053,x2054,x2051,x2055,x2056),f105(x2053,x2054,x2052,x2055,x2056)) % 1.60/1.58 [206]~E(x2061,x2062)+E(f105(x2063,x2064,x2065,x2061,x2066),f105(x2063,x2064,x2065,x2062,x2066)) % 1.60/1.58 [207]~E(x2071,x2072)+E(f105(x2073,x2074,x2075,x2076,x2071),f105(x2073,x2074,x2075,x2076,x2072)) % 1.60/1.58 [208]~E(x2081,x2082)+E(f44(x2081,x2083),f44(x2082,x2083)) % 1.60/1.58 [209]~E(x2091,x2092)+E(f44(x2093,x2091),f44(x2093,x2092)) % 1.60/1.58 [210]~E(x2101,x2102)+E(f91(x2101,x2103),f91(x2102,x2103)) % 1.60/1.58 [211]~E(x2111,x2112)+E(f91(x2113,x2111),f91(x2113,x2112)) % 1.60/1.58 [212]~E(x2121,x2122)+E(f95(x2121,x2123),f95(x2122,x2123)) % 1.60/1.58 [213]~E(x2131,x2132)+E(f95(x2133,x2131),f95(x2133,x2132)) % 1.60/1.58 [214]~E(x2141,x2142)+E(f84(x2141,x2143,x2144,x2145),f84(x2142,x2143,x2144,x2145)) % 1.60/1.58 [215]~E(x2151,x2152)+E(f84(x2153,x2151,x2154,x2155),f84(x2153,x2152,x2154,x2155)) % 1.60/1.58 [216]~E(x2161,x2162)+E(f84(x2163,x2164,x2161,x2165),f84(x2163,x2164,x2162,x2165)) % 1.60/1.58 [217]~E(x2171,x2172)+E(f84(x2173,x2174,x2175,x2171),f84(x2173,x2174,x2175,x2172)) % 1.60/1.58 [218]~E(x2181,x2182)+E(f80(x2181),f80(x2182)) % 1.60/1.58 [219]~E(x2191,x2192)+E(f85(x2191,x2193),f85(x2192,x2193)) % 1.60/1.58 [220]~E(x2201,x2202)+E(f85(x2203,x2201),f85(x2203,x2202)) % 1.60/1.58 [221]~E(x2211,x2212)+E(f69(x2211),f69(x2212)) % 1.60/1.58 [222]~E(x2221,x2222)+E(f79(x2221),f79(x2222)) % 1.60/1.58 [223]~E(x2231,x2232)+E(f104(x2231,x2233,x2234,x2235,x2236),f104(x2232,x2233,x2234,x2235,x2236)) % 1.60/1.58 [224]~E(x2241,x2242)+E(f104(x2243,x2241,x2244,x2245,x2246),f104(x2243,x2242,x2244,x2245,x2246)) % 1.60/1.58 [225]~E(x2251,x2252)+E(f104(x2253,x2254,x2251,x2255,x2256),f104(x2253,x2254,x2252,x2255,x2256)) % 1.60/1.58 [226]~E(x2261,x2262)+E(f104(x2263,x2264,x2265,x2261,x2266),f104(x2263,x2264,x2265,x2262,x2266)) % 1.60/1.58 [227]~E(x2271,x2272)+E(f104(x2273,x2274,x2275,x2276,x2271),f104(x2273,x2274,x2275,x2276,x2272)) % 1.60/1.58 [228]~E(x2281,x2282)+E(f103(x2281,x2283,x2284,x2285),f103(x2282,x2283,x2284,x2285)) % 1.60/1.58 [229]~E(x2291,x2292)+E(f103(x2293,x2291,x2294,x2295),f103(x2293,x2292,x2294,x2295)) % 1.60/1.58 [230]~E(x2301,x2302)+E(f103(x2303,x2304,x2301,x2305),f103(x2303,x2304,x2302,x2305)) % 1.60/1.58 [231]~E(x2311,x2312)+E(f103(x2313,x2314,x2315,x2311),f103(x2313,x2314,x2315,x2312)) % 1.60/1.58 [232]~E(x2321,x2322)+E(f81(x2321,x2323,x2324,x2325,x2326),f81(x2322,x2323,x2324,x2325,x2326)) % 1.60/1.58 [233]~E(x2331,x2332)+E(f81(x2333,x2331,x2334,x2335,x2336),f81(x2333,x2332,x2334,x2335,x2336)) % 1.60/1.58 [234]~E(x2341,x2342)+E(f81(x2343,x2344,x2341,x2345,x2346),f81(x2343,x2344,x2342,x2345,x2346)) % 1.60/1.58 [235]~E(x2351,x2352)+E(f81(x2353,x2354,x2355,x2351,x2356),f81(x2353,x2354,x2355,x2352,x2356)) % 1.60/1.58 [236]~E(x2361,x2362)+E(f81(x2363,x2364,x2365,x2366,x2361),f81(x2363,x2364,x2365,x2366,x2362)) % 1.60/1.58 [237]~E(x2371,x2372)+E(f40(x2371,x2373,x2374,x2375,x2376),f40(x2372,x2373,x2374,x2375,x2376)) % 1.60/1.58 [238]~E(x2381,x2382)+E(f40(x2383,x2381,x2384,x2385,x2386),f40(x2383,x2382,x2384,x2385,x2386)) % 1.60/1.58 [239]~E(x2391,x2392)+E(f40(x2393,x2394,x2391,x2395,x2396),f40(x2393,x2394,x2392,x2395,x2396)) % 1.60/1.58 [240]~E(x2401,x2402)+E(f40(x2403,x2404,x2405,x2401,x2406),f40(x2403,x2404,x2405,x2402,x2406)) % 1.60/1.58 [241]~E(x2411,x2412)+E(f40(x2413,x2414,x2415,x2416,x2411),f40(x2413,x2414,x2415,x2416,x2412)) % 1.60/1.58 [242]~E(x2421,x2422)+E(f25(x2421,x2423,x2424,x2425),f25(x2422,x2423,x2424,x2425)) % 1.60/1.58 [243]~E(x2431,x2432)+E(f25(x2433,x2431,x2434,x2435),f25(x2433,x2432,x2434,x2435)) % 1.60/1.58 [244]~E(x2441,x2442)+E(f25(x2443,x2444,x2441,x2445),f25(x2443,x2444,x2442,x2445)) % 1.60/1.58 [245]~E(x2451,x2452)+E(f25(x2453,x2454,x2455,x2451),f25(x2453,x2454,x2455,x2452)) % 1.60/1.58 [246]~E(x2461,x2462)+E(f107(x2461,x2463),f107(x2462,x2463)) % 1.60/1.58 [247]~E(x2471,x2472)+E(f107(x2473,x2471),f107(x2473,x2472)) % 1.60/1.58 [248]~E(x2481,x2482)+E(f99(x2481,x2483,x2484,x2485),f99(x2482,x2483,x2484,x2485)) % 1.60/1.58 [249]~E(x2491,x2492)+E(f99(x2493,x2491,x2494,x2495),f99(x2493,x2492,x2494,x2495)) % 1.60/1.58 [250]~E(x2501,x2502)+E(f99(x2503,x2504,x2501,x2505),f99(x2503,x2504,x2502,x2505)) % 1.60/1.58 [251]~E(x2511,x2512)+E(f99(x2513,x2514,x2515,x2511),f99(x2513,x2514,x2515,x2512)) % 1.60/1.58 [252]~E(x2521,x2522)+E(f38(x2521,x2523,x2524),f38(x2522,x2523,x2524)) % 1.60/1.58 [253]~E(x2531,x2532)+E(f38(x2533,x2531,x2534),f38(x2533,x2532,x2534)) % 1.60/1.58 [254]~E(x2541,x2542)+E(f38(x2543,x2544,x2541),f38(x2543,x2544,x2542)) % 1.60/1.58 [255]~E(x2551,x2552)+E(f97(x2551,x2553,x2554,x2555),f97(x2552,x2553,x2554,x2555)) % 1.60/1.58 [256]~E(x2561,x2562)+E(f97(x2563,x2561,x2564,x2565),f97(x2563,x2562,x2564,x2565)) % 1.60/1.58 [257]~E(x2571,x2572)+E(f97(x2573,x2574,x2571,x2575),f97(x2573,x2574,x2572,x2575)) % 1.60/1.58 [258]~E(x2581,x2582)+E(f97(x2583,x2584,x2585,x2581),f97(x2583,x2584,x2585,x2582)) % 1.60/1.58 [259]~E(x2591,x2592)+E(f90(x2591,x2593),f90(x2592,x2593)) % 1.60/1.58 [260]~E(x2601,x2602)+E(f90(x2603,x2601),f90(x2603,x2602)) % 1.60/1.58 [261]~E(x2611,x2612)+E(f78(x2611,x2613),f78(x2612,x2613)) % 1.60/1.58 [262]~E(x2621,x2622)+E(f78(x2623,x2621),f78(x2623,x2622)) % 1.60/1.58 [263]~E(x2631,x2632)+E(f37(x2631,x2633,x2634,x2635,x2636),f37(x2632,x2633,x2634,x2635,x2636)) % 1.60/1.58 [264]~E(x2641,x2642)+E(f37(x2643,x2641,x2644,x2645,x2646),f37(x2643,x2642,x2644,x2645,x2646)) % 1.60/1.58 [265]~E(x2651,x2652)+E(f37(x2653,x2654,x2651,x2655,x2656),f37(x2653,x2654,x2652,x2655,x2656)) % 1.60/1.58 [266]~E(x2661,x2662)+E(f37(x2663,x2664,x2665,x2661,x2666),f37(x2663,x2664,x2665,x2662,x2666)) % 1.60/1.58 [267]~E(x2671,x2672)+E(f37(x2673,x2674,x2675,x2676,x2671),f37(x2673,x2674,x2675,x2676,x2672)) % 1.60/1.58 [268]~E(x2681,x2682)+E(f48(x2681,x2683,x2684),f48(x2682,x2683,x2684)) % 1.60/1.58 [269]~E(x2691,x2692)+E(f48(x2693,x2691,x2694),f48(x2693,x2692,x2694)) % 1.60/1.58 [270]~E(x2701,x2702)+E(f48(x2703,x2704,x2701),f48(x2703,x2704,x2702)) % 1.60/1.58 [271]~E(x2711,x2712)+E(f101(x2711,x2713,x2714,x2715,x2716),f101(x2712,x2713,x2714,x2715,x2716)) % 1.60/1.58 [272]~E(x2721,x2722)+E(f101(x2723,x2721,x2724,x2725,x2726),f101(x2723,x2722,x2724,x2725,x2726)) % 1.60/1.58 [273]~E(x2731,x2732)+E(f101(x2733,x2734,x2731,x2735,x2736),f101(x2733,x2734,x2732,x2735,x2736)) % 1.60/1.58 [274]~E(x2741,x2742)+E(f101(x2743,x2744,x2745,x2741,x2746),f101(x2743,x2744,x2745,x2742,x2746)) % 1.60/1.58 [275]~E(x2751,x2752)+E(f101(x2753,x2754,x2755,x2756,x2751),f101(x2753,x2754,x2755,x2756,x2752)) % 1.60/1.58 [276]~E(x2761,x2762)+E(f86(x2761),f86(x2762)) % 1.60/1.58 [277]~E(x2771,x2772)+E(f92(x2771,x2773),f92(x2772,x2773)) % 1.60/1.58 [278]~E(x2781,x2782)+E(f92(x2783,x2781),f92(x2783,x2782)) % 1.60/1.58 [279]~E(x2791,x2792)+E(f94(x2791,x2793),f94(x2792,x2793)) % 1.60/1.58 [280]~E(x2801,x2802)+E(f94(x2803,x2801),f94(x2803,x2802)) % 1.60/1.58 [281]~E(x2811,x2812)+E(f98(x2811,x2813,x2814,x2815,x2816),f98(x2812,x2813,x2814,x2815,x2816)) % 1.60/1.58 [282]~E(x2821,x2822)+E(f98(x2823,x2821,x2824,x2825,x2826),f98(x2823,x2822,x2824,x2825,x2826)) % 1.60/1.58 [283]~E(x2831,x2832)+E(f98(x2833,x2834,x2831,x2835,x2836),f98(x2833,x2834,x2832,x2835,x2836)) % 1.60/1.58 [284]~E(x2841,x2842)+E(f98(x2843,x2844,x2845,x2841,x2846),f98(x2843,x2844,x2845,x2842,x2846)) % 1.60/1.58 [285]~E(x2851,x2852)+E(f98(x2853,x2854,x2855,x2856,x2851),f98(x2853,x2854,x2855,x2856,x2852)) % 1.60/1.58 [286]~E(x2861,x2862)+E(f35(x2861,x2863,x2864),f35(x2862,x2863,x2864)) % 1.60/1.58 [287]~E(x2871,x2872)+E(f35(x2873,x2871,x2874),f35(x2873,x2872,x2874)) % 1.60/1.58 [288]~E(x2881,x2882)+E(f35(x2883,x2884,x2881),f35(x2883,x2884,x2882)) % 1.60/1.58 [289]~E(x2891,x2892)+E(f33(x2891,x2893,x2894),f33(x2892,x2893,x2894)) % 1.60/1.58 [290]~E(x2901,x2902)+E(f33(x2903,x2901,x2904),f33(x2903,x2902,x2904)) % 1.60/1.58 [291]~E(x2911,x2912)+E(f33(x2913,x2914,x2911),f33(x2913,x2914,x2912)) % 1.60/1.58 [292]~E(x2921,x2922)+E(f96(x2921,x2923),f96(x2922,x2923)) % 1.60/1.58 [293]~E(x2931,x2932)+E(f96(x2933,x2931),f96(x2933,x2932)) % 1.60/1.58 [294]~E(x2941,x2942)+E(f106(x2941,x2943,x2944,x2945,x2946),f106(x2942,x2943,x2944,x2945,x2946)) % 1.60/1.58 [295]~E(x2951,x2952)+E(f106(x2953,x2951,x2954,x2955,x2956),f106(x2953,x2952,x2954,x2955,x2956)) % 1.60/1.58 [296]~E(x2961,x2962)+E(f106(x2963,x2964,x2961,x2965,x2966),f106(x2963,x2964,x2962,x2965,x2966)) % 1.60/1.58 [297]~E(x2971,x2972)+E(f106(x2973,x2974,x2975,x2971,x2976),f106(x2973,x2974,x2975,x2972,x2976)) % 1.60/1.58 [298]~E(x2981,x2982)+E(f106(x2983,x2984,x2985,x2986,x2981),f106(x2983,x2984,x2985,x2986,x2982)) % 1.60/1.58 [299]~E(x2991,x2992)+E(f34(x2991,x2993,x2994,x2995),f34(x2992,x2993,x2994,x2995)) % 1.60/1.58 [300]~E(x3001,x3002)+E(f34(x3003,x3001,x3004,x3005),f34(x3003,x3002,x3004,x3005)) % 1.60/1.58 [301]~E(x3011,x3012)+E(f34(x3013,x3014,x3011,x3015),f34(x3013,x3014,x3012,x3015)) % 1.60/1.58 [302]~E(x3021,x3022)+E(f34(x3023,x3024,x3025,x3021),f34(x3023,x3024,x3025,x3022)) % 1.60/1.58 [303]~P1(x3031)+P1(x3032)+~E(x3031,x3032) % 1.60/1.58 [304]~P2(x3041)+P2(x3042)+~E(x3041,x3042) % 1.60/1.58 [305]~P3(x3051)+P3(x3052)+~E(x3051,x3052) % 1.60/1.58 [306]~P4(x3061)+P4(x3062)+~E(x3061,x3062) % 1.60/1.58 [307]~P6(x3071)+P6(x3072)+~E(x3071,x3072) % 1.60/1.58 [308]~P26(x3081)+P26(x3082)+~E(x3081,x3082) % 1.60/1.58 [309]~P15(x3091)+P15(x3092)+~E(x3091,x3092) % 1.60/1.58 [310]~P27(x3101)+P27(x3102)+~E(x3101,x3102) % 1.60/1.58 [311]~P21(x3111)+P21(x3112)+~E(x3111,x3112) % 1.60/1.58 [312]~P28(x3121)+P28(x3122)+~E(x3121,x3122) % 1.60/1.58 [313]P9(x3132,x3133,x3134,x3135)+~E(x3131,x3132)+~P9(x3131,x3133,x3134,x3135) % 1.60/1.58 [314]P9(x3143,x3142,x3144,x3145)+~E(x3141,x3142)+~P9(x3143,x3141,x3144,x3145) % 1.60/1.58 [315]P9(x3153,x3154,x3152,x3155)+~E(x3151,x3152)+~P9(x3153,x3154,x3151,x3155) % 1.60/1.58 [316]P9(x3163,x3164,x3165,x3162)+~E(x3161,x3162)+~P9(x3163,x3164,x3165,x3161) % 1.60/1.58 [317]~P7(x3171)+P7(x3172)+~E(x3171,x3172) % 1.60/1.58 [318]~P14(x3181)+P14(x3182)+~E(x3181,x3182) % 1.60/1.58 [319]~P19(x3191)+P19(x3192)+~E(x3191,x3192) % 1.60/1.58 [320]P8(x3202,x3203)+~E(x3201,x3202)+~P8(x3201,x3203) % 1.60/1.58 [321]P8(x3213,x3212)+~E(x3211,x3212)+~P8(x3213,x3211) % 1.60/1.58 [322]~P25(x3221)+P25(x3222)+~E(x3221,x3222) % 1.60/1.58 [323]~P16(x3231)+P16(x3232)+~E(x3231,x3232) % 1.60/1.59 [324]~P17(x3241)+P17(x3242)+~E(x3241,x3242) % 1.60/1.59 [325]~P18(x3251)+P18(x3252)+~E(x3251,x3252) % 1.60/1.59 [326]~P23(x3261)+P23(x3262)+~E(x3261,x3262) % 1.60/1.59 [327]~P20(x3271)+P20(x3272)+~E(x3271,x3272) % 1.60/1.59 [328]P10(x3282,x3283,x3284)+~E(x3281,x3282)+~P10(x3281,x3283,x3284) % 1.60/1.59 [329]P10(x3293,x3292,x3294)+~E(x3291,x3292)+~P10(x3293,x3291,x3294) % 1.60/1.59 [330]P10(x3303,x3304,x3302)+~E(x3301,x3302)+~P10(x3303,x3304,x3301) % 1.60/1.59 [331]~P22(x3311)+P22(x3312)+~E(x3311,x3312) % 1.60/1.59 [332]~P24(x3321)+P24(x3322)+~E(x3321,x3322) % 1.60/1.59 [333]~P29(x3331)+P29(x3332)+~E(x3331,x3332) % 1.60/1.59 [334]~P32(x3341)+P32(x3342)+~E(x3341,x3342) % 1.60/1.59 [335]~P30(x3351)+P30(x3352)+~E(x3351,x3352) % 1.60/1.59 [336]~P31(x3361)+P31(x3362)+~E(x3361,x3362) % 1.60/1.59 [337]P13(x3372,x3373,x3374,x3375)+~E(x3371,x3372)+~P13(x3371,x3373,x3374,x3375) % 1.60/1.59 [338]P13(x3383,x3382,x3384,x3385)+~E(x3381,x3382)+~P13(x3383,x3381,x3384,x3385) % 1.60/1.59 [339]P13(x3393,x3394,x3392,x3395)+~E(x3391,x3392)+~P13(x3393,x3394,x3391,x3395) % 1.60/1.59 [340]P13(x3403,x3404,x3405,x3402)+~E(x3401,x3402)+~P13(x3403,x3404,x3405,x3401) % 1.60/1.59 [341]P12(x3412,x3413,x3414,x3415,x3416)+~E(x3411,x3412)+~P12(x3411,x3413,x3414,x3415,x3416) % 1.60/1.59 [342]P12(x3423,x3422,x3424,x3425,x3426)+~E(x3421,x3422)+~P12(x3423,x3421,x3424,x3425,x3426) % 1.60/1.59 [343]P12(x3433,x3434,x3432,x3435,x3436)+~E(x3431,x3432)+~P12(x3433,x3434,x3431,x3435,x3436) % 1.60/1.59 [344]P12(x3443,x3444,x3445,x3442,x3446)+~E(x3441,x3442)+~P12(x3443,x3444,x3445,x3441,x3446) % 1.60/1.59 [345]P12(x3453,x3454,x3455,x3456,x3452)+~E(x3451,x3452)+~P12(x3453,x3454,x3455,x3456,x3451) % 1.60/1.59 [346]P5(x3462,x3463)+~E(x3461,x3462)+~P5(x3461,x3463) % 1.60/1.59 [347]P5(x3473,x3472)+~E(x3471,x3472)+~P5(x3473,x3471) % 1.60/1.59 [348]P11(x3482,x3483,x3484,x3485,x3486,x3487)+~E(x3481,x3482)+~P11(x3481,x3483,x3484,x3485,x3486,x3487) % 1.60/1.59 [349]P11(x3493,x3492,x3494,x3495,x3496,x3497)+~E(x3491,x3492)+~P11(x3493,x3491,x3494,x3495,x3496,x3497) % 1.60/1.59 [350]P11(x3503,x3504,x3502,x3505,x3506,x3507)+~E(x3501,x3502)+~P11(x3503,x3504,x3501,x3505,x3506,x3507) % 1.60/1.59 [351]P11(x3513,x3514,x3515,x3512,x3516,x3517)+~E(x3511,x3512)+~P11(x3513,x3514,x3515,x3511,x3516,x3517) % 1.60/1.59 [352]P11(x3523,x3524,x3525,x3526,x3522,x3527)+~E(x3521,x3522)+~P11(x3523,x3524,x3525,x3526,x3521,x3527) % 1.60/1.59 [353]P11(x3533,x3534,x3535,x3536,x3537,x3532)+~E(x3531,x3532)+~P11(x3533,x3534,x3535,x3536,x3537,x3531) % 1.60/1.59 % 1.60/1.59 %------------------------------------------- % 1.60/1.59 cnf(1154,plain, % 1.60/1.59 (P1(f50(f50(f51(x11542),x11541),f50(a52,x11541)))), % 1.60/1.59 inference(equality_inference,[],[573])). % 1.60/1.59 cnf(1166,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),f2(a114)),f14(x11661,f21(f115(x11661,a49)))))), % 1.60/1.59 inference(equality_inference,[],[678])). % 1.60/1.59 cnf(1171,plain, % 1.60/1.59 (~P1(f50(f50(f28(f115(x11712,a49)),x11711),x11711))), % 1.60/1.59 inference(equality_inference,[],[774])). % 1.60/1.59 cnf(1181,plain, % 1.60/1.59 (P9(x11811,x11812,f97(x11813,x11812,x11811,f41(x11812,x11811,x11814,x11813)),f41(x11812,x11811,x11814,x11813))+E(f41(x11812,x11811,x11814,x11813),f21(f115(x11811,a49)))), % 1.60/1.59 inference(equality_inference,[],[920])). % 1.60/1.59 cnf(1185,plain, % 1.60/1.59 (~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11852),x11851)),f10(x11853,x11851)))), % 1.60/1.59 inference(equality_inference,[],[948])). % 1.60/1.59 cnf(1188,plain, % 1.60/1.59 (E(x11881,x11882)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11883),x11883)),f11(x11884,x11881,x11882)))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x11884),a5))), % 1.60/1.59 inference(equality_inference,[],[992])). % 1.60/1.59 cnf(1189,plain, % 1.60/1.59 (E(x11891,x11892)+~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x11893),x11893)),f12(x11894,x11891,x11892)))+~P1(f50(f50(f51(f115(f118(a112,a112),a49)),x11894),a5))), % 1.60/1.59 inference(equality_inference,[],[993])). % 1.60/1.59 cnf(1216,plain, % 1.60/1.59 (P1(f50(f27(a114,x12161),f50(f50(f13(a114),x12162),x12161)))), % 1.60/1.59 inference(rename_variables,[],[417])). % 1.60/1.59 cnf(1219,plain, % 1.60/1.59 (P1(f50(f50(f28(a114),x12191),f50(a23,x12191)))), % 1.60/1.59 inference(rename_variables,[],[404])). % 1.60/1.59 cnf(1232,plain, % 1.60/1.59 (P1(f50(f50(f28(a114),x12321),f50(a23,f50(f50(f13(a114),x12322),x12321))))), % 1.60/1.59 inference(rename_variables,[],[434])). % 1.60/1.59 cnf(1252,plain, % 1.60/1.59 (E(f26(a114,x12521),x12521)), % 1.60/1.59 inference(rename_variables,[],[385])). % 1.60/1.59 cnf(1257,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),f50(f50(f13(a114),x12571),x12572)),x12572))), % 1.60/1.59 inference(rename_variables,[],[482])). % 1.60/1.59 cnf(1260,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),f50(f50(f13(a114),x12601),x12602)),x12602))), % 1.60/1.59 inference(rename_variables,[],[482])). % 1.60/1.59 cnf(1269,plain, % 1.60/1.59 (E(f26(a114,x12691),x12691)), % 1.60/1.59 inference(rename_variables,[],[385])). % 1.60/1.59 cnf(1272,plain, % 1.60/1.59 (~E(f50(a23,x12721),x12721)), % 1.60/1.59 inference(rename_variables,[],[463])). % 1.60/1.59 cnf(1275,plain, % 1.60/1.59 (~P1(f50(f50(f51(x12751),x12752),f21(f115(x12751,a49))))), % 1.60/1.59 inference(rename_variables,[],[479])). % 1.60/1.59 cnf(1284,plain, % 1.60/1.59 (~P1(f50(f27(a114,f50(a23,x12841)),x12841))), % 1.60/1.59 inference(rename_variables,[],[477])). % 1.60/1.59 cnf(1289,plain, % 1.60/1.59 (P1(f50(f50(f28(a114),x12891),f50(a23,x12891)))), % 1.60/1.59 inference(rename_variables,[],[404])). % 1.60/1.59 cnf(1296,plain, % 1.60/1.59 (~P1(f50(f27(a114,f50(a23,x12961)),x12961))), % 1.60/1.59 inference(rename_variables,[],[477])). % 1.60/1.59 cnf(1299,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),f50(f50(f13(a114),x12991),x12992)),x12992))), % 1.60/1.59 inference(rename_variables,[],[482])). % 1.60/1.59 cnf(1310,plain, % 1.60/1.59 (P1(f50(f27(a114,x13101),f50(f50(f13(a114),x13102),x13101)))), % 1.60/1.59 inference(rename_variables,[],[417])). % 1.60/1.59 cnf(1315,plain, % 1.60/1.59 (~P1(f50(f27(a114,f50(a23,x13151)),x13151))), % 1.60/1.59 inference(rename_variables,[],[477])). % 1.60/1.59 cnf(1318,plain, % 1.60/1.59 (~P1(f50(f27(a114,f50(a23,x13181)),x13181))), % 1.60/1.59 inference(rename_variables,[],[477])). % 1.60/1.59 cnf(1330,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),f50(f50(f13(a114),x13301),x13302)),x13302))), % 1.60/1.59 inference(rename_variables,[],[482])). % 1.60/1.59 cnf(1336,plain, % 1.60/1.59 (P1(f50(f27(a114,x13361),f50(f50(f13(a114),x13362),x13361)))), % 1.60/1.59 inference(rename_variables,[],[417])). % 1.60/1.59 cnf(1342,plain, % 1.60/1.59 (P1(f50(f27(a114,x13421),x13421))), % 1.60/1.59 inference(rename_variables,[],[395])). % 1.60/1.59 cnf(1351,plain, % 1.60/1.59 (P1(f50(f50(f28(a114),x13511),f50(a23,x13511)))), % 1.60/1.59 inference(rename_variables,[],[404])). % 1.60/1.59 cnf(1354,plain, % 1.60/1.59 (P1(f50(f27(f115(x13541,a49),f21(f115(x13541,a49))),x13542))), % 1.60/1.59 inference(rename_variables,[],[429])). % 1.60/1.59 cnf(1357,plain, % 1.60/1.59 (P1(f50(f50(f28(a114),x13571),f50(a23,x13571)))), % 1.60/1.59 inference(rename_variables,[],[404])). % 1.60/1.59 cnf(1364,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),x13641),x13641))), % 1.60/1.59 inference(rename_variables,[],[473])). % 1.60/1.59 cnf(1369,plain, % 1.60/1.59 (P1(f50(f50(f51(x13691),x13692),f50(a52,x13692)))), % 1.60/1.59 inference(rename_variables,[],[1154])). % 1.60/1.59 cnf(1378,plain, % 1.60/1.59 (~P1(f50(f50(f51(x13781),x13782),f21(f115(x13781,a49))))), % 1.60/1.59 inference(rename_variables,[],[479])). % 1.60/1.59 cnf(1381,plain, % 1.60/1.59 (P1(f50(f27(f115(x13811,a49),x13812),x13812))), % 1.60/1.59 inference(rename_variables,[],[409])). % 1.60/1.59 cnf(1388,plain, % 1.60/1.59 (~P1(f50(f50(f51(x13881),x13882),f21(f115(x13881,a49))))), % 1.60/1.59 inference(rename_variables,[],[479])). % 1.60/1.59 cnf(1405,plain, % 1.60/1.59 (~P1(f50(f50(f28(a114),f50(f50(f13(a114),x14051),x14052)),x14051))), % 1.60/1.59 inference(rename_variables,[],[483])). % 1.60/1.59 cnf(1418,plain, % 1.60/1.59 (P9(a114,a114,a23,x14181)), % 1.60/1.59 inference(rename_variables,[],[413])). % 1.60/1.59 cnf(1430,plain, % 1.60/1.59 (~P1(f50(f50(f51(f118(a112,a112)),f50(f50(f31(a112,a112),x14301),x14302)),f10(x14303,x14302)))), % 1.60/1.59 inference(rename_variables,[],[1185])). % 1.60/1.59 cnf(1440,plain, % 1.60/1.59 (E(f26(a114,x14401),x14401)), % 1.60/1.59 inference(rename_variables,[],[385])). % 1.60/1.59 cnf(1442,plain, % 1.60/1.59 (E(f26(a114,x14421),x14421)), % 1.60/1.59 inference(rename_variables,[],[385])). % 1.60/1.59 cnf(1444,plain, % 1.60/1.59 (~E(f50(a23,x14441),x14441)), % 1.60/1.59 inference(rename_variables,[],[463])). % 1.60/1.59 cnf(1464,plain, % 1.60/1.59 (P1(f50(f50(f51(x14641),x14642),f50(a52,x14642)))), % 1.60/1.59 inference(rename_variables,[],[1154])). % 1.60/1.59 cnf(1468,plain, % 1.60/1.59 (~E(f50(a23,x14681),x14681)), % 1.60/1.59 inference(rename_variables,[],[463])). % 1.60/1.59 cnf(1472,plain, % 1.60/1.59 (E(f26(a114,x14721),x14721)), % 1.60/1.59 inference(rename_variables,[],[385])). % 1.60/1.59 cnf(1475,plain, % 1.60/1.59 (E(f26(a114,x14751),x14751)), % 1.60/1.59 inference(rename_variables,[],[385])). % 1.60/1.59 cnf(1478,plain, % 1.60/1.59 (P9(x14781,x14781,f3(x14781),x14782)), % 1.60/1.59 inference(rename_variables,[],[415])). % 1.60/1.59 cnf(1480,plain, % 1.60/1.59 (P9(x14801,x14801,f3(x14801),x14802)), % 1.60/1.59 inference(rename_variables,[],[415])). % 1.60/1.59 cnf(1484,plain, % 1.60/1.59 (P8(x14841,f21(f115(x14841,a49)))), % 1.60/1.59 inference(rename_variables,[],[393])). % 1.60/1.59 cnf(1486,plain, % 1.60/1.59 (P8(x14861,f21(f115(x14861,a49)))), % 1.60/1.59 inference(rename_variables,[],[393])). % 1.60/1.59 cnf(1532,plain, % 1.60/1.59 ($false), % 1.60/1.59 inference(scs_inference,[],[459,481,1185,1430,1171,1166,1154,1369,1464,463,1272,1444,1468,415,1478,1480,424,385,1252,1269,1440,1442,1472,1475,413,1418,358,359,361,363,364,365,371,373,375,379,416,387,393,1484,1486,391,471,395,1342,404,1219,1289,1351,1357,405,476,409,1381,473,1364,420,479,1275,1378,1388,477,1284,1296,1315,1318,450,429,1354,417,1216,1310,1336,418,452,482,1257,1260,1299,1330,483,1405,434,1232,435,437,609,635,659,725,738,773,814,815,816,817,871,960,961,962,963,1075,1076,1077,1078,2,505,554,560,561,564,569,617,760,776,991,1181,6,7,490,570,572,598,601,634,640,662,677,680,683,697,709,727,732,734,736,737,740,741,757,759,856,857,868,902,908,942,947,953,955,956,957,967,976,998,1001,1006,1027,1034,1042,1059,1060,1087,1092,578,600,602,603,608,620,701,721,726,739,789,931,968,969,970,984,985,1188,1189,3,303,516,530,532,537,596,597,681,682,692,809,920,935,964,313,314,316,320,321,576,621,655,657,658,666,686,687,691,708,711,715,716,791,795,802,808,914,922,943,966]), % 1.60/1.59 ['proof']). % 1.60/1.59 % SZS output end Proof % 1.60/1.59 % Total time :0.510000s %------------------------------------------------------------------------------